Suppose that two identical firms produce widgets and that they are the only firms in the market. their costs are given by c1 = 60q1 and c2 = 60q2, where q1 is the output of firm 1 and q2 the output of firm 2. price is determined by the following demand curve:
p = 300 – q
where q = q1 + q2.

a. find the cournot-nash equilibrium. calculate the profit of each firm at this equilibrium.
b. suppose the two firms form a cartel to maximize joint profits. how many widgets will be produced? calculate each firm’s profit.
c. suppose firm 1 were the only firm in the industry. how would market output and firm 1’s profit differ from that found in part (b) above?
d. returning to the duopoly of part (b), suppose firm 1 abides by the agreement, but firm 2 cheats by increasing production. how many widgets will firm 2 produce? what will be each firm’s profits?

Consider the following calculations

Explanation:

a. π1 = P Q1 − C1 = (300 − Q1 − Q2 )Q1 − 60Q1 = 300Q1 − Q1^2 − Q1 Q2 − 60Q1

π2 = P Q2 − C2 = (300 − Q1 − Q2 )Q2 − 60Q2 = 300Q2 − Q1 Q2 − Q2^2-60Q2

Take the FOCs:

∂π/(∂Q1)= 300 − 2Q1 − Q2 = 0 ⇒ Q1 = 120 − 0.5Q2

∂π/(∂Q2)= 300 − Q1 − 2Q2 = 0 ⇒ Q2 = 120 − 0.5Q1

Q1 = 120 − 0.5[120 − 0.5Q1 ] = 60 − 0.25Q1 ⇒ Q1 = 80

Similarly find Q2 = 80 such that π1 = π2 = 6, 400.

b. The two firms act as a monopolist, where each firm produces an equal share of total output. Demand is given by P = 300 − Q, M R = 300 − 2Q, and M C = 60. Set M C = M R tofind that Q = 120 and Q1 = Q2 = 60, respectively. Therefore:

π1 = π2 = 180 × 60 − 60 × 60 = 7, 200.

c. It would be higher because they could make more money.

d. Firm 2 knows that Q1 = 60 and given the reaction function derived in part (a) firm 2 sets Q2 = 120 − 0.5 × 60 = 90. Overall, QT = 150 and P = 300 − 150 = 150. Hence:

π1 = 150 × 60 − 60 × 60 = 5, 400

π2 = 150 × 90 − 60 × 90 = 8, 100.

answer'; i believe the correct answer is (15,000) workers a year are treated for injuries caused by jacks, lifts or jack stands;

answer: in the short-run firms will respond by raising the price of turkey.

explanation: initially the long-run equilibrium is at a price of $5 per pound of turkey and a quantity of 50 million pounds per year. now, when webmd claims that a protein found in turkey will increase your expected lifespan by 4 years. the consumers demand for turkey will increase at every price shifting the demand curve to the right from d1 to d2. while, there will be no change in the supply curve in the short-run as it is not possible for producers to adjust supply so quickly. as a result the new equilibrium will occur at a higher price and a higher quantity of turkey.

thus, in the short run firms will respond by increasing the price of turkey, selling more quantity at a higher price and earning economic profits.