Question

The (total) cost function is given by C = 60 + 80q – 15q² + 2q³, where q is the quantity produced by the firm.

1. Find the break-even point (q and AC).
2. Find the shut-down point (q and AVC).
3. 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.
4. If the price is P = 100, calculate the profit-maximizing firm’s profit.

Please type it down so that I can read it not hand writing except the graph thank you so much

Answer 1

C = 60 + 80q – 15q2 + 2q3

AC = C/q = 60/q + 80 – 15q + 2q2

AVC = TVC/q= 80 – 15q + 2q2

MC =dC/dq= 80- 30q+ 6q2

Breakeven point is at the minimum of AC.

AC = 60/q + 80 – 15q + 2q2

AC =dAC/dq= -60/q^2 – 15 + 4q=0

q=4.49

Shutdown point is at the minimum of AVC.

AVC= d AVC/dq= -15+4q=0

q= 15/4= 3.75

If Price P= 100, ATC=69.4, Q=5.6

Profit=(P-ATC)*Q =(100-69.4)*5.6= $171.36