Answer the problem set without limitation of page and word.

1. We analyzed carbon taxes as a way to account for externalities arising from burning fossil fuels in cars. Another policy that has been implemented in the United States has been to subsidize electric vehicles. (a) Start by drawing a graph with the following, using price on the y-axis and quantity on the x-axis i. A demand (marginal private benefit) curve ii. A supply (marginal private cost) curve iii. Market equilibrium (b) Assume that consumers are choosing between electric cars and a higher-emitting form of transportation (e.g., gasoline-powered cars). In this case, choosing an electric car produces a positive externality from the amount of greenhouse gas emissions averted. Assume that this is a fixed amount per unit. i. On your graph, draw the marginal external benefit curve (or line), and the marginal social benefit curve. ii. Identify the deadweight loss from the market equilibrium in part (a) (c) The government wants to provide a per-unit subsidy on electric cars. i. Describe in words the economic rationale for the subsidy. ii. What will the optimal subsidy be? (d) On a new graph, display the following: i. Marginal private and social benefit curves ii. Marginal private cost curve iii. Equilibrium under the subsidy iv. Total amount of the subsidy (e) In this setup, we can classify two types of consumers: marginal consumers, whose behavior is changed by the incentive