Given P=140-0.6Q, TC1=7q1, TC2=0.6q2 the power of 2. A. Determine the short run equilibrium output of each duopoly ignoring their Independence ( with naive assumptions). B. What is the short run market price ? C. Find the demand functions of the duopolies ( the reactions curves or graphic solution of cournot model & draw) & show the short run output levels. D. calculate the short run profit of each duopoly & the industry profit. E. verify the economic profit of each duopoly graphically.
Given P=140-0.6Q, TC1=7q1, TC2=0.6q2 the power of 2. A. Determine the short run equilibrium output of each duopoly ignoring their Independence ( with naive assumptions). B. What is the short run market price ? C. Find the demand functions of the duopolies ( the reactions curves or graphic solution of cournot model & draw) & show the short run output levels. D. calculate the short run profit of each duopoly & the industry profit. E. verify the economic profit of each duopoly graphically.
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P=140-0.6Q, TC1=7q1, TC2=0.6q2 the power of 2. A. Determine the short run equilibrium output of each duopoly ignoring their Independence ( with naive assumptions). B. What is the short run market price ? C. Find the demand functions of the duopolies ( the reactions curves or graphic solution of cournot model & draw) & show the short run output levels. D. calculate the short run profit of each duopoly & the industry profit. E. verify the economic profit of each duopoly graphically.
Adugna
Apr 28, 2016
To solve this problem, we will go step by step:
A. Determine the short run equilibrium output of each duopoly ignoring their independence (with naive assumptions).
In a duopoly, each firm maximizes its profit by choosing its output level. To find the equilibrium output, we need to set the marginal cost equal to the marginal revenue for each firm.
For Firm 1:
Marginal Cost (MC1) = Total Cost1 (TC1) / Output1 (q1) = 7
Marginal Revenue (MR1) = Price (P) + (Output1(q1) * Slope(P)) = 140 - 0.6Q + (q1 * -0.6) = 140 - 0.6Q - 0.6q1
Setting MC1 = MR1:
7 = 140 - 0.6Q - 0.6q1
Rearranging the equation, we get:
Q = (140 - 7 - 0.6q1) / 0.6
For Firm 2, the process is the same, but we use TC2 and MR2 instead:
MC2 = 0.6
MR2 = 140 - 0.6Q - 0.6q2
Setting MC2 = MR2:
0.6 = 140 - 0.6Q - 0.6q2
Rearranging the equation, we get:
Q = (140 - 0.6 - 0.6q2) / 0.6
B. Find the short-run market price.
To find the short-run market price, we need to equate the total quantity produced (Q) by both firms with the market demand equation.
Market Quantity (Q) = Output1 (q1) + Output2 (q2)
Q = q1 + q2
Substituting the values of q1 and q2 we found earlier into this equation, we get:
Q = (140 - 7 - 0.6q1) / 0.6 + (140 - 0.6 - 0.6q2) / 0.6
Simplifying the equation, we can find the value of Q.
C. Find the demand functions of the duopolies (the reaction curves or graphic solution of Cournot model) & show the short-run output levels.
To find the demand functions of the duopolies, we need the reaction curves, which show each firm's output as a function of the competitor's output.
For Firm 1:
Firm 1's reaction function is derived by rearranging the equation we found earlier for Q:
q1 = (Q - q2(0.6)) / 0.6
For Firm 2:
Firm 2's reaction function is derived similarly:
q2 = (Q - q1(0.6)) / 0.6
To show the short-run output levels, we can plot these reaction curves on a graph, with q1 on the x-axis and q2 on the y-axis.
D. Calculate the short-run profit of each duopoly & the industry profit.
To calculate the short-run profit for each firm, we need to subtract their total cost from their total revenue.
For Firm 1:
Profit1 = Revenue1 - Cost1
Profit1 = (P * q1) - TC1
Profit1 = (140 - 0.6Q - 0.6q1) * q1 - 7q1
For Firm 2, the process is the same:
Profit2 = (P * q2) - TC2
Profit2 = (140 - 0.6Q - 0.6q2) * q2 - 0.6q2
To find the industry profit, we simply add the profits of both firms together.
E. Verify the economic profit of each duopoly graphically.
To verify the economic profit graphically, we can plot the total revenue, total cost, and profit functions on a graph. By analyzing the intersection points and slopes of these functions, we can determine their economic profits.