1.5 — Solving the Consumer’s Problem - Practice Problems

Question 1

Suppose you can watch movies in the theater (t) and streaming at home (s), and earn utility according to the utility function: u(t,s)=4ts

Where your marginal utilities are: MUt=4sMUs=4t

Part A

Put t on the horizontal axis and s on the vertical axis. Write an equation for MRSt,s

Part B

Would bundles of (2,2) and (1,4) be on the same indifference curve?

Part C

Sketch this indifference curve.

Question 2

You can get utility from consuming Soda (s) and Hot dogs (h), according to the utility function:

u(s,h)=√sh

The marginal utilities are:

MUs=0.5s−0.5h0.5MUh=0.5s0.5h−0.5

You have an income of $12, the price of Soda is $2, and the price of a Hot dog is $3. Put Soda on the horizontal axis and Hot dogs on the vertical axis.

Part A

What is your utility-maximizing bundle of Soda and Hot dogs?

Part B

How much utility does this provide?