Question

2. The (total) cost function is given by C = 50 + 60Q – 18Q2 + 2Q3
a. Write down the fixed cost function FC(Q).
b. Write down the variable cost function VC(Q).
c. Write down the marginal cost function MC(Q).
d. Write down the average fixed cost function AFC(Q).
e. Write down the average variable cost function AVC(Q).
f. Write down the average total cost function AC(Q).
g. Find the break-even point (Q and AC).
h. Find the shut-down point (Q and AVC).

Answer 1

Answer to Question #90682, Economics / Microeconomics

$$C = 50 + 60Q - 18Q^2 + 2Q^3$$

a) $FC(Q) = 50$

b) $VC(Q) = 60Q - 18Q^2 + 2Q^3$

c) $MC(Q) = 60 - 36Q + 6Q^2$

d) $AFC(Q) = \frac{50}{Q}$

e) $AVC(Q) = 60 - 18Q + 2Q^2$

f) $AC(Q) = \frac{50}{Q} + 60 - 18Q + 2Q^2$

g) At Breakeven MC=AC,

$$60 - 36Q + 6Q^2 = \frac{50}{Q} + 60 - 18Q + 2Q^2$$ $$18Q = \frac{50}{Q} - 4Q$$ $$22Q^2 = 50$$ $$Q = 5\sqrt{\frac{1}{11}}$$

h) At Shut down MC=AVC, $60 - 36Q + 6Q^2 = 60 - 18Q + 2Q^2$

$$-18Q = -4Q^2$$ $$Q = 4.5$$

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