Suppose there are two firms in a market who each simultaneously choose a quantit

Question

Suppose there are two firms in a market who each simultaneously choose a quantity. Firms 1s quantity is q1 and firms 2s is q2. Therefore the market quantity is Q=q1+q2. The market demand curve is given by P=100-4Q. Also, each firm has constant marginal cost = 28. There are no fixed costs.

MR1=100-8q1-4q2
MR2=100-4q1-8q2

I found the output of each firm to be 6 for each and the market price to be 52

a.) What is the deadweight loss that results from this duopoly?
b.) How much profit does each firm make?
c.) Suppose firm 2 produced 2 units of output, how much output should firm 1 produce in order to max profit?

Explanation / Answer

Profit for firm 1 = (price-cost)*quantity I'm going to use q and z for q1 and q2. firm 1: P=(100-4(q+z)-28)*q -4 q^2-4 q z+72 q taking the derivative with respect to q: dP=0=-8q-4z+72 since they have the same marginal cost it's also dP=0=-8z-4q+72 Solving I agree with you about the profit. Now assuming there was infinite firms we would have MC=MR or 28 be the price. This would need 100-4Q=28, or 18=Q. It's lost q*change in p/2 so it should just be 24*6/2=72. B) well let's go back to the profit function: P=-4 q^2-4 q z+72 q P=-4*6^2-4*6^2+72*6=144 if you don't understand my above work it's the same as 52-28 profit per unit * 6 or units sold = 144 C. P=100-4(q+2) Profit = (price-cost) * quantity So Revenue =(100-4(q+2)-28)*q=64 q-4 q^2 derivative: 64-8q=0 So they should make 8 units.

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.