Solutions to Microeconomic Problems

Problem 1: Pareto Efficiency with Cookies

There are two consumers — 1 and 2 — in an endowment economy witha single good (cookies).  Person 1’s utility isu1=c1and person 2’s utility isu2= 2c2wherec1andc2are each person’s cookie consumption.  The total supply of cookies is48.a.   Explain briefly why any allocation of cookies must be Pareto efficient,so long as all cookies are consumed.b.  [6 marks] Find and draw the utilities possibility frontier, assuming that the gov-ernment can make lump-sum transfers.  Find thecookieallocation that will resultif the government is (i) Utilitarian and (ii) Rawlsian, and show the utility distri-bution on your diagram.c.   Assume that person 1 starts with all the cookies, and that 25% of cookiesbreak when they are transferred.  Find and draw the new (second-best) utilitiespossibility frontier.  Find thecookieallocation that will result if the government is(i) Utilitarian and (ii) Rawlsian, and show the utility distribution on your diagram.d.  Assume that each person starts with 24 cookies, and that 25% of cookiesbreak when they are transferred.  Find and draw the new (second-best) utilitiespossibility frontier.  Find thecookieallocation that will result if the government is(i) Utilitarian and (ii) Rawlsian, and show the utility distribution on your diagram.e.   Explain briefly why the second theorem of welfare economics is satisfiedif no cookies break when transferred.
2.A government is considering creating a new national park. If it is created,the demand for trips to the park is estimated to bep= 140−2Yeach year for years0 (this year), 1 and 2, whereYis number of trips people will make to the park.  Otherbenefits are (i) a fall in pollution worth$1000 each year and (ii) intangible benefits of$x.  Assume that the cost of creating the park is$18,000 in year 0,  and entry to thepark will be free for visitors.  Let the social discount rate,r, be 0.1.a  Calculate  the  consumers’  surplus  the  park  would  create  in  each  year.Using your answer, and the three-year time span, what value ofxis necessary forthe park to pass a cost-benefit test?b.   Assume that the park needs someone to look after it,  which means apark ‘ranger’ will be hired at$2,000 each year.  Recalculate the intangible benefitsneeded for the park project to pass a cost-benefit test.c.  How would your answers change in parts (a) and (b) ifr= 0.05 instead?Calculate the new values.3. Consider the following cost-benefit problem: A government is consideringbuilding a new bridge between Towns E and F. It costs$2 million to build in year 0,and it will last for two years (years 1 and 2) once it is built.  The benefits of the bridgeare (a) in each of years 1 and 2, there will be$200,000 in benefits from cleaner air (sincetrips from E to F will be shorter) and (b) in years 1 and 2, the price of a trip for travelerswill fall from$5 to$3.  Market demand each year isx= 800,000−20,000p, wherexisnumber of trips andpis price.  The interest rate isr= 0.1.a.   Show that the bridge project should go ahead.  What is the benefit tocost ratio?b.  Suppose that the estimated value of a human life is$500,000.  If we buildthe bridge to be wider when we build it in year 1, this will save 1 life in each ofyears 1 and 2.  What is the maximum cost of making the bridge wider,C, thatwill justify doing this?c.  Given that we make the bridge wider at costCabove, will the benefitto cost ratio change?  Explain your answer.
4.[20 marks] Thelma and Louise are neighbours.  During the winter,  any snowplowthat  clears  the  front  of  Thelma’s  house  will  also  clear  the  front  of  Louise’s  house.Thelma’s marginal benefit from snowplowing is 12−Z, whereZis the number of hoursspent  plowing  the  street.   Louise’s  marginal  benefit  is  8−2Z.   The  marginal  cost  ofsnowplowing is$16 per hour (and assume no fixed costs).a.  [6 marks] Draw each person’sM Bcurve and the sum of theirM Bcurves.  Findthe efficient level ofZ.b. Calculate each person’stotalbenefit from the efficientZ.  Suppose theefficientZcould be provided by each sharing the cost of snbowplowing equally.Would both people agree to this policy?b. If snowplowing is financed by distortionary taxation, then the MCF oftax revenue,R, isM CF= 1 + 0.0002441R2.  Assuming that all revenue is spent onprovidingZ(andM R= 0) find the new efficient level ofZ.  Draw this situationon a diagram, including the newM C∗M CFcurve.5] There are 3 consumers with demands for fireworks,F. Person 1’s demandisP= 60−F, person 2’s demand isP= 100−Fand person 3’s isP= 140−F.  Themarginal cost ofFisM C=F.  What is the economically efficient level ofF?  Explainyour answer using a well-labeled diagram that includes the aggregateM Bcur