Question

Consider a perfectly competitive market with demand and supply Qd = 1550 – 3P and Qs = -50+5P

The firm’s costs are described by the equations TC = 2500 – 5q +q2 and MC = -5 + 2q

a. Find the equilibrium price and quantity in the market.

b. Find the profit maximizing quantity for the firm.

c. Find the firm’s profit.

d. How many identical firms are in this market in the short run?

Now consider the long-run where economic profit goes to zero. (That was a hint)

e. Find the firm’s long-run profit maximizing output.

f. Find the long-run price in the market.

g. Find the long-run quantity demanded in the market.

h. How many identical firms are in this market in the long run?

Answer 1

Ans)- Q_d= 1550 – 3P , Q_S= -50+5P

TC = 2500 – 5q + q² , MC = -5 +2q

a) At equilibrium, Quantity supply equals quantity demand in the market.

i.e. at Equilibrium

Quantity demand (Q_d) = Quantity supply (Q_S)

1550 -3P = -50 +5P

1550 +50 = 5P +3P

1600 = 8P

[P = 200] --------------------------------Equilibrium market price

Put P=200 in demand function

Q_d= 1550 – 3*200

Q_d=1550 – 600

[Q_d=950 and also Q_s=950]

Hence, the equilibrium market price would be 200 and equilibrium market quantity would be 950.

b) Profit maximising price and quantity for the firm

Profit maximising condition for firm-

MR =MC

We have, Total Revenue (TR) = P*quantity

From demand curve,

Q = 1550 -3P

So, the firm will also face the same demand curve for his product.

Let’s say that the firm is producing ‘q’ quantity of the product. So, the demand curve of the firm would be,

q = 1550 – 3P

3P = 1550 – q

P = (1550-q)/3

So,

TR = P*q

TR = [(1550-q)/3]*q

TR = [1550q – q²]/3

Differentiate W.r.t. q to find MR

MR = [1550 – 2q]/3

Hence, we have profit maximising condition

MR = MC

[1550 – 2q]/3 = -5 + 2q

1550 – 2q = 3(-5 +2q)

1550 -2q = -15 + 6q

1550 – 15 = 6q + 2q

1535 = 8q

[q = 1535/8= 191.87 or 192]

Hence, the profit maximising quantity for the firm would be 192 units.

c) Profit of the firm:

Total Profit = TR – TC

                     = P*q – TC

Put P = 200, q = 192 and TC = 2500 – 5q + q²

Total Profit = 200*192 – (2500 – 5q + q²)

= 38,400 – 2500 + 5*192 – (192)²

= 38,400 – 2500 + 960 – 36,864

[Total profit = -4]

Hence, the required firms profit would be -4 i.e. loss of 4.

d) Total market quatity (Q) is 950.

Each firm is producing a quantity of , q=192

So,

[No. of identical firm = 950/192 = = 4.94 i.e. 5 firms]

Hence, there will be 5 identical firms in the market.