微观经济学作业答案4知识讲解

Managerial EconomicsHOMEWOEK SET#4 Name:Class:Student #:(Due day: Next class)Part 1:1. Price ceiling are inefficient because:a)both producers and consumers lose.b)Producers lose, consumers may gain or lose, but a loss occurs onnet.c)Producers lose, consumer gain, but a loss occurs on net.d)Producers and consumer may gain or lose, but a loss occurs on net.e)None of the above is correct.Choose: b) Consumers gain from a lower price, but lose because they are able to buy less. Produces clearly lose from the regulated price. There is always a welfare loss from price ceilings ( assuming that the price ceiling is binding).Figure 12. Refer to Figure 1. At price 0E and quantity Q*, consumer surplus isthe areaa)0FCQ*.b)AFC.c)EFC.d)AEC.e)none of the above.Choose: c)3.Refer to Figure 1. At price 0E and quantity Q*, producer surplus isthe areaa)0ACQ*.b)0ECQ*.c)0FCQ*.d)EFC.e)none of the above.Choose: e) Producer surplus is the area ECA.4.Refer to Figure 1. At price 0E and quantity Q*, the deadweight lossisa)0ACQ*.b)0ECQ*.c)0FCQ*.d)EFC.e)none of the above.Choose: e) The deadweight loss is 0.5. Refer to Figure 1. At price 0H and quantity Q1, consumer surplus isthe areaa)EDGF.b)0FGQ1.c)HFGB.d)EFC.e)none of the above.Choose: c)6. Refer to Figure 1. At price 0H and quantity Q1, producer surplus isthe areaa)0ABQ1.b)0EDQ1.c)AHB.d)0FGQ1.e)none of the above.Choose: c)7. Refer to Figure 1. At price 0H and quantity Q1, the deadweight lossisa)DGC.b)BDC.c)BGC.d)0FGQ1.e)none of the above.Choose: c)8.If the supply of basketball is perfectly elastic, a tax of $3 perbasketball will increase the consumer price by:a)$3.b)More than $1.50, but less than $3.c)$1.50.d)Less than $1.50.e)$0 (the price to consumers will not change)Choose: a) All of the tax is passed on to consumers with perfectly elastic supply.9. For a monopolist, changes in demand will lead to changes ina)price with no change in output.b)output with no change in price.c)both price and quantity.d)any of the above can be true.Choose: c)10. Monopoly power results from the ability toa)set price equal to marginal cost.b)equate marginal cost to marginal revenue.c)set price above average variable cost.d)set price above marginal cost.Choose: d)11. The percentage "markdown" due to monopsony power is equal toa)(P - MC)/Pb)1/EDc)(MV - P)Pd)P[1 + (1/ED)]Choose: c)12. Lerner＇s index of monopoly power is L=(P-MC)/P.This implies that:a) L=0 for a perfectly competitive firm.b)the larger L is the smaller the degree of monopoly power.c)L always has a value between zero and one.d)the larger L is the higher profits are.e)a) and c)Choose:e) Recall that P=MC for a competitive firm, so L=0 in that case. With In general, 0<L<1.13. A jewelry store does not set fixed prices for its produces. Instead,the manager decides how much to charge each customer for each item.In this case, the store is practicing:a) first-degree price discrimination.b) second-degree price discrimination.c) third-degree price discrimination.d) tying.e) None of the above is correct.Choose:a) Each customer pays the manager＇s estimate of their reservation price.In a competitive market, the following supply and demand equations are given:Supply P = 5 + 0.36Q Demand P = 100 - 0.04Qwhere P represents price per unit in dollars, and Q represents rate ofsales in units per year.a)Determine the equilibrium price and sales rate.b)Determine the deadweight loss that would result if the government wereto impose a price ceiling of 40 dollars per unit.Solution:a.Equate supply and demand to get equilibrium values.5+0.36Q=100-0.04Q0.4Q=95Q=237.5 units per yearThe equilibrium price isP = 5 + 