Question

2. Suppose the same firm's cost function is Cliq) = 4 = 1 +16.ece +16. Tore=8 = -1 a. Find variable cost, fixed cost, average cost, average variable cost, and average fixed cost. (Hint: Marginal cost is given by MC = 8q.) b. Show the average cost, marginal cost, and average variable cost curves on a graph c. Find the output that minimizes average cost d. At what range of prices will the firm produce a positive output? e. At what range of prices will the firm earn a negative profit? f. At what range of prices will the firm earn a positive profit?

Answer 1

Solution:

Firm's cost function: C(q) = 4q² + 16

a. Variable cost is that part of total cost which depends on quantity (hence, is variable) and on the other hand, fixed cost is the part which is independent of quantity. So,

Total variable cost, TVC = 4q²

Total fixed cost, TFC = 16

Average cost values are total values divided by quantity

Average cost, AC = (4q² + 16)/q = 4q + 16/q

Average variable cost, AVC = 4q²/q = 4q

Average fixed cost, AFC = 16/q

b.

c. Finding point which minimizes average cost:

We can directly see from the above graph that this occurs at point (2, 16), that is at 2 units of output, where average cost is $16 per unit.

In general, minimum of average cost (or any cost function other than marginal cost) occurs where it equals the marginal cost, that is, the marginal cost curve intersects the average cost curve at its minimum. Then, mathematically:

AC = MC

4q + 16/q = 8q

16 = (8q - 4q)*q

4q² = 16

Then, q = (16/4)^1/2 = 2 units

And, at this point MC (= AC) = 8*2 = 16

d. The shutdown point for a firm is the minimum average variable cost. The AVC curve is intersects MC curve at origin (see from the graph). So any point beyond that will be produced by the firm. So, positive output will be produced for all positive price range.

e. The supply curve for firm is the marginal cost curve itself after crossing the minimum average variable cost point. Thus, the MC curve beyond origin marks the supply curve for this firm.

Profit = total revenue - total cost

Profit = price*quantity - average total cost*quantity

So, profit will be negative when total revenue < total cost

This is same as saying price < average total cost

We saw from part (c) and graph as well that price lies below average total cost till 2 units of quantity. So, price range giving out negative profit is (0, 16).

f. Corresponding to the above part and following that reasoning, profit is positive when price is higher than average total cost. So, required price range is starting from 16 to all further higher price range: (16, infinity)