5) Industry demand is given by:

QD = 1,000 – P

All firms in the industry have identical and constant marginal and average costs of $50/unit. 

a. If the industry is perfectly competitive, what will industry output be? What will be the equilibrium price? What profit will each firm earn? 

b. Now suppose that there are five firms in the industry, and that they collude to set price. What price will they set? What will be the output of each firm? 

a. MR = P = MC=50 

Since it is perfect competition = No profit Profit = 0 

P=50;

Q= 1, 000 – P = 1,000 – 50 = 950 

b. TR=P*Q Q = 1,000 – P P = 1,000 – Q;

TR = (1,000 – Q) Q = 1,000Q – Q²

MR= dTR/dQ; =1,000-2Q

MR= 50 add into equation; = 50 = 1,000– 2Q; = 2Q = 950; = Q= 950/2=475 = Q = 475;P =1, 000– 475=525; P = 525

So, Q = 475; P = 525Five firms in the industry; Output =Q/5=475/5=95Output Quantity = 95

6) A monopolist sells to two consumer groups, students and non-students. Demand for students: Q = 500 - 1/2P and MR=500 –P. Demand for non-students: Q = 750 - 2P and MR=750 – 4P. MC = 20. 

Find the Price and Quantity combination that maximizes profit in each market if the two consumer groups can be separated (price discrimination).

The rule for profit-maximization is MR = MC.

Setting MR = MC for the students: 500 – P = 20;P= 480 The profit-maximizing price.

To find the quantity, substitute P into the demand curve for the students:

Q = 500 – 1/2P. Substituting in P Q = 500 –1/2(480); Q = 500 – 240;Q = 260 Profit-maximizing quantity for the students.

Setting MR = MC for the non-students:

750 – 2P = 20. 2P = 730. P = 365. Profit-maximizing price for the non-student.

To find the quantity, substitute P* into the demand curve for the non-students:

Q = 750 – 2P. Substituting in P* Q = 750 – 2(365); Q = 750 – 730; Q = 20Profit-maximizing quantity for the non-student group.

7) A monopolistic firm operates in two separate markets. No trade is possible between market A and market B. The firm has calculated the demand functions for each market as follows:

Market A P = 15 – QMarket B P = 11 – Q

The company estimates its total cost function to be TC= 4Q. Calculate:

A. Quantity, total revenue and profit when the company maximizes its profit and charges the same price in both markets.

Market A = P = 15 – Q1

Market B = P = 11 – Q2

Price in Market A = Price Market B

P1 = P2;

Q1= 15 – P;Q2 = 11 – P;Total Q = Q1 + Q2;

Q = 15 – P + 11 – P;Q = 26 – 2P;

Transform to: P = 13 – Q/2

Derive Profit Function:

Profit, Π = TR – TC; Π = P*Q – TC; Π = (13 – Q/2) Q – 4Q; Π = 13Q – Q2/2 – 4Q; Π = 9Q – Q2/2;

∏= d∏/dQ; Π = 9 – Q= 0; Q = 9; add into equation;

P = 13 – Q/20P = 13 – 9/2P = 8.5

P IN MARKET A = P IN MARKET BQ1 = 15 – P = 6.5Q2 = 11 – P =2.5

To find profit. Find Profit Without Price Discrimination:

Π = 9Q – Q2/2 = 9(9) – (9)2/2; = 81 – 40.5 = 40.5Total Revenue = P*Q

TR = (13 – Q/2) Q = 76.5

B. Quantity, total revenue and profit when the company charges different prices in each market and maximizes its total profit.

Market A = P1 = 15 – Q1

Market B = P2 = 11 – Q2

Price Market A ≠ Price Market B;

= Q1 + Q2 = 4; add into equation; Profit = TR1 + TR2 – TC; TC= 4Q. = P* Q1 + P* Q2 – 4Q; = (15 – Q1) Q1 + (11 – Q2) Q2 – 4(Q1 + Q2); = 15 Q1 – Q1

2 + 11 Q2 – Q22– 4Q1 – 4Q2;

= – Q12 + 11Q1 – Q2

2 + 7Q2;

∏ = – Q12 + 11Q1 – Q2

2 + 7Q2;

∏= d∏/dQ1; = 11 – 2Q1; Q1= 5.5

∏= d∏/dQ2; = 7– 2Q2; Q2= 3.5

So, Q1= 5.5; Q2= 3.5

Demand Market A P1 = 15 – Q1 = 9.5; Demand Market B P2 = 11 – Q2 = 7.5 So, total revenue TRT = 15 Q1 – Q1

2 + 11Q2 – Q22

= 15 (5.5) – (5.5) 2 + 11(3.5) – (3.5) 2

= 78.5

So, profit ∏ = – Q1

2 + 11Q1 – Q22 + 7Q2;

= 11(5.5) – (5.5) 2 – (3.5) 2 + 7 (3.5) = 42.5