Economics
Economics
5th Edition
ISBN: 9781319066604
Author: Paul Krugman, Robin Wells
Publisher: Worth Publishers
Question
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Chapter 10.A, Problem 6P
To determine

Concept introduction:

Budget Line: It is defined as the combination of all the goods that a consumer can purchase, exhausting all his income. The formula for the budget line is:

M=XPx+YPy

Here,

    X is the quantity of good X.

    Y is the quantity of good Y.

    M is the total income.

    Px is the price of good X.

    Py is the price of good Y.

Slope of the Budget line: It is defined as the ration of price, in the above case the slope is PxPy

Marginal Rate of Substitution: It is defined as the quantity of goods sacrificed for the additional unit of another good. The formula for it is:

MRSxy=MUxMUy

Here,

    MRSxy is the marginal rate of substitution of x and y

    MUx is the marginal utility of x

    MUy is the marginal utility of y

Optimality Rule: According to the indifference curve approach, the consumer achieves its optimum bundle at appoint where

M=XPx+YPyMRSxy=PxPy

Expert Solution & Answer
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Explanation of Solution

a. Mrs. Kory’s optimum bundle for chocolates and albums.

It is given that the total income is $50. Cost of the album and chocolate is $10 and $2 respectively. The marginal rate of substitution of the album in place of chocolate is 1.

By optimality rule,

M=APa+CPc$50=4×$10+5×$2$50=$50

MRSac=PaPc ...................(1)

Here,

    MRSac is the marginal rate of substitution of a and c

    Pa is the price of album.

    Pc is the price of chocolate.

    A is the quantity of album.

    C is the quantity of chocolate.

Substitute $10 for Pa $2 for Pc and 1 for MRSac in equation (1)

    1$10$215

    • So, the bundle (4, 5) is on the budget line, but is not the optimal solution as it does not satisfy the optimality condition.

    • In the above case, Mrs. Kory values the album more than that of chocolate so, MRSac is less than the price ratio.

    • Hence, she should buy more chocolates and less albums such that the optimal condition is fulfilled.

Conclusion:

Bundle (4, 5) is not an optimal bundle, Mrs. Kory must buy more cups of hot chocolate and less albums.

b. Mrs. Kory’s optimum bundle for chocolates and albums

It is given that the total income is $50 and cost of the album and chocolate is $10 and $2 respectively.

By optimality rule,

M=APa+CPc$50=2×$10+15×$2$50=$50

MRSac=PaPc ............(2)

MRSac=MUaMUcMRSac=255MRSac=5

Here,

    MUa is the marginal utility of album.

    MUc is the marginal utility of chocolate.

Substitute $10 for MUa $2 for MUc and 5 for MRSac in equation (2):

    5=$10$25=5

  • So, the bundle (2, 15) is on the budget line and is an optimal solution, as it satisfies the optimality condition.
  • In the above case, Mrs. Kory is exchanging five chocolates for one more album. And the price of the album is five times that of the chocolate, so the optimality exists.

Conclusion:

Bundle (4, 5) is not an optimal bundle, Mrs. Kory must buy more cups of hot chocolate and less albums.

c. Mrs. Kory’s optimum bundle for chocolates and albums

It is given that the total income is $50 and cost of the album and chocolate is $10 and $2 respectively. The marginal rate of substitution of the album in place of the chocolate is 5

By optimality rule,

MAPa+CPc$501×$10+10×$2$50$30

Substitute $10 for Pa $2 for Pc and 5 for MRSac in equation (1)

5=$10$25=5

So, the bundle (1, 10) is not on the budget line, no need to check the second condition

Conclusion:

Bundle (1, 10) is not an optimal bundle, as it is not on the budget line.

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