Ann's money income is $250, the price of X is $3, and the price of Y is $2. Given these prices and income, Ann buys 60 units of X and 35 units of Y. Call this combination of X and Y bundle J. At bundle J Ann's MRS is 2. Given these prices and income, what is Ann's equilibrium consumption of X? A) X 60 D) None of the statements is correct.

Question

Ann's money income is $250, the price of X is $3, and the price of Y is $2. Given these prices and income, Ann buys 60 units of X and 35 units of Y. Call this combination of X and Y bundle J. At bundle J Ann's MRS is 2. Given these prices and income, what is Ann's equilibrium consumption of X?
A) X < 60
B) X = 60
C) X > 60
D) None of the statements is correct.

Quizplus · Accepted Answer

If Ann is not consuming 60 units of X at bundle J, she could increase her total utility without spending more money by reducing consumption of good Y and increasing consumption of good X. This means that the MRS at bundle J is not equal to the slope of the budget line, so she has not yet reached her equilibrium consumption. In this case, since Ann's MRS is 2 and the price ratio is 3/2, she is willing to give up 2 units of Y for 3 units of X. She can continue to increase her consumption of X until the marginal rate of substitution equals the slope of the budget line (which is the price ratio of X and Y), which occurs at a consumption of 90 units of X and 5 units of Y. However, since Ann's income and the market prices do not allow her to reach this consumption bundle, her equilibrium consumption of X is between 60 and 90. Thus, the answer is C.

Ann's Money Income Is $250, the Price of X Is