Question

Lagoon has two food stores Buck's and Combo's. It costs $1 to make one of Buck's bread loaves and $2 to make one of Combo's cheese rounds. Let P1 denote Buck's price and P2 denote Combo's price per product. Let Q1 and Q2 denote the demand for each store's product. The store's demands are given by:
Q1 = 14 - P1 - 0.5P2,
Q2 = 19 - 0.5P1 - P2
a. Are the store's products substitutes or complements? How do you know?
b. Write the profit function for Buck's in terms of P1 and P2. Write the profit function for Combo's in terms of P1 and P2.

Answer 1

Answer:

a. Complements

b. $X(P_1,P_2) =-P_1^2-P_2^2-P_1P_2+16P_1+21.5P_2-52$

Explanation:

a. Analyzing the demand equations for both products, a negative relationship between demand and price can be observed for both goods. This means that an increase in price for the cheese rounds causes a decrease in demand for bread, while an increase in price for bread causes a decrease in demand for cheese rounds. This relationship is exhibited when goods are complements.

b. The profit from each store is given by:

$X_1 = Q_1*(P_1-\ 1)\\X_2 = Q_2*(P_1-\ 2)$

Total profit is given by:

$X_1 =(14-P_1 - 0.5P_2)*(P_1-\ 1)\\X_1=14P_1-P_1^2 - 0.5P_1P_2-14+P_1 + 0.5P_2\\X_2 = (19 - 0.5P_1 - P_2)*(P_2-\ 2)\\X_2=19P_2-0.5P_1P_2-P_2^2-38+P_1+2P_2\\X(P_1,P_2) =X_1+X_2\\X(P_1,P_2) =-P_1^2-P_2^2-P_1P_2+16P_1+21.5P_2-52$