Question

a. A consumer’s MRSxy is currently equal to 6. The consumer is currently consuming 12 units of X and 10 units of Y. Would the consumer prefer another market basket consisting of 13 units of X and 7 units of Y?

Explain carefully, you may draw a diagram to support your answer.

b. Draw a carefully labeled graph showing the consumer’s optimal combination of two goods.

c. State the equation that holds true at the optimal point.

d. Explain what this equation means in words that could be understood by someone who is not taking the class.   

Answer 1

No, the consumer would not prefer another market basket consisting of 13 units of X and 7 units of Y. This is because, the very fact that consumer is consuming 12 units of X and 10 units of Y shows that, the rational consumer is operating at the optimum point where the rate at which the consumer is willing to give up one good for the other (marginal rate of substitution) is equal to the rate at which the market is ready to exchange one good for the other (price ratio).

At the optimum point following equation holds

Marginal Rate of Substitution (MRS_XY) = P_X/P_Y

P_X = Price of X

P_Y = Price of Y

MRS = Marginal Utility of X/Marginal Utility of Y

MRS measures the amount of good Y that one is willing to pay for a marginal amount of extra consumption of good X. In reality how much one actually has to pay depends on the price of the good. When the two ratios are equal the consumer has no incentive to move from it, that is why it is called the optimum point.