Suppose that a consumer buys only two goods, X and Y. At the current consumption bundle, the marginal rate of substitution is 4, the price of Good X is $22, and the price of Good Y is $11.

1. Suppose that a consumer buys only two goods, X and Y. At the current consumption bundle, the marginal rate of substitution is 4, the price of Good X is $22, and the price of Good Y is $11.

 a. How many units of Good Y is the consumer willing to give up to obtain one more unit of Good X? How many units of Good X is the consumer willing to give up to obtain more unit of Good Y?

b. How many units of Good Y does the consumer have to give up to obtain one more unit of Good X? How many units of Good X does the consumer has to give up to obtain more one unit of Good Y?

 c. Is the consumer making an optimal choice? Why or why not?

d. If the consumer is a utility-maximizer, what should the consumer do? What is the consequence of this change? Explain your reasoning.

2. The following table shows the marginal utility for each of six units of X and Y. The price of X is $4 and the price of Y is $2.

Quantity  1     2    3     4   5      6

 MUX      20   16   12  10  8     6

MUY 1     14   12   8     6  5   4

a. Suppose that the consumer’s income is $20. Assuming that the consumer is a utility maximizer, use marginal analysis to determine the optimal consumption of good x and good y, respectively. Show your work.

b. Suppose that the consumer instead has $26 to spend. Assuming that the consumer is a utility maximizer, use marginal analysis to determine the optimal consumption of good x and good y, respectively. Show your work.

3. Use the following graph showing a consumer’s budget line and some indifference curves to answer the following questions. You must show work. The consumer’s income is $600. Q uantity of Y 40 30 A 20 10 III II B 0 10 20 30 I 40 50 Q uantity of X

a) Given the information provided: What is the price of Good X? What is the price of Good Y? How did you find your answers?

b) Suppose that the consumer is currently at consumption bundle A, use marginal analysis to explain why bundle A is not optimal. Explain your answer.

c) At the optimal consumption bundle, what is the Marginal Rate of Substitution? Explain how you found this answer. Interpret the meaning of the Marginal Rate of Substitution at this bundle.

d) Suppose that the prices of Good X and Good Y remain unchanged, under what circumstances would the consumer be able to reach indifference curve III? Explain your answer.