Question

1. In the utility function , does Y exhibit diminishing marginal rate of substitution? Please show your work.

2. What is the no-waste condition for the utility function

Express your answer in terms of y as a function of x.

Answer 1

Here, we see that when two commodities Xand Y are taken on the x axis and y axis and as we increase the consumption of x, the marginal rate of substitution( slope of IC) diminishes, hence the IC is convex to the origin. However, if we increase Y, MRS would increase as MRS=Y/X. Thus, Y does not exhibit diminishing MRS.

2. No waste condition is depicted in utility functions like perfect complements, U= min( ax, by). This no waste condition is obtained where ax=by i.e. at the kink. It can be shown through,