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: \[u(t,s)=4ts\]
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?