Managerial Economics ECO510 final exam

Q # 7:

Given demand Q = 60 – 2P

Supply = 5P - 10

a) The equilibrium price is where demand equals supply

So 60 – 2P = 5P – 10

7P = 70

P = 10

b) In a perfect competition the market maximizing output is given by MR = MC

We have R = PQ

And C = 16 + Q2 + 2Q

So MR = d/dQ (PQ) = P

And MC = d/dQ (16 + Q2 + 2Q) = 2Q + 2

Now MR = MC

P = 2Q + 2

Q = (P – 2)/2

At P = 10, Q = (10-2)/2 = 4

Therefore the profit maximizing output is Q = 4

c) The total profit is given by

Profit = R – C

= PQ – (16 + Q2 + 2Q)

= (10)(4) – (16 + (4)2 + 2(4))

= 40 – (16 + 16 + 8)

= 40 – 40 = 0

d) Since the maximum profit is zero, the other firms will stay in the market and the outcome will persist in the long run

Q # 8

a) Total Revenue equation

Consider Q1 + Q2 in the price equation. Total revenue equation can be calculated as follows:

Total revenue equation = P x Q

= (100 – Q)Q

= 100Q – Q2

Hence the total revenue equation is 100Q – Q2

b. Output of each firm in competitive market:

According to cournot, equilubrium duopoly market share is 1:2. Output of the firm can be calculated as follows:

Managerial Cost = Price

25 = 100 –Q1 – Q2

25 = 100 – Q1 – Q2 (Q1 = 2Q2 According to cournot equilubrium)

Q1 = 37.5 – 0.5Q2 (solve with cournot equilubrium which is Q1 = 2Q2)

Q1 = 18.75

Q2 = 37.5

Price of each firm in competitive market:

Price of the firm is calculated as:

Price = 100 – Q1 – Q2

= 100 – 18.75 – 37.5

= 43.75

Hence, each firm price is $43.75

c. Output of each firm in the in cartel:

Marginal costs for the firms are 50. Output of the firm is calculated as follows:

Marginal Cost = Price

50 = 100 – Q1 – Q2

50 = 100 – 2Q2 – Q2 (According to cournot equilibrium Q1 = 2Q2)

Q1 = 16.67

Q2 = 33.33

Hence the output of firm 1 is 16.67 and the output of firm 2 is 33.33

Price of the each firm in the cartel:

It is calculated as:

Price = 100 – Q1 – Q2

= 100 – 16.67 – 33.33

Price is calculated to be $50

d. Difference in part b and c:

The total output in the competitive market is more and the price is calculated to be lesser in comparison to the cartel total output and price.