Assume that a monopolist produces a good at marginal cost 1. Assume that demand

Question

Assume that a monopolist produces a good at marginal cost 1. Assume that demand is given by P D (q) = 10 2q.

(i) What is the optimal quantity and price chosen by the monopolist? Assume that a tax of $t is imposed on every unit that is produced by the monopolist.

(ii) What is the optimal quantity and price (as a function of t) chosen by the monopolist?

(iii) How much does the price increase when t increases from 0 to $1? Assume now that a tax of $2 is imposed on the monopolistís proÖts.

(iv) What is the e§ect of this tax on the price and quantity chosen by the monopolist?

Explanation / Answer

Monopolist = a person who has control over the market. Its a situation where there is only 1 seller and many buyers.

MC = 1

P = 10-2q

TR = (Price * Quantity) = P*q = q(10-2q) = 10q - 2q2

Derivating TR with respect to q will give us MR = 10-4q

Equilibrium : 10-4q=1 , 4q = 9 , q = 9/4 Now price will be 10-2*(9/4) = 10-4.5 = $5.5

the second part says that a tax is imposed on every unit . The tax will be on the TC = Q + TQ So now the MC = 1+T

2. The optimal Quantity and price will be :

MR = MC : 10-4q = 1+t , -4q = t-9 , q = (9-t)/4 and price will be 10-2*(9-t)/4 )

3. So Before tax price = 5.5$

After tax = $1 Price will be (10-2*(9-t)/4 ) = 10-2*(9-1 )/4 ) = 10- 2*(2) = $6 SO the prices increases by 0.5$ after tax is imposed.

4. Now a tax of $2 is imposed, so the quantity will be q = (9-t)/4 = 9-2/4 = 7/4

Price will be : 10-2*(9-2 )/4 = 10 - 2*(7/4) = 10-3.5 = 6.5 So the quantity falls and the price increases as the taxes are imposed.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.