Question

Monopoly:
Assume:
P = 16 – 2Q
TC = 3Q^2 + 4Q + 3
Find: P,Q, TR,TC, profit, and elasticity at profit max. Please show all your work

Answer 1

P = 16 - 2Q

TR = P * Q = 16Q - 2Q²

MR = 16 - 4Q

TC = 3Q² + 4Q + 3

MC = 6Q + 4

The profit maximization condition is:

MR = MC

16 - 4Q = 6Q + 4

10Q =16 - 4 = 12

Q = 12 / 10 = 1.2

P = 16 - 2Q = 16 - 2(1.2) = $13.6

TR = P * Q = 13.6 * 1.2 = $16.32

TC = 3Q² + 4Q + 3 = 3(1.2)² + 4(1.2) + 3

= 4.32 + 4.8 + 3 = $12.12

Profit = TR - TC = 16.32 - 12.12 = $4.2

The inverse demand function is:

Q = 8 - 0.5P

Elasticity = (∆Q / ∆P) * (P / Q) [ ∆Q / ∆P is the price coefficient in the demand function]

= -0.5 * (13.6 / 1.2)

= -5.67

The absolute value of elasticity is 5.67