1.4 — Utility Maximization — Practice

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You can get music via downloads ( $d$ ) or concert tickets ( $t$ ). You have $60 to spend each week, and the price of a download is $3 and the price of a concert ticket is $10. Put $d$ on the horizontal axis and $t$ on the vertical axis.

Question 1

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

Where your marginal utilities are: $\begin{aligned} M U_{t} & = 4 s \\ M U_{s} & = 4 t \end{aligned}$

Part A

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

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:

$u (s, h) = \sqrt{s h}$

The marginal utilities are:

$\begin{aligned} M U_{s} & = 0.5 s^{- 0.5} h^{0.5} \\ M U_{h} & = 0.5 s^{0.5} h^{- 0.5} \end{aligned}$

You have an income of $12, t h e p r i c e o f S o d a i s$ 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?

Last updated on Feb 6, 2022