Question

Practice Question 4. The inverse demand curve a monopoly faces is p = 30 – Q. The firm's total cost function is C(Q) = 0.5Q² and thus marginal cost function is MC(Q) = Q. (a) Determine the monopoly quantity, price and profit, and calculate the CS, PS and social welfare under the monopoly. (b) Determine the socially optimal outcome and calculate the CS, PS and social welfare under the social optimum. (c) Calculate the deadweight loss due to the monopolist behaviour of this firm. (d) Assume that the government puts a price ceiling on the monopolist at P = 18. Determine and plot the demand and marginal revenue function of the monopoly under this regulation. How much output will the monopolist produce? What will be the profit of the monopolist? Determine the impact of this price ceiling on the deadweight loss. (e) Assume that the government put a price ceiling on the monopolist in order to maximize the total (i.e. consumer plus producer) surplus. What price ceiling should it choose? How much output will the monopolist produce at this price ceiling? What will the profit of the monopolist be? What is the DWL?

Answer 1

An unregulated monopolist maximizes his profit at the condition MR=MC . He charges a higher price and produces lower quantity than that of perfectly competitive markets . Due to this distortion a deadweight loss takes place in the economy . The govt. , in order to take care of consumers can impose a price ceiling to lower the price charged by monopolist which shrinks his profit and reduces the amount of deadweight loss in the economy.  

14. Inverse demand curve: p=30-9 Total cost function: C (Q) = 0.5 Q² Marginal cost function : MCQ) - Q P Mcc@)=Q Athyes - Prime a) Monopolist maximizes his profit at MR=me TR= p. Q = 30Q- Q2 MRad(TR) = 30-20 d@ MR-Me 5b 30-2Q = Q => 3Q = 30 pe = @= 10 b=30-Q = 30-10=20 porofit = TR - TC = 30 (10)-(10) -0.5 (10) = 300-100- 50 = 150 : of 10 35 MR 9 Q figure (1)

C5 = 1/2x(base x height) = 1/a x[10 x (30-20)]= 1/2* (10x10) = 1/2x100 = 50 PS = A + - (10x10)+ 1/2x (10xio) = 100*50= 150 Social Welfare = 150+50 = 200

" T ULUU MC(C)=G 30% b) Here, socially optimal outcome is when p=me => 30-6=8 => 2Q = 30 15 2 MR 30 G P= 30-6= 30-15=15 figure (2) cs = 1/2x (15x15) = 1/2x225 = 112.5 PS= 112x (15*15) = 1/2x225 = 112.5 social welfare = (112-5+112-5) =225.0 = 225 C) Deadweight loss undeor monopolist (figure 17 = 1/2*[(20-10)x (15-10)] = 1/2 x (10x5) - 1/2X50 =25
d.

Now, if due to price ceiling, the price is fixed at p=18 monopolist's demand function 18= 30 - Q 58 212-Q - Q = 12 MA

Herre, he poroduces 6=12 at P=18 Therefore, TB = P. G = 18*12 =216 TC = 0.50r = 1128144=72 porofit = (216-72)=144 which is less than earlier porofit= 150

Due to Price ceiling, the deadweight loss has Shorinked much more than that of an absence of purice ceiling. In this cale, at P=18, D and MR corre coincide and become horizontal hits the demand curve as soon as it over the demand curve us touched though, the ♡ curre again becomes downward sloping again. Her is a kink in the demand curre. The MR eurve is broken into ..Hence, there 2 ports and MR-Me eis not possible Monopolist has to poroduce Q-12 at P = 18. I his profit is lower. Deadweightloss still exists, but is much lower than unoregulated monopoly

DWL Me D2MB P-18 DEMO R AMRI Nie 10 12 MR