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
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
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