# 1.4 — Utility Maximization — Practice

# 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?