Assume that a consumer has the utility function U(x,y) = (3x + 1)y, where x and

Question

Assume that a consumer has the utility function U(x,y) = (3x + 1)y, where x and y represent the quantities of two goods, X and Y. Calculate the consumers marginal utilities for good X and for good Y. A consumer has diminishing marginal utility for a good if her marginal utility for that good decreases as she consumes more of it, holding constant her consumption of other goods. Does this consumer have diminishing marginal utility for good X? Does she have diminishing marginal utility for good Y? Calculate the consumers marginal rate of substitution of X for Y.

Explanation / Answer

(a) utility function U (x.y) = 3xy + y ; (Marginal utility of X)MUx = dU / dx = 3y and (Marginal utility of Y)MUy = dU / dy = 3x + 1

(b) Diminishing marginal utility corresponds to the condition that double derative should be negative i.e. d2U / df2 < 0. In this question d2U / dx2 = d2U / dy2 = 0. So neither good X nor good Y have diminishing marginal utility.

(c) Consumer's marginal rate of substitution MRSxy = MUy / MUx = (3x + 1) / 3y

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