1.Suppose that a consumer buys only two goods, X and Y. At the current consumption bundle,...

1.Suppose that a consumer buys only two goods, X and Y. At the current consumption bundle, the marginal rate of substitution is 3, the price of Good X is $4, and the price of Good Y is $2.

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? Explain your reasoning.

Solutions

Expert Solution

a. Units of Good Y is the consumer willing to give up to obtain one more unit of Good X = MRS = 3
Units of Good X is the consumer willing to give up to obtain more unit of Good Y = 1/MRS = 1/3

b. Units of Good Y does the consumer have to give up to obtain one more unit of Good X = Price of X/Price of Y = 4/2 = 2 (price ratio)
Units of Good X does the consumer has to give up to obtain more one unit of Good Y = Price of Y/Price of X = 2/4 = 1/2

c. No, the consumer is not making an optimal choice as she her MRS = 3 whereas her price ratio is 2. So, these two are not equal implying she is giving up more than she is actually required to. So, consumer is not making an optimal choice. Optimal choice occurs when MRS = price ratio.

d. We can see that MRS > price ratio as 3 > 2, so to maximize the utility consumer should increase the consumption of good X and decrease the consumption of good Y until MRS and price ratio becomes equal. This is because as consumption of good X is increased then marginal utility of X will decline and as consumption of good Y is decreased then marginal utility of Y will increase so MRS will decline until it becomes equal to the price ratio.

Rahul Sunny answered 1 year ago

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