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?