Suppose a consumer buys only 2 goods - x and y and has an utility function given by U(x,y) Give an example of a utility function U(x,y) that exhibits increasing marginal rate of substitution.

Answer 1

An utility function that exhibits increasing MRS_x,y is U(x,y) = Ax² + By².

MRS_x,y = MU_x/MU_y where MU_x is the marginal utility of good x and MU_y is the marginal utility of good y.

For U(x,y) = Ax² + By², MU_x = 2Ax, MU_y = 2By.

So, MRS_x,y = 2Ax/2By = Ax/By, which increases as the consumer increases consumption of x and reduces the consumption of y along an indifference curve. Thus, this utility function exhibits increasing marginal rate of substitution. The indifference curves corresponding to this utility function are concave to the origin.