P = 1200 - 4Q (demand curve for the monopoly) C = 8600 + 32Q + Q 2 (total cost f
ID: 1190316 • Letter: P
Question
P = 1200 - 4Q (demand curve for the monopoly)
C = 8600 + 32Q + Q2 (total cost function for the monopoly)
MC = 32 + 2Q (marginal cost function for the monopoly)
**Please round all answers to TWO decimal places**
To maximize profit, the monopolist should produce ___ units of output.
The company's profit -maximizing price is $___
The monopolist's profit is $___
Suppose the government imposes a specific tax of $200 per unit on the monopolist. To maximize profit, the monopolist should now produce ___ units of output. When the tax is imposed, the monopolist's profit-maximizing price becomes $___. As a result of the tax, the monopolist raises its price by _____ (Choose one: more than the tax/the same amount as the tax/less than the tax).
Explanation / Answer
TR for the monopolist =P*Q
P*Q or TR=1200Q-4Q2
MR= dTR/dQ = 1200-8Q
And MC = 32+2Q
Then the equilibrium condition MTR=MC
We have
1200-8Q = 32+2Q
10Q = 1168
Q = 116.8 or 117 units
The price at which monopolist will sell will be
P = 1200-4*116.8
=733
Profit = TR-TC
=12000*116.8-4*116.82 – 8600-32*116.8-116.82
=1321051.2
After tax
The new MC or the supply curve will be
32+2Q-200
Or
MC = 2Q-168
The new equilibrium
MR=MC
1200-8Q = 2Q-168
10Q = 1368
Q = 136.8
The price at which monopolist will sell will be
P = 1200-4*136.8
=652.8
Profit = TR-TC
=12000*136.8-4*136.82-8600-32*136.8-136.82
=1535051
Related Questions
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.