Question $1$: Short answer

Please be concise. None of the answers require more than a brief paragraph.

a$)(3$ points$)$ In the spring of $2020,$ many restaurants were still operating even if their profits cannot cover their total costs. At what prices would these restaurants have shut down completely $($even in the short run$)?$

b$)(3$ points$)$ You work as a marketing analyst for a pharmaceutical firm, and you are trying to gather information about the marginal cost of production for a competing firm. You know that they have a patent on a popular medication that sells for $\backslash (\backslash$$ $20\backslash )$ per dose, and you believe the elasticity of demand for this product is roughly $-4.$ Assuming the competing firm acts as a profit$-$maximizing monopolist, what is your best guess of its marginal cost of production?

c$)(3$ points$)$ Amazon conducted a pricing experiment and by randomly selecting users and give them a $20\backslash \%$ discount for their Prime membership. It is observed that these users are $\backslash (10\backslash \%\backslash )$ more likely than others to join as a Prime member. What is the demand elasticity? Is the current price optimal for Amazon?

d$)(3$ points$)$ A local bakery uses both machines $\backslash (($m$)\backslash )$ and labor $\backslash (($l$)\backslash )$ to make their product. Suppose that they hire a consultant to estimate their marginal return of investments $($MPI$\text{'}$s$)$ for machines and labor. They find that their MPI for labor is $0\mathrm{.}06$ and their MPI for machine is $0\mathrm{.}09.$ How should they adjust their plan?