Answer to Question #285948 in Microeconomics for Nancy

Question

if a duopolist has a linear demand curve of the form Q=400-P.Assuming each firm has total cost (TC=3000+100Q).Calculate the profit maximizing price quantity combinations using the following oligopoly pricing models listed below demonstrating that

a)Under the cournot model,both firms will earn the same level of profit and determine industry profit and explain why this should be the case.

b)Under the cartel model each firm earns a higher profit that under cournot

c)Under the quasi competitive model,the firm will make a loss equivalent to fixed cost

Answer 1

A)This model assumes that the firms produce a homogeneous product and that the market demand curve is known. The profit-maximizing output of the first firm (Qt) varies depending on how, in the opinion of its management (top managers), the output of the second firm (Q2) will grow. As a result, each firm constructs its own response curve. Each firm's response curve tells us how much it will produce with the expected output of its competitor. At equilibrium, each firm sets its output according to its reaction curve, so the equilibrium level of output is at the intersection of the two reaction curves. This equilibrium is called a Cournot equilibrium. In this equilibrium, each duopolist sets the volume of production that maximizes its profits for a given volume of production of a competitor. A Cournot equilibrium is an example of what in game theory is called a Nash equilibrium, where each player playing poker does the best he can with the given actions of his opponents. As a result, no player has any incentive to change his behavior.

MC=AC=100

$Q1=\frac{400-100}{3}=100$

$Q2=\frac{400-100}{3}=100$

$Q=\frac{2(400-100)}{3}=200$

$P=\frac{400+2\times100}{3}=200$

every duopolist enterprise makes a profit:

$Profit=\frac{(400-100)^2}{9}=10000$

B)we consider ourselves as a single enterprise

$Q=\frac{400-100}{2}=150$

$Q1=Q2=\frac{400-100}{4}=75$

$Profit=\frac{(400-100)^2}{4}=22500$

C)

$P=AC=\frac{3000}{Q}+100$

P=400-Q

$400-Q=\frac{3000}{Q}+100$

$300-Q=\frac{3000}{Q}$

$300Q-Q^2-3000=0$

Q1=290

Q2=10

Q=300

P=100

$Profit=TR-TC=300\times100-(3000+100\times10)-(3000+100\times290)=30000-4000-32000=-6000$