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: \[\begin{align*} MU_t&=4s\\ MU_s&=4t\\ \end{align*}\]

Part A

Put $t$ on the horizontal axis and $s$ on the vertical axis. Write an equation for $MRS_{t,s}$

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:

\[u(s,h)=\sqrt{sh}\]

The marginal utilities are:

\[\begin{align*} MU_s&=0.5s^{-0.5}h^{0.5} \\ MU_h&=0.5s^{0.5}h^{-0.5} \\ \end{align*}\]

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?