Consider the market for paper. Let market demand be given by inverse demand function P d (Q) = 60 − Q, where Q is tons of paper demanded at price P (Q). There are 20 paper mills supplying the market. Each acting as a price taker. Eac paper mill has a cost function C(Q) = 10Q2 , where Q is one ton of paper produced. When a mill produces paper it also causes pollution down river. A mill does not face any liability due to this pollution but it has been estimated that the external cost associated with its production is EC(Q) = 10Q2 . 1. What is a mill’s optimal level of paper production at given price P, Q∗ (P)? 2. Determine market supply of paper and find the market equilibrium. What is the market equilibrium price and quantity? 3. What is the socially efficient level of paper production, Qef f icient, that is the level of market production and consumption that maximizes total surplus? 4. Calculate the deadweight loss in the market equilibrium. Comment on the reason for the existence of the deadweight loss. 5. Suppose the 20 firms are merged into a single firm that acts as a monopolist. The monopolist’s cost function is C m(Q) = 20C(Q/20). Determine the monopoly outcome for the paper market. Determine total surplus. Compare the outcome with the competitive market equilibrium and that of the socially efficient output level. Compare and contrast with the usual intution that a monopoly will reduce total surplus relative the perfectly competitive equilibrium outcome.

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Explanation:

Demand for paper is given below:

P(Q)=60-Q,

Number of paper mills=20

The cost curve for firm is given below:

C(Q)=10Q2

The external cost in terms of pollution down river by production of paper is given below:

EC(Q)=10Q2

a. The optimal level of paper production by market can be calcuated by equating MC=P

20Q=P

Q=P/20

b. The optimal level of paper production by market can be calcuated by equating MC=P.

MC=20Q

60-(20Q)=20Q

Q=60/40

Q=1.5

Total quanity by 20 firms will be 1.5*20=30

c. The socially efficient level of paper output is calcuated below:

MC+EC'=20Q+20Q

60-(20Q)=40Q

Q=60/60

Q=1

Total quanity by 20 firms will be 1*20=20

The price will be P=60-20=40

d, The deadweight loss occurs as market price increases and quantity decreases due to the external cost . The deadweight loss is calcuated below:

DWL=(1/2)*change in price* change in quantity

=(1/2)*10*10=50

e. 20 firms merged into one firm to make monopoly firm. The cost function for the monopoly is given below:

Cm(Q)=20*10(Q/20)2

The marginal cost for the monopoly firm will be

MCm=Q

The marginal revenue for the firm is 60-2Q

For optimal output MR is equated to MC

60-2Q=Q

Q=20

P=40.

The monopoly outcome is below the perfect competition outcome and price is higher in comparison to perfect competition. The monopoly outcome is same as socially efficient outcome.

The total surplus for this outcome is sum of consumer surplus and producer surplus and subtraction of external cost

TS=CS+PS-EC

=(1/2)*20*20+(1/2)*40*20-10(20)2

=600-4000=-3400

Due to the external effects the total surplus to the society is negative. In perfect competition this effect is not considered and output produced is high therefore, the external cost will be higher with higher output leading to higher negative social surplus. Generally the monopoly outcome reduces the total social surplus but in case of externality, the monopoly total surplus is higher than the perfect competition.

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explanation:

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