2 Consider a perfectly competitive market in the short run M

2. Consider a perfectly competitive market in the short run. Market de- mand is given by P 10 - Q. Let n be the number of firms in the short run. Find the short run equilibrium price and quantity for the cost functions and the number of firms below (a) TC 2+4+242, n-6 3. For the following cost functions find the long run equilibrium price in a perfectly competitive market. Depict this long run equilibrium price on a picture to improve your understanding (a) TC- 100012q 10q2 (b) TC 250 12q+10q2 (c) TC = 3600 + 120 100q2 (d) TC-2712q 3q2 (e) TC 128+12q+242

Solution

(2)

Firm\'s supply function is its Marginal cost (MC) function. If there are n firms,

Market supply (Q) = nq, therefore

q = Q/n

Equilibrium is obtained by equating market demand and market supply.

(a) TC = 2 + q + 2q²

MC = dTC/dq = 1 + 4q

Firm supply function: P = 1 + 4q

Q = 6n, or q = Q/6

P = 1 + 4 x (Q/6) = 1 + (2Q/3)

P = (3 + 2Q) / 3

Equating with market demand,

10 - Q = (3 + 2Q) / 3

30 - 3Q = 3 + 2Q

5Q = 27

Q = 5.4 (Market quantity)

q = 5.4/6 = 0.9

P = 10 - 5.4 = 4.6

(b) TC = 2 + 3q + 2.5q²

MC = dTC/dq = 3 + 5q

Firm supply: P = 3 + 5q

Q = 5n, or q = Q/5

P = 3 + 5 x (Q/5) = 3 + Q

Equating with market demand,

10 - Q = 3 + Q

2Q = 7

Q = 3.5

q = 3.5/5 = 0.7

P = 10 - 3.5 = 6.5

(c) TC = 2 + 5q + 3q²

MC = dTC/dq = 5 + 6q

Firm supply: P = 5 + 6q

Q = 4q, so q = Q/4

P = 5 + 6 x (Q/4) = 5 + 1.5Q

Equating with market demand,

10 - Q = 5 + 1.5Q

2.5Q = 5

Q = 2

q = 2/4 = 0.5

P = 10 - 2 = 8

(d) TC = 2 + 3q + 3.5q²

MC = dTC/dq = 3 + 7q

Firm supply: P = 3 + 7q

Q = 3q, so q = Q/3

P = 3 + 7 x (Q/3)

Equating with market demand,

10 - Q = 3 + (7Q/3)

30 - 3Q = 9 + 7Q

10Q = 21

Q = 2.1

q = 2.1/3 = 0.7

P = 10 - 2.1 = 7.9

NOTE: As per Chegg Answering Policy, first 4 parts of the first question are answered.