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 |
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
7. Suppose the same firm's cost function is C=40* +16 a. Find variable cost, fixed cost,...
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need help with 5 and 6
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Q: Suppose a firm's total cost function is TC = 16 + 5Q + 4Q2 . What is the output level that minimizes average total cost?
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