Consider two firms with constant marginal and average costs equal to 10. Market
ID: 1200086 • Letter: C
Question
Consider two firms with constant marginal and average costs equal to 10. Market demand is Q = 500 – 20P. Firms choose quantities simultaneously as in the Cournot model. The solution for the Nash Equilibrium gives a total output equal to what number? and total market profit equal to what number? (NOTE: Write your first answer in number format, with 2 decimal places of precision level; do not write your answer as a fraction. Use a period for the decimal separator and a comma to separate groups of thousands.) Show all steps.
Explanation / Answer
Demand function: Q=500-20P
Or. P=25-0.05Q
Since there are 2 firms producing together, the demand function becomes:
P=25-0.05(Q1+Q2)
MC1 = MC2 = 10
Calculate the Cournot model equilibrium by calculating the reaction functions of the two firms. This can be seen as below:
Firm 1:
Equate MR1 = MC1
That is, 25 - 0.05Q2 - 0.1Q1 = 10
This gives Q1 = 150-0.5Q2
Firm 2:
Equate MR2 = MC2
That is, 25 - 0.05Q1 - 0.1Q2 = 10
This gives Q2 = 150-0.5Q1
Substitute the reaction functions of both the firms into each other calculated above to find the output produced by each firm.
This comes out to be: Q1 = Q2 = 100 units.
Price = 25-0.05(Q1+Q2) = $15
Profit = TR-TC = PQ1 + PQ2 - TC1 - TC2 = 1500+1500-1000-1000 = $1000 (profit).