Question

3.Firm A and Firm B are the only two firms in the housing market. Both these firms produce the same type of houses. They face the following market demand curve: Q= 28-(1/5) P where Q= QA + QB

(PLEASE ASSIST WITH QUESTIONS : E~I)

a. Write the demand equation in terms of Q.

b. Write down the total revenue functions for both firms in terms of QA & QB TR

c. Write down the marginal revenue (MR) functions for both firms in terms of QA & QB.

d. Suppose Marginal cost (MC) for both firms is 20. Find out the reaction curve for both firms.

e. Solve the two equations of part d. simultaneously to calculate the Cournot equilibrium. How much will each firm produce individually? What is the total output produced by the two firms collectively?

f. The total cost function is given by the following equation TC=20Q. What are each firm’s total profits?

g. Suppose these firms collude and decide to split profits evenly. How much will each firm produce in such a case? What will be the total output produced by the two firms? What will be each firm’s total profit?

h. Suppose these firms produce competitively without taking the other firm’s quantity into consideration. How much will each firm produce now? What will be the total output produced by the two firms? What will be each firm’s total profit?

i.Draw the reaction curves of both these firms and show the Cournot equilibrium. On your graph also show the collusive equilibrium and the competitive equilibrium. Compare these three equilibriums.

(PLEASE ASSIST WITH QUESTIONS : E~I)

Answer 1

E).

Here the market demand is “Q=28-P/5”, => “P=140-5*Q”, => where “Q=Qa+Qb”. The reaction function of “firm A” and “firm B” are given below.

=> qA = 12 – qB/2, the reaction function of firm A.

=> qB = 12 – qA/2, the reaction function of firm B. Now, if we solve simultaneously then the optimum solution is “qA=qB=8”.

So, here each produce “8 units” and the total output supplied by both firm is “8+8=16 units”.

F).

Now, the market price is “P=140-5*q”, “P=140-5*16 = 60 > 0”. Now, the cost function is given by “TC=20*q”.

=> the profit function is “Aa = P*qA - TC”, => Aa = 60*8 – 20*8 = 320”. Similarly, the profit of “firm B” is “Ab= 320”. So, under the information given each firm earn “$320”.

G).

Now, the market demand function is “P=140-5*q”, => MR = 140-10*q. Now, the total cost function is “TC=20*q”, => MC=20”. Now, at the equilibrium “MR” must be equal to “MC”.

=> MR = MC, => 140 – 10*q = 20, => q=120/10 = 12, => the market price is “P=140-5*q = 140-5*12 = 80”.

So, here under collusion each firm produce “12/2 = 6 units” and the profit earned by each firm is given below.

=> Aa = P*qa – TC = 80*6 – 20*6 = 360 > 320. So, under collusion each firm produce “6 units” and earn “$360” as profit.

H).

Now, under the competitive market the “P” must be equal to “MC”, => P=MC.

=> 140-5*q = 20, => q=120/5 = 24. So, the total output supplied by both firm is “qa=qb=24/2=12 units”.

The market price is “P=MC=20”. So, under the competitive market the market price and the output supplied by both firms are “qa=qb=12 units”. Since, here “P=MC”, => each firm earn normal profit, => economic profit is zero.