Please show work. Two symmetric firms in a Bertrand duopoly face the inverse mar
ID: 1195445 • Letter: P
Question
Please show work.
Two symmetric firms in a Bertrand duopoly face the inverse market demand P = 60 - 3Q, and the marginal costs of the two firms are $6. Also, fixed costs are zero for both firms. What will the market price be? A) $10. B) $15. C) $6. D) $8. 3Two symmetric firms in a Bertrand duopoly face the inverse market demand P = 60 - 3Q, and the marginal costs of the two firms are $6. Also, fixed costs are zero for both firms. How much output will each firm produce? A) 15. B) 18. C) 9. D) 30.
Explanation / Answer
1. Bertrand's equilibrium occurs when P1=P2=MC, which is same as perfect competition. Therefore the market price will be $6.
2. Total Quantity will be 18, by substituting P in demand equation. Thus each firm produces 9 units.
3. Profit function is Profit1 = q1 (150-2(q1+q2)) - 6q1.
Proft2 = q2(150-2(q1+q2)) - 6q2.
To know the maximum profit, differentiate the first equation with q1 and equate it with 0;
150-4q1-2q2-6=0; in this case both q1 and q2 are identical and are same. Hence, q1=q2=24. Total industrial output is 48.
4. Profit equals to 24*48 = 1152.