Q 9,10 9. Consider a market in which the supply and demand curves are:. q 120-2
ID: 1108020 • Letter: Q
Question
Q 9,109. Consider a market in which the supply and demand curves are:. q 120-2 pb qs = 4 p where q and q are the quantities demanded and supplied, and pD and pS are the prices paid by the buyer and received by the seller, measured in dollars. a. Find the equilibrium in the absence of government intervention. Find consumer and producers surplus. b. Suppose that the government levies a tax of 6 dollars on each unit of the good exchange. Find the changes in consumer surplus, producer surplus, and the surplus collected by the government. Find the welfare costs of the tax. c. Suppose that the government instead places a subsidy of 3 dollars on each unit of the good exchanged. Find the new equilibrium. Find the changes in consumer surplus, producer surplus, and the surplus collected by the government. Find the welfare costs of the subsidy 10. Two firms are ordered by the federal government to reduce pollution. Firm A's marginal costs associated with pollution reduction is MC 20+40. Firm B's marginal costs associated with pollution reduction is MC-10+80. The marginal benefit of pollution reduction is MB-400-40 What is the socially optimal level of each firm's pollution reduction? Compare the social efficiency of three possible outcomes: a. b. i. require all firms to reduce pollution by the same amount. ii. charge a common tax per unit of pollution. iii. require all firms to reduce pollution by the same amount, but allow pollutionpermits to be bought and sold.
Explanation / Answer
a)qd=120-2pd and qs=4ps At equilibrium qd=qs suppose P is the price at that intersection 4P=120-2P this gives P=20 and hence qs=qd=80
Consumer surplus From Demand curve at qd=0 pd=60 hence area under the curve=1/2*(60-20)*80=1600
For Producer surplus from supply curve at qs=0 ps=0 hence area under the curve=1/2*(20-0)*80=800
b) if tax of $6 is levied the Pd=pd+6 in this case demand curve will become qd=120-2(pd+6) for equilibrium
qd=qs this will give P=18and qd=qs=72
consumer surplus will be at qd=0 pd=54 therfor consumer surplus=1/2*(54-18)*72=1296
similarily producer surplus=1/2*(18-0)*72=648
Surplus by government=6*72=432
Total surplus=1296+648+432=2376
Without intervention surplus(from a)=1600+800=2400
Welfare cost of Tax =2400-2376=24
c) In case of subsidy
qd=120-2(pd-3) Equilibrium Price=120-2(P-3)=4P this gives P=21 and Q=84
Consumer surplus=1/2*(63-21)*84=1764
Producer surplus=1/2*(21-0)*84=882
GOvernment surplus=-3*84=-252
Total surplus=1764+882-252=2394
Witghout intervention surplus=2400
Welfare cost =2400-2394=6
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