Question #90684

2. The (total) cost function is given by C = 50 + 60Q – 18Q2 + 2Q3

i. Draw a graph to illustrate AC, AVC, and MC functions for quantities Q on the interval between 1 and 10. Make sure you show (put the numbers there) where exactly the MC curve intercepts AVC and AC curves.

j. If the price is P = 60, calculate the profit-maximizing firm’s profit.

i. Draw a graph to illustrate AC, AVC, and MC functions for quantities Q on the interval between 1 and 10. Make sure you show (put the numbers there) where exactly the MC curve intercepts AVC and AC curves.

j. If the price is P = 60, calculate the profit-maximizing firm’s profit.

Expert's answer

C = 50 + 60Q – 18Q2 + 2Q3

i. AC = C/Q, AVC = (C - FC)/Q, MC = ∆C/∆Q.

j. If the price is P = 60, then:

P = MC,

MC = C' = 60 - 36Q + 6Q^2 = 60,

6Q(Q - 6) = 0,

Q1 = 0 or Q2 = 6 units.

TP = TR - C = 60*6 - (50 + 60*6 - 18*36 + 2*216) = 166 is the profit-maximizing firm’s profit.

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