Question

Part 1 (1 point) D See Hint John's utility is a function of housing (21), measured in square feet of housing space, and food consumption (2x2), measured in dollars. His utility function can be written as 4, 374x + 2x2. What is John's marginal rate of substitution when he has 729 square feet of housing and $145.00 of food consumption? Part 2 (1 point) ♡ See Hint John's utility is a function of housing (x1), measured in square feet of housing space, and food consumption (x2), measured in dollars. His utility function can be written as 4, 374x,? + 2x2. What is John's marginal rate of substitution when he has 729 square feet of housing and $384.00 of food consumption?

Answer 1

Note that MRS = -MUx1 / MUx2

MUx1 = U'(x1) = (1/3)*4374*(x1)^(-2/3)

MUx2 = U'(x2) = 2

Hence MRS = -(1/3)*4374*(x1)^(-2/3) / 2 = -729(x1)^(-2/3)

Part 1) Here x1 = 729

Hence MRS = -729* (729)^(-2/3) = -9

Therefore MRS = -9

Part 2) Here x1 = 729

Hence again MRS = -9