Asked by Daisy Terrado on Jun 18, 2024
Verified
Two individuals, Dave and Bob, consume two goods, X and Y. The utility functions for the two individuals are given as:
Bob's utility function:
UB = 30X0.25Y0.75
Dave's utility function:
UD = 50X0.5Y0.5
Bob is currently consuming 5 units of X and 10 units of Y. Dave is currently consuming 12 units of X and 8 units of Y. The current prices of X and Y are $10 and $15, respectively.
a. Determine the marginal rate of substitution for each individual.
b. In light of the information given above, have the two individuals achieved exchange equilibrium? Would it be possible to make one individual better off without harming the other? If the individuals have achieved exchange equilibrium, are other equilibrium combinations of X and Y between the individuals possible?
Marginal Rate
The amount by which a quantity changes with respect to a change in another quantity, often used in the context of taxes or productivity.
Utility Function
Formula that assigns a level of utility to individual market baskets.
- Ascertain and calculate marginal substitution rates in scenarios aiming at utility maximization.
- Investigate trade interactions among individuals to identify transactions that are beneficial to all involved parties.
- Describe the importance of market prices in the achievement of competitive balance and the effective distribution of resources.
Verified Answer
ST
Sushan ThapaJun 18, 2024
Final Answer :
a. 
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b.Exchange equilibrium requires that each individuals MRS be equated to the ratio of the prices. 
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Dave's equilibrium condition: Y = (2/3)x 
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Bob's equilibrium condition: 
Bob is currently consuming 5 units of X and 10 units of Y which satisfies the condition 
Dave is currently consuming 12 units of X and 8 units of Y which satisfies the condition 
The two individuals have achieved exchange equilibrium, so it would not be possible to make one better off without harming the other.
The exchange equilibrium is not unique. There are an infinite number of possibilities (assuming partial units) that can satisfy the conditions for equilibrium.
= = = = = = b.Exchange equilibrium requires that each individuals MRS be equated to the ratio of the prices. = = = = Dave's equilibrium condition: Y = (2/3)x = = Bob's equilibrium condition: Bob is currently consuming 5 units of X and 10 units of Y which satisfies the condition Dave is currently consuming 12 units of X and 8 units of Y which satisfies the condition The two individuals have achieved exchange equilibrium, so it would not be possible to make one better off without harming the other.The exchange equilibrium is not unique. There are an infinite number of possibilities (assuming partial units) that can satisfy the conditions for equilibrium.
Learning Objectives
- Ascertain and calculate marginal substitution rates in scenarios aiming at utility maximization.
- Investigate trade interactions among individuals to identify transactions that are beneficial to all involved parties.
- Describe the importance of market prices in the achievement of competitive balance and the effective distribution of resources.