Asked by Dillon Bannister on Jun 24, 2024
Verified
Milton consumes two commodities in a perfect market system.The price of x is $4 and the price of y is $1.His utility function is U(x, y) xy.He is endowed with 76 units of good x and no y.Find his consumption of good y.
A) 76
B) 157
C) 152
D) 162
E) None of the above.
Perfect Market System
A market structure characterized by an ideal scenario where there are many buyers and sellers, all having perfect information and no transaction costs, leading to efficient pricing.
Utility Function
A mathematical representation that describes the level of satisfaction or happiness that a consumer derives from consuming a set of goods and services.
Consumption
The act of using goods and services to satisfy needs or desires.
- Appraise how modifications in prices shape the consumption activities for diverse products.
Verified Answer
BR
BINOY RAJESHJun 26, 2024
Final Answer :
C
Explanation :
Since Milton has no initial endowment of good y, he can only consume y by purchasing it with the money he gets by selling some of his good x.
Let Milton consume x and y in quantities x1 and y1 respectively. Then his total expenditure would be:
4x1 + y1 = income or 4x1 = income - y1
As Milton wants to maximize his utility, he will choose the quantities of x and y such that their marginal utilities are equal to each other:
MUx/MUy = Px/Py
=> MUx/MUy = 4
=> (d/dx (xy))/ (d/dy (xy)) = 4
=> y/x = 4/1
=> y1/x1 = 4/1
=> y1 = 4x1
Substituting this value in the budget equation, we get:
4x1 + 4x1 = income
=> x1 = income/8
As Milton is endowed with 76 units of good x, his maximum income would be 4*76 = 304
Therefore, his consumption of good x would be:
x1 = 304/8 = 38
And his consumption of good y would be:
y1 = 4x1 = 4*38 = 152
Hence, the answer is C) 152.
Let Milton consume x and y in quantities x1 and y1 respectively. Then his total expenditure would be:
4x1 + y1 = income or 4x1 = income - y1
As Milton wants to maximize his utility, he will choose the quantities of x and y such that their marginal utilities are equal to each other:
MUx/MUy = Px/Py
=> MUx/MUy = 4
=> (d/dx (xy))/ (d/dy (xy)) = 4
=> y/x = 4/1
=> y1/x1 = 4/1
=> y1 = 4x1
Substituting this value in the budget equation, we get:
4x1 + 4x1 = income
=> x1 = income/8
As Milton is endowed with 76 units of good x, his maximum income would be 4*76 = 304
Therefore, his consumption of good x would be:
x1 = 304/8 = 38
And his consumption of good y would be:
y1 = 4x1 = 4*38 = 152
Hence, the answer is C) 152.
Learning Objectives
- Appraise how modifications in prices shape the consumption activities for diverse products.