Consider a monopolist in a market with linear inverse demand p(q) = 4 minus q/2.

Question

Consider a monopolist in a market with linear inverse demand p(q) = 4 minus q/2. The monopolist's cost function is c(q) = 2q. Write down the monopolist's profit function. Compute the profit-maximizing quantity and the corresponding price. Consider Exercise 2. Assume that a 2% tax is levied on the monopolist's profits. Does this have any effect on its choices of output level and output price? Consider now a quantity tax of $1 per output unit sold. Compute the optimal output level and the corresponding output price. How does this tax affect the monopolist's choices of output and price, and its profits? We say that the monopolist passes on the tax to the consumer if it raises the price by more than the tax ($1 here). Is this the case with the quantity tax in (2)?

Explanation / Answer

Profit tax reduces profit from p to p-.02p but it does not effect on the output quantity, price and demand.

because the maximisation of before tax and aftertax method is same

like

a profit miximisation level is MR=MC and its drown from same equation as in the exercise 2

.p(q)=4-0.5q
0.5q=4-p
q=8-2p
c=2q

MC=MR
MC=2

TR=pq
=(4-0.5q)q
=4q-0.5q2
MR=4-q
MC=MR
2=4-q
q=2

p=4-1=3

and the mew profit is just 2% less than the yearlier profit

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