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5. In a market, demand is given by P = 100-Q, and the (private) marginal cost of production for the aggregation of all firms (the industry supply curve) is given by MC = 2Q. Pollution by the industry creates external damages given by the (constant) marginal external cost curve MEC = 20.

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Kristelle Balando
Kristelle BalandoLv10
29 Sep 2019

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Related questions

Two hundred paper mills compete in the paper market. The total cost of production (in dollars) for each mill is given by the formula TC=500Q^mill + (Q^mill)^2 where Q^mill indicates the mill's annual production in thousands of tons. The marginal cost of production is MC=500 + 2Q^mill. The external cost of a mill's production (in dollars) is given by the formula EC=40Q^mill + (Q^mill)^2 and the marginal external cost of production is MEC=40+2Q^mill. Finally, annual market demand (in thousands of tons) is given by the formula Qd=150,000 - 100P where P is the price of paper per ton. Using algebra, find the competitive equilibrium price and quantity, as well as the efficient quantity. Calculate the magnitude of the deadweight loss resulting from the externality. Illustrate your solution with graphs.

1)Suppose the market demand function (expressed in dollars) for a normal product is P = 100 - 2Q and the Supply Curve is P= 100 + 2Q, where P is the price of the product and Q is the quantity demanded or supplied. Assume that the Marginal External Cost curve is MEC = 5 + 0.5Q. Here are the specific questions: 

a.In a competitive market

i.What is the equilibrium price and quantity?

ii. How much is the Consumer Surplus?

iii. How much is Producer Surplus (P.S.)?

iv. How is the total external cost (TEC)?

v.What the Total Welfare (sum of C.S. and P.S. minus TEC)?

The market demand for gadgets is given by Qd=100-3p, where Qd is the quantity of gadgets demanded and p is the price of a gadget in dollars. The market supply is given byQs= p, where Qs is the quantity of gadgets supplied. The production of gadgets releases a toxic effluent into the water supply. The marginal external cost can be described by MEC(Q)= 2Q.

a) Compute consumer surplus, producer surplus, and the cost of pollution at the market equilibrium.

b) Compute consumer surplus, producer surplus, and the cost of pollution at the social optimum.

c) Suppose the government is considering imposing a tax of $T per unit on the producers. Find the level of the tax that ensures the socially optimal amount of gadgets will be produced in a competitive equilibrium.

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