Question

7. Suppose the same firm's cost function is C=40* +16 a. Find variable cost, fixed cost, average cost, average variable cost, and average fixed cost. 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

a) VC is 4q^2. FC is 16. AVC is VC/q = 4q and AFC is FC/q = 16/q. AC is TC/q = 4q + 16/q

b) The graph plot is shown below for quantity 0 to 6 units

Quantity	Total cost	Marginal cost	Fixed cost	Variable cost	Average variable cost	Average total cost
0	16		16	0
1	20	4	16	4	4	20
2	32	12	16	16	8	16
3	52	20	16	36	12	17
4	80	28	16	64	16	20
5	116	36	16	100	20	23
6	160	44	16	144	24	27

Cost of production 23 23 24 20 2020 Dollars 0 1 2 5 6 3 4 Quantity Marginal cost ---Average variable cost ---Average total cost

c) AC is 4q + 16/q. AC is minimum when AC'(q) = 0.

4 - 16/q^2 = 0

q = 4^0.5 = 2 units.

Hence at q = 2 units, AC is minimized

d) Since AVC is 4q, for q = 0 AVC is 0 and for q = 1 AVC is 4. If price falls below $4, firm produces nothing. Hence for prices = $4 and above, firm produces positive output

e) Profit is negative when P < ATC. We see that ATC is minimum at 4*2 + 16/2 = $16. Hence for price level less than $16, there are economic losses

f) Here, for price level more than $16, there are economic profits