0.36(237.5) = $90.50 per unit.b.With a price ceiling of $40, the deadweight loss is the triangle between supply and demand bounded by Q of 237.5 and the new sales rate at P of 40.Rearrange supply in terms of P.P = 5 + 0.36QAt P = 40,Q' = 97.22 units per year.The base of the triangle (rotated 90 degrees) is the vertical distance between the heights of supply and demand when Q = 97.22Height of demand = P = 100 - 0.04(97.22) = 96.11Height of supply = P = 5 + 0.36(97.22) = 40.00Triangle base is the difference =56.11Height of triangle = Q - Q' = 237.5 – 97.22 = 140.28Deadweight loss = 1/2 b h = (1/2)(56.11)(140.28) = $3935.5650352030 50 100Hawkins has a monopoly on Oatmeal Stout in the local market. The demand is: 1100250.2=-⇔=-D Q P P Q The resulting marginal revenue function is()50.=-MR Q Q Hawkins marginal cost of producing Oatmeal Stout is()15.2=+MC Q Q Calculate Hawkins profit maximizing output. Calculate the social cost of Hawkins monopoly power.Solution:Hawkins will set marginal revenue equal to marginal cost to find optimal output. ()()150530.2=-==+⇒=MR Q Q MC Q Q Q At this output level, Hawkins charges $35 per unit. The choke price is $50 while Hawkins reservation price is $5. Consumer surplus is ()1503530225.2=-=CS Producer surplus is PS = 0.5(20 - 15)(30) + (35 – 20)(30) = 675. Total surplus in the local Oatmeal Stout market is $900 when Hawkins has monopoly power. If Hawkins did not have monopoly power, the price of Oatmeal Stout would equal Hawkins marginal cost. We can find this output level by setting consumer's price as a function of output equal to Hawkins marginal cost.1150545.22=-==+⇒=P Q MC Q Q At this output level, the price of Oatmeal Stout is $27.50. Consumer surplus is ()15027.5045506.25.2'=-=CS Producer surplus is ()127.50545506.25.2'=-=PS Total surplus when Hawkins does not have monopoly power would be $1,012.50. Thus, society loses 112.50 of surplus due to Hawkins’ monopoly power in the local Oatmeal Stout market.The manufacturing of paper products causes damage to a local river when the manufacturing plant produces more than 1,000 units in a period. To discourage the plant from producing more than 1,000 units, the local community is considering placing a tax on the plant. The long-run costcurve for the paper producing firm is: ()2,,1500=+q C q t tq where q is thenumber of units of paper produced and t is the per unit tax on paper production. The relevant marginal cost curve is: (),.750=+q MC q t t If the manufacturing plant can sell all of its output for $2, what is the firm's optimal output if the tax is set at zero? What is the minimum tax rate necessary to ensure that the firm produces no more than 1,000 units? How much are the firm's profits reduced by the presence of a tax?Solution:In the absence of a tax, we know the plant will maximize profits where marginal cost is equal to the price (given average costs exceed the market price). That is, ()(),0021,500.750=+=⇒=q MC q q Thus, without a tax, we know the plant will produce at a level that will cause damage to the river. The firms profits at thislevel are: ()()()21,50021,50001,5001,500.1,500⎧⎫⎪⎪=-+=⎨⎬⎪⎪⎩⎭π To ensure that the plant doesn'tgo beyond 1,000 units of production, the community needs to make sure the firm's marginal cost is equivalent to the market price at 1,000 units or less. That is, ()1000121000,221.75033=+=⇒=-=MC t t t A tax of 23 or greater will ensure the plant will not produce beyond 1,000 units. If we set the tax rate at 23, the firm'sprofits will be: ()()()21,0002221,0001,000666.1,50033⎧⎫⎪⎪=-+=⎨⎬⎪⎪⎩⎭π Implementation of a tax equal to 2/3 will result in profits declining by 55.6%.。