Question

Mitchell‘s money income is $150, the price of X is $2, and the price of Y is $2. Given these prices and income, Mitchell buys 50 units of X and 25 units of Y. Call this combination of X and Y bundle J. At bundle J, Mitchell’s MRS is 2. Given these prices and income, what is Mitchell‘s equilibrium consumption of X? A. X < 50 B. X = 50 C. X > 50 D. None of the preceding statements is correct.

Answer 1

we can solve this intuitively. we know at the optimal level of consumption, MRS = price ratio. since price of x = price of y = 2. therefore at optimal level MRS = 2/2 = 1. at bundle J, the value of MRS is 2 which is greater than 1. we know that as we move along the indifference curve( as we increase the value of x) the value of MRS is decreases, assuming it is a normal convex function. so for if we want to move from point J to the optimal level of consumption then we would have to decrease our MRS from 2 to 1. as we said earlier when MRS decreases the value of x consumed increases. so as we move from J to the optimal level of consumption the amount of x consumed will greater than 50 which was consumed earlier. hence the correct answer is c