Question

4. (20 points) Suppose that, in the basic one-period model, there is no government spending and no taxes. Production by the representative firm produces pollution in proportion to the amount of output produced. Given any consumption bundle (a consumption-leisure pair), the consumer is worse of the more pollution there is. a. In a diagram, show the competitive equilibrium and the Pareto optimum. Show that the competitive equilibrium is not Pareto optimal, and explain why. Is more or less output produced in the competitive equilibrium than at the Pareto optimum? Explain. a. Now, suppose that the government imposes a proportional tax t on the output of the firm, and rebates the proceeds of the tax in a lump-sum fashion, as a transfer TR to the representative consumer. Show that the tax can be set in such a way that the competitive equilibrium is Pareto optimal. Explain your results. 5. (20 points) Suppose the government's goal is to reduce the unemployment rate. Some legislators propose that the government should give a subsidy s to any firm that hires a worker. Some other legislators argue that it would be more efective to simply pay consumers to stay home rather than searching for work; that is, anyone who chooses not to participate in the labor force should receive a payment q. Which policy is more efective in achieving the government's goal? Explain using the two-sided search model, with the aid of diagrams. In your answer, do not concern yourself with how the subsidies from the government are financed.]

Answer 1

Production by firm produces pollution in proportion to the amount of output produced. So, the producer is better off when the pollution level is high. But, Pollution provides disutility to the consumer. This means that the interest of the two parties is in the opposite direction.

PAGE NO.: PICENO 2 Oy EPRODUCTION EXTERNALLIY :- . Si unit of output x: writ _pollutiow +4 : consuspion Cs (S.x) : cost of fim is dependent level_d outputpadduced and of polledies 'genisated. on ghanditu consumiblica money | ACs (S.x) xo & ACLS, An co Points XA and xp are parto efficient and any such point where IC of two parties are tanfent to each other are pareto efficient. would In order to maximise its profit firm Il produce the quantity output 'holderen Ps = AG ( 5 2 - MG _AS_ 0 = AC (5 x) = MC competitive Equilibrium in this case would be nchise price ratio is defined and at that lend. 1 palce level demand and supply of each | Resduct is equal But in this case, the price of pollution is not defined i price Jos pollution and ...wowapending to this much higher level La pollution is generated as compared to retinal level of pollution • Quantity of pallation pollution Ichere M of pollition seduces profit maxmasing quantity a n extra 'zero re to Therefore, competiline amis na pauts splinal.

PAGE NO: 3 POENO: 4 H o nesnment the output on SMA imperes a propostrenal tax I COST MC -D curre ? um . The form was facing incassect price for one of its product i.e. pollution . To impose cosser sotial cost- government unsposed Back Now, the profit maximising problem can be Written as A max t = Ps.S - Cs (S.x All- - tx - Xpoutput- de Optimal conditions for him will be (first order condition) Ps = ACIS X) AS... = -AC( Jucare negatine produción externality, there is always oner production of output. SMC: Social marginal coss- MC : marginal cost Xp : output poreduced- ts i socially optimal-output thus, muose output is produced whether, competitive equilibrium than at the pareto - This tax is known as pigouvian tax and it implies that the size of tax must be equal to mangial external cost at efficient level Therefore, paruto efficient level of pollution is achieved. Thus, the competitive equilibrium is paruto eptural after nippoing this tax optimal