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Asked by Josie Pagnucco on May 11, 2024

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Sarah and Jane are two representative individuals living in an economy that produces two goods, X and Y. Sarah's and Jane's utility functions are given as:
Sarah: US = 100X0.5Y0.5
Jane: UJ = 50X0.4Y0.6
The market determined prices of X and Y are $10 and $20, respectively. Current outputs are 58 units of X per time period and 36 units of Y. Jane's current income is $600 per time period, while Sarah's income is $700 per time period.
a. Write expressions for Sarah and Jane's marginal rates of substitution.
b. Determine the quantities of X and Y that Sarah and Jane should consume in equilibrium.
c. Do the values calculated in part (b) satisfy the conditions for equilibrium in exchange? Explain using numbers.
d. Examine your answers in parts (b) and (c). If equilibrium has not been achieved, what would be necessary to reach equilibrium? If equilibrium has been achieved, comment on the process by which equilibrium was reached.

Marginal Rates

The amount of change in a variable (often related to costs or taxes) associated with a one-unit change in another variable.

Utility Functions

Mathematical representations describing the level of satisfaction or utility that a consumer derives from consuming a good or combination of goods.

Equilibrium

A state of balance in a market, where demand equals supply, and economic forces are at rest.

  • Define and evaluate marginal rates of substitution within utility maximization challenges.
  • Acquire knowledge of welfare economics principles, specifically the utility possibilities frontier, and how it showcases the efficient use of resources.
  • Scrutinize trading situations between people to discover exchanges that provide mutual advantage.
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JH
Julia HannahMay 11, 2024
Final Answer :
a.Jane's MRS: a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. Sarah's MRS: a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. b.For equilibrium, each individual must equate MRS to a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. . a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. For Jane: a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. , Y = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. X
For Sarah: a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. , a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. ∙ a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. Y = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. X
To determine quantities substitute into each individuals budget constraint.
Jane's budget constraint: 600 = 10X + 20Y
Substitute Y = (1/2)X
600 = 10X + 20(1/2)X
600 = 10X + 10X
X = 30
600 = 10(30) + 20Y
300 = 20Y
Y = 15
Jane should consume 30 units of X and 15 units of Y.
Sarah's budget constraint: 700 = 10X + 20Y
Substitute Y = (3/4)X
700 = 10X + 20(3/4)X
700 = 25X
X = 28
700 = 10(28) + 20Y
420 = 20Y
Y = 21
Sarah should consume 28 units of X and 21 units of Y.
c.In equilibrium MRSJ should equal MRSS. a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. Jane is consuming 15 units of Y and 30 units of X. a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. X
Sarah is consuming 21 units of Y and 28 units of X. a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. = a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. does equal a.Jane's MRS: = = = Sarah's MRS: = = = b.For equilibrium, each individual must equate MRS to . = = For Jane: = , Y = X For Sarah: = , = ∙ Y = X To determine quantities substitute into each individuals budget constraint. Jane's budget constraint: 600 = 10X + 20Y Substitute Y = (1/2)X 600 = 10X + 20(1/2)X 600 = 10X + 10X X = 30 600 = 10(30) + 20Y 300 = 20Y Y = 15 Jane should consume 30 units of X and 15 units of Y. Sarah's budget constraint: 700 = 10X + 20Y Substitute Y = (3/4)X 700 = 10X + 20(3/4)X 700 = 25X X = 28 700 = 10(28) + 20Y 420 = 20Y Y = 21 Sarah should consume 28 units of X and 21 units of Y. c.In equilibrium MRS<sup>J</sup> should equal MRS<sup>S</sup>. = Jane is consuming 15 units of Y and 30 units of X. = = = X Sarah is consuming 21 units of Y and 28 units of X. = = = does equal , and it is also True that the two individuals are consuming the available quantities of X and Y. d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences. , and it is also True that the two individuals are consuming the available quantities of X and Y.
d.Equilibrium has been achieved. The equilibrium involves an equilibrium in resource markets determining Jane's and Sarah's incomes, in the product market allocating L and K between X and Y, and the condition for efficiency in output that matches production to Jane and Sarah's preferences.

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