Question

Price of premium VT cheddar cheese is $100 per kg. The cost function of a perfectly competitive cheese-producing firm is

C=52q-q2+13q3+4.67        q is in thousand kg

1. COST CONCEPTS

Write down the expressions for the following cost concepts

1. FC

2. VC

3. AFC

4. AVC

5. ATC

6. MC

1. 2. PROFIT MAX
2. Solve for the profit maximizing (or loss-minimizing) quantity of the firm
3. Solve for the profit (loss) at this quantity

C. SHUTDOWN

Solve for the shutdown price (and quantity)

D. SUPPY CURVE

Write down the expression for the supply curve of this firm

E. ILLUSTRATE

            Illustrate your answers in B to D

Answer 1

Given,

Average total cost = TC /q

Or, ATC = AFC + AVC

Marginal cost, MC = ∆TC/∆q

Differentiate C wrt q, we get

A. Profit will be maximized at the point where MC = P (since perfect competition).

Price = $ 100

On solving the above expression we get

q = 1.13533 thousand kg

Other root is negative and quantity cannot be negative therefore, consider positive root.

Profit = 100 × 1.13553 - ( 52×1.13553 -1.13553^2 +13 × 1.13553^3 + 4.67) = $ 32.09

The firm will shutdown at a price where average variable cost is minimum. Determine the quantity at which AVC is minimum.

AVC = 52 - q + 13q^2

Differentiate AVC and equate it to zero,

AVC' = -1 + 26q

Equate it to zero

26q - 1 = 0

=> q = 1/26 = 0.038461 thousand units.

Minimum AVC = 52 - 0.038461 + 13×0.038461^2 = $ 52.98

The firm will shut down when the market price is less than equal to $ 52.98.

The supply curve of the perfectly competitive firm is represented by the marginal.cost curve starting from the minimum AVC.

Supply curve would be,

P = 52.98 - 2q + 39q^2