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Chapter 6: 4RQ (page 133)

Show a consumer鈥檚 budget constraint and indifference curves for wine and cheese. Show the optimal consumption choice. If the price of wine is \(3 per glass and the price of cheese is \)6 per pound, what is the marginal rate of substitution at this optimum?

Short Answer

Expert verified

The consumer鈥檚 budget constraint and indifference curves for wine and cheese are below:

The optimal consumption choice is given by point A.

The marginal rate of substitution between cheese and wine will be 2.

Step by step solution

01

Explanation

Consider the diagram below:

The budget line and the indifference curve are shown in the graph.

The tangency of the budget line and the indifference curve is where the optimum bundle of wine and cheese occurs.

02

Optimum consumption bundle

The optimum level will be at point A, and the W* and C* are the amount of wine and cheese consumed.

03

Marginal Rate of substitution

The marginal substitution rate is the rate at which the consumer is willing to substitute wine for more cheese. The marginal rate of substitution equates with the price ratio at the optimum level of consumption, i.e., .

Thus, the marginal rate of substitution is 2 (=6/3) at the optimum level.

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Most popular questions from this chapter

If people do not have a complete mental picture of total utility for every level of consumption, how can they find their utility-maximizing consumption choice?

At two points on an indifference curve,

a. the consumer has the same income.

b. the consumer has the same marginal rate of substitution.

c. the bundle of the goods cost the consumer the same amount.

d. the bundle of goods that yield the consumer same satisfaction.

1. Jeremy is deeply in love with Jasmine. Jasmine lives where cell phone coverage is poor, so he can either call her on the land-line phone for five cents per minute or he can drive to see her, at a round-trip cost of \(2 in gasoline money. He has a total of \)10 per week to spend on staying in touch. To make his preferred choice, Jeremy uses a handy utilimometer that measures his total utility from personal visits and from phone minutes. Using the values in Table 6.6, figure out the points on Jeremy鈥檚 consumption choice budget constraint (it may be helpful to do a sketch) and identify his utility-maximizing point.

Take Jeremy鈥檚 total utility information in Exercise 6.1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremy鈥檚 utility.

Maya divides her income between coffee and croissants (both of which are normal goods). An early frost in Brazil causes a large increase in the price of coffee in the United States.

a. Show the effect of the frost on Maya鈥檚 budget constraint.

b. Show the effect of the frost on Maya鈥檚 optimal consumption bundle, assuming that the substitution effect outweighs the income effect for croissants.

c. Show the effect of the frost on Maya鈥檚 optimal consumption bundle, assuming that the income effect outweighs the substitution effect for croissants.
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