Economics 321: Public EconomicsProf. Marika CabralTA: Katherine KeislerFall 2016UT AustinProblem Set 2 Solutions1. A government is considering paving a highway with a newly developed “wear-proof” material. Paving the highway would cost $2 billion today, but it wouldsave $300 million in maintenance costs for each of the next 10 years. Use theconcept of present value to determine whether the project is worthundertaking if the government can borrow at an interest rate of 5%. Is itworth it if the interest rate is 0%? 10%? A politician says to you, “I don’t carewhat the interest rate is. The project is clearly a good investment: it more thanpays for itself in only 7 years, and all the rest is money in the bank.” What’swrong with this argument, and why does the interest rate matter?As the following table shows, the project is worth undertaking at 0% and 5%interest, but it is not worth undertaking at 10%. The politician’s argument isincorrect because it fails to take into account the interest the government must payon the money borrowed to finance the project.2. How might large federal deficits affect future economic growth? How wouldyour answer change if foreign confidence in the ability of the United States torepay its debts erodes?When governments run deficits, they compete with private individuals to borrowloanable funds. With increased deficits, the total demand for loanable fundsincreases, driving up the rate of interest. The quantity of private investment in assetsthat improve economic productivity therefore falls. This is the basic theory ofcrowding out. If international investors/savers lose faith in the ability of the United States to repayits debt, the supply curve of loanable funds will become steeper: foreigners willsupply additional loanable funds only if they receive higher interest rates tocompensate them for what they perceive to be a riskier investment. This means thatdeficit spending will have larger effects on interest rates, and it will crowd outprivate investment to an even greater extent.3. Suppose that a firm’s marginal production costs are given by MC = 10 + 3Q.The firm’s production process generates a toxic waste, which imposes anincreasingly large cost on the residents of the town where it operates: themarginal external cost associated with the Qth unit of production is given by6Q. What is the marginal private cost associated with the 10th unitproduced? What is the total marginal cost to society associated withproducing the 10th unit (the marginal social cost of the 10th unit)?The marginal private cost is 10 + 3(10) = 40. The external cost associated withthe 10th unit is 6(10) = 60. So the marginal social cost of producing the 10th unitis 100.4. Answer the following two questions for each of the following examples: (i)smoking by individuals; (ii) toxic waste production by firms; (iii) researchand development by a high-tech firm; and (iv) individual vaccination againstcommunicable illness.a. Is there an externality? If so, describe it, including references towhether it is positive or negative, and whether it is a consumption orproduction externality.i. Smoking by individuals generates negative consumptionexternalities by generating secondhand smoke. ii. Toxic waste production by firms generates negative productionexternalities be-cause the harm (or toxicity) is a by-product of thefirm’s production. iii. Research and development by a high-tech firm generates positiveproduction externalities when the results of that research expandthe knowledge and productivity of all firms. iv. Individual vaccinations generate positive consumption externalitiesby reducing the number of people in the population who have acommunicable illness. When the number of infected people isreduced, the probability of catching the illness is reduced foreveryone.b. If there is an externality, does it seem likely that private markets willarise that allow this externality to be internalized? Why or why not.i. The problem of secondhand smoke is unlikely to be solved byprivate markets. Smoke is widely dispersed, making it difficult toaccount for and negotiate with every affected person. In addition,the value of smoking a single cigarette is likely to be small relativeto the transaction costs of negotiating the solution. ii. The problem of toxic waste might be amenable to a private marketsolution. The generator can be easily identified, and a finite numberof people in a localized town or community are likely to beaffected. If local residents have property rights to restrict toxicwaste production, it should be relatively easy for a firm whichplaces a high value on the ability to produce toxic waste tocompensate them in exchange for the right to pollute. iii. A firm that purchases a patent or license is in some sense using amarket mechanism to partially compensate the researching firm forits contribution to the knowledge base. However, it is hard tocompletely restrict or contain the flow of information. It is unlikelythat a private market for intellectual property could completelyinternalize this externality. iv. Private compensation for the reduced risk of exposure associatedwith vaccinations seems unlikely. It would be virtually impossibleto identify the beneficiaries of in-creased vaccination rates.5. Suppose that demand for a product is Q = 1,200 – 4P and supply is Q = –200 + 2P. Furthermore, suppose that the marginal external damageof this product is $8 per unit. How many more units of this product willthe free market produce than is socially optimal? Calculate thedeadweight loss associated with the externality.To answer this question, first calculate what the free market would do bysetting demand equal to supply:1,200 – 4P = –200 + 2P, or 1,400 = 6P. P ≈ 233.33,so QFree Market = 1,200 – 4(233.33) ≈ 266.67.The socially optimal level occurs when the marginal external cost is includedin the calculation. Suppose the $8 externality were added to the price eachconsumer had to pay. Then demand would be Q = 1,200 – 4(P + 8).Solving for P, 1,200 – 4(P + 8) = –200 + 2P, or P = 228.