Question

3. A firm in a perfectly competitive market has the following cost function: c(y) = 4y² + 450.

a. If the market price of their product is $200, how many units should they produce, and what will their profits be? Should they shut down or exit the market? (2 points)

b. If the market price falls to $50, how many units should they produce, and what will their profits be? Should they shut down or exit the market? (3 points)

c. What is the long run equilibrium price & quantity? (3 points)

Answer 1

Marginal cost (MC) = dc(y)/dy = 8y

(a)

Perfectly competitive firm equates price with MC.

8y = 200

y = 25

Revenue (TR) = p x y = 200 x 25 = 5,000

C(y) = (4 x 25 x 25) + 450 = 2,500 + 450 = 2,950

Profit = TR - C(y) = 4,000 - 2,950 = 2,050

Since profit is positive, firm will not shut down or exit.

(b)

When p = 50,

8y = 50

y = 6.25

TR = 50 x 6.25 = 312.5

C(y) = (4 x 6.25 x 6.25) + 450 = 156.25 + 450 = 606.25

Profit = 312.5 - 606.25 = - 293.75 (loss)

Here,

TVC = 4y²

AVC = TVC/y = 4y

When y = 6.25,

AVC = 4 x 6.25 = 25

Even though firm is making a loss, since price is higher than AVC, firm will not shut down.

(c)

In long run equilibrium, P = MC = AC, where

AC = C(y)/y = 4y + (450/y)

Equating with MC,

4y + (450/y) = 8y

4y = 450/y

4y² = 450

y² = 112.5

y = 10.61

Price = MC = 8 x 10.61 = 84.88