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Cost Function

Suppose there are only two donut shops, Brenda’s and Julie’s. These two donut shops produce identical products. Demand for donuts is given by the function: Q = 75 – P, where Q is the quantity of donuts and P is the price. Suppose that total costs for Bren

Suppose there are only two donut shops, Brenda’s and Julie’s. These two donut shops produce identical products. Demand for donuts is given by the function: Q = 75 – P, where Q is the quantity of donuts and P is the price. Suppose that total costs for Brenda’s is given by TCBrenda = 0.1Q2Brenda and total costs for Julie’s donuts is given by TCJulie = 5QJulie

a) If the two firms compete and choose output such that price equals marginal cost, what is the profit-maximizing level of output for Brenda’s donuts? What is the profit-maximizing level of output for Julie’s donuts?

b) If the two firms compete and choose output such that price equals marginal cost, what is the market price?

c) What is the joint profit for the two firms when they compete?

d) If the two firms instead secretly collude and behave as a cartel, what is the profit-maximizing level of output for Brenda’s donuts? What is the profit-maximizing level of output for Julie’s donuts?

e) If the two firms secretly collude and behave as a cartel, what is the market price?

f) What is the joint profit for the two firms when they secretly collude and behave as a cartel?

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