Economics 321: Public Economics Prof. Marika Cabral TA: Katherine Keisler Fall 2016 UT Austin Problem Set 1 Solutions 1. One rationale for imposing taxes on alcohol consumption is that people who drink alcohol impose negative spillovers on the rest of society—for example through loud and unruly behavior or intoxicated driving. If this rationale is correct, in the absence of governmental taxation, will people tend to consume too much, too little, or the right amount of alcohol? People demand goods primarily on the basis of their own enjoyment of that good. They tend to underweight the impact of their consumption on the well-being of others. In the absence of taxes on alcohol, people will tend to consume too much of it. That is, they will tend to consume more than they would if they took the harm they cause others into account. 2. Proper hygiene, such as regular hand-washing, can greatly limit the spread of many diseases. How might this suggest a role for public interventions? What kinds of public interventions might be possible? Suggest three distinct types of possible interventions. Individuals tend to ignore the external costs they impose on others by failing to wash their hands frequently enough (or by failing to employ other sorts of hygienic practices). This suggests that they tend to wash their hands less than optimally and that there may there- fore be a role for public interventions. One possible intervention would be a requirement that individuals wash their hands after using restrooms. (Such regulations are imposed for employees at businesses, for example.) A second possible intervention is public provision of hand-washing facilities. This would reduce the cost of hand-washing, thereby encouraging individuals to engage in that activity more frequently. A third possibility would be an advertising campaign to encourage hand-washing. 3. There are typically two distinct rationales for government intervention. Which of these apply to the government provision of education? Explain your answer. The two distinct rationales for government intervention are market failure and redistribution. Market failure is the problem that the market economy failed to deliver the most efficient outcome. Redistribution is shifting of resources between social groups. The market failure rationale applies to the government provision of education. Individuals tend to ignore the external benefit benefits of education (e.g. more education is associated with lower crime rates and higher tax revenues). If education is priced by the market, the market price of education would make people have less education than optimal level because the social value exceeds the private value. Public provision of education corrects the market failure and helps to bring theeducation to optimal level. In practice, the provision of public education involves redistribution as well. While all children have access to K-12 education, this education is funded by tax dollars that vary according to wealth. Education is funded primarily through local property tax revenue where the tax shares are determined by property values (housing wealth). 4. Draw the demand curve Q = 200 – 10P. Calculate the price elasticity of demand at prices of $5, $10, and $15 to show how it changes as you move along this linear demand curve. One way to sketch a linear demand function is to find the x (Q) and y (P) intercepts. Q = 0 when P = $20. When P = 0, Q = 200. Solving for P = $5, Q = 200 – 10(5) = 200 – 50 = 150. Similarly, solving for P = $10, Q = 200 – 10(10) = 100. And solving for P = $15, Q = 200 – 150 = 50. Price elasticity is the percent change in the quantity purchased divided by the percent change in price. To calculate these percentage changes, divide the change in each variable by its original value. Moving in $5 increments: As P increases from $5 to $10, Q falls from 150 to 100. Therefore, P increases by 100% (5/5) as Q falls by 33% (50/150). Elasticity = –0.33/1.00 = –0.33. As P increases from $10 to $15, Q falls from 100 to 50. P increases by 50% (5/10) as Q falls by 50% (50/100). Elasticity = –0.5/0.5 = –1.0. As P increases from $15 to $20, Q falls from 50 to 0. P increases by 33% (5/15) and Q increases by 100% (50/50). Elasticity is –1.0/0.33 = –3.03. Even though the magnitude of the change remains the same (for every $5 increase in price, the quantity purchased falls by 50), in terms of percentage change elasticity of demand increases in magnitude as price increases. 5. Consider an income guarantee program with an income guarantee of $6,000 and a benefit reduction rate of 50%. A person can work up to 2,000 hours per year at $8 per hour. a. Draw the person’s budget constraint with the income guarantee. A person will no longer be eligible for benefits when he or she works 1,500 hours and earns $12,000 (guarantee of $6,000/50%).b. Suppose that the income guarantee rises to $9,000 but with a 75% reduction rate. Draw the new budget constraint. Benefits will end under these conditions when earned income is $9,000/.75 =$12,000, just as shown in a. The difference is that the all-leisure income is higher, but the slope of the line segment from 500 hours of leisure to 2,000 hours of leisure is flatter. c. Which of these two income guarantee programs is more likely to discourage work? Explain. A higher income guarantee with a higher reduction rate is more likely to discourage work for two reasons. First, not working at all yields a higher income. Second, a person who works less than 1,500 hours will be allowed to keep much less of his or her earned income when the effective tax rate is 75%. With a 75% benefit reduction rate, the effective hourly wage is only $2 per hour (25% of $8). 6. Give an example of a social welfare function that represents each of the following preferences: (a) The policymaker cares about each individual's utility equally. SWF = U1 + U2 + … + UN Ui is utility of individual i(b) The policymaker cares only about the worst off person in society. SWF = min (U1, U2, . . ., UN) Ui is utility of individual i (c) The policymaker cares only about efficiency. SWF = Y1 + Y2 + … + YN Yi is income of individual i 7. Consider a free market with demand equal to Q = 1,200 – 10P and supply equal to Q =20P. a. What is the value of consumer surplus? What is the value of producer surplus? The first step is to find the equilibrium price and quantity by setting quantity