Question

3. The market illustrated below has inverse demand p(Q) = 130 - 3Q and industry-wide marginal cost MCQ) = 10 + 2Q. If production is competitive, this is the market (inverse) supply curve. If production is consolidated under a monopolist, this is the monopolist's MC curve. a. Suppose there is a monopolist. Explain how marginal revenue for a monopolist is different than for a firm under perfect competition. Then derive the profit-maximizing market outcome (including the monopoly price and quantity Qm and Pm). b. Now suppose the market operates under perfect competition, but with a per-unit tax t = $30. Determine the market equilibrium and illustrate on a diagram. As a follow-up, determine the relationship Q(T) that gives the equilibrium market quantity as a function of the tax rate. C. If you invert the relationship from part (b), you have t(Q), the tax the government would need to set if it wishes the market quantity to be Q. Then total tax revenue is T(Q) = T(Q).Q. (This may be useful for the intuition that's requested below.] Determine whether total welfare in this market is higher (i) under a monopoly, or (ii) under perfect competition with an "empire-building" government that maximizes total tax revenue T(Q). For (ii), make the usual assumption that tax revenue is spent on something useful i.e., not wasted). Illustrate both cases on a single diagram. Do your best to explain why your comparison turns out as it does. [Applying intuition about the components of marginal revenue MR(Q) to the "marginal tax revenue" T'(0) might be helpful.] p(Q) = 130 - 32 MCQ) = 10 + 2Q (S(p) = {p – 5)

Answer 1

A)In perfect competition ,firm is not price setter instead ,they are price taker ,so at price determined by industry,they sell ,so by every unit they get same Revenue so marginal cost is straight line.

Monopolist is price setter so instead selling at a given price ,it can sell at various price ,which changes the revenue from additional units. Because Monopolist facing downward sloping demand,so selling additional units it needs to decrease price which lead to decrease in revenue by selling additional unit,so marginal revenue is deceasing.

Monopoly equilibrium at MR=MC

P=130-3Q

MR=130-6Q

MC=10+2Q

MR=MC

130-6Q=10+2Q

120=8Q

Qm=15

Pm=130-3*15=130-45=85

B)MC after 30 tax,

MC=10+2Q+30=40+2Q

Perfect competition equilibrium at P=MC

130-3Q=40+2Q

90=5Q

Q=90/5=18

P=130-3*18=130-54=76

Equilibrium at P=MC

MC with tax,

MC=10+2Q+t

P=MC

130-3Q=10+2Q+t

120-t=5Q

Q(t)=24-0.2t

C)120-t=5Q

t(Q)=120-5Q

R(Q)=t(q)*q=120q-5*q^2

∆R(q)/∆q=120-10Q

Putting derivative to zero obtain tax Revenue Maximizing quantity.

120-10Q=0

Q=120/10=12

P=130-3*12=130-36=94

The monopoly will higher total surplus than tax revenue Maximizing equilibrium as price is lower and quantity is higher in Monopoly equilibrium compare to Revenue Maximizing equilibrium.