Question

Problem 3 You've been hired as a new manager for a local restaurant. While the restaurant serves many things, they are known for their wood-fired pizza and locally-sourced beer. Since both products are generally purchased at the same time, we consider them as complements. Thus, if you sell a lot of pizza, you would also expect to sell a lot of beer and vice versa. (a) Explain what pricing strategy would you use to maximize profits. Use general terms for your answer (high price, low price, etc) (b) Now, let's assume you've estimated the following profit function: π = PaeerQ Beer + PPizzaQ Pizza-CBeerQ Beer-CpizzaQ Pizza )izza 20

To fix that problem, I'm going to change the third question a little. In part b, you do not need to find the optimal quantity and price. To get full credit, you simply need to find the price of pizza and beer as a function of the other (ex. Pp = 50 - 5Pb) then interpret it. In my example, this tells me that if the price of beer goes up, the price of pizza goes down (you can plug in some numbers to test it).

Answer 1

$\small P_B=6.3+0.3(32+0.75P_B)=15.9+0.225P_B$

$\small \therefore P_B=\frac{15.9}{1-0.225}=20.5$

$\small \therefore P_P=32+.75\left (20.5 \right )=47.375$

$\small \therefore Q_B=7.875$

$\small \therefore Q_P=66.25$

$\small \therefore \pi=2953$