Question

PLEASE ANSWER ALL BOLDED PARTS!! MUST ANSWER PART A AND B PLEASE.

1. 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-PB eerą Beer + PPizza.Q Pizza-C Beerą Beer-C Pizza «Pizza

You’ve also estimated the following equations:

What is the profit maximizing price and quantity for pizza and beer? What is your profit? HINT: Find marginal profit with respect to PBeer and PP izza, then use substitution. For part b, use the demand not the inverse demand. In other words, substitute the Q function I gave you into the total revenue and multiply everything by P.

Answer 1

a). In case of complementary goods above I.e. bear and pizza we will adopt low price strategy, other wise if an increase in price of comodity affects the demand for the commodity, it will automatically affects the demnadand for the complementary good also'. If the price of pizza is increas ed there is more possibility that demand for both goods will come down. As from the result in part B , it also becomes clear that the optimal prices being higher than margonalinal costs, and also both the proice are in huge difference,, the firm is incurring huge lossez , that can only be tackled by reducing prices.

b)
pi = P_Beer Q_Beer + P_pizza Q_pizza - C_Beer Q_Beer - C_pizza Q_pizza For simplicity B = Beer & Z = pizza pi = P_b[63 - 5P_B + P_Z] + P_Z[120 - 2P_Z + 2P_B] - C_B Q_B - C_Z Q_Z = 63P_B - 5P^2_B + P_B P_Z + 120P_Z - 2P^2_Z + 2P_B P_Z -2(63 - 5PB + P_Z) - 5(120 - 2P_Z + 2P_B) pi = 63P_b - 5P_B^2 + 120P_Z - 2P^2_Z + 2P_B P_Z - 2 times 63 + 10P_B - 2P_Z - 600 + 10P_Z - 10P_B ---(1) pi'P_B = 63 - 10P_B + P_Z + 2P_Z + 10 - 10 = 0 = 63 - 10P_B + 3P_Z = 0 = > 10P_B = 63 + 3P_Z ---(II) Now, pi'P_2 = P_B - 2 + 120 - 4P_B + 2P_B + 10 = 0 3(63 + 3PZ)/10 + 128 - 4P_Z = 0 189 + 9P_Z + 1280 - 40P_Z = 0 times 10 1469 - 31P_Z = 0 P_Z = 1469/31 = 47.387 Now P_B = 63 + 3(47.387)/10 = 205.16128/10 = 20.51612
One important point is that profit the firm is getting at derived optimal prices is in negative. So it faces

Optimal price for pizza =47.387

optimal prize for bear= 20.51612

Optimal quantity for pizza = 66.25824

Optimal quantity for bear= 7.806

profit = -4004.8071