2. Suppose that the inverse demand curve for paper is p = 500 – 3Q, the private

Question

2. Suppose that the inverse demand curve for paper is p = 500 – 3Q, the private total cost is Cp = 20Q + Q2 . During the production of paper, pollution is generated and the total external cost from pollution is Ce =3.5 Q2.

2.1 What is the unregulated competitive equilibrium?

2.2 What is the social optimum? What specific tax (per unit of output) results in the social optimum if a perfectly competitive market exists?

2.3 Assume that a monopoly market structure exists. What is the unregulated monopoly equilibrium? What specific tax (per unit of output) results in the social optimum?

Explanation / Answer

2.1 Under perfect competition, the equilibrium occurs when price equals marginal cost.

Marginal cost is 20 + 2Q.

Thus, the equilibrium occurs when,

P = MCp

500 - 3Q =20 + 2Q

500 - 20 = 5Q

Q = 96

unregulated competitive equilibrium occur at Q = 96

2.2 The socially optimal level of wheat occurs when

P = MCp + MCE

MCE = d(Ce)/dQ = 7Q

500 - 3Q = 20 + 2Q + 7Q

Q = 40

Specific tax (per unit of output) results in the social optimum if a perfectly competitive market exists

P = MCP + t

500 - 3Q = 20 + 2Q + t

we know that socially optimal level of output Q = 40, put Q in the equation

500 - 3*40 = 20 + 2*40 + t

280 = t

2.3  Under monopoly, the equilibrium occurs when marginal revenue equals marginal cost.

Marginal revenue is 500 -6Q.

Thus, the equilibrium occurs when, MR = MCp

500 - 6Q = 20 + 2Q

Q = 60

the unregulated monopoly equilibrium occurs at Q = 60.

- specific tax (per unit of output) results in the social optimum

MR = MCp + t

500 - 6Q = 20 + 2Q + t

Q = 40 at social optimal level

500 - 6*40 = 20 + 2*40 + t

260 - 100 = t

t = 160

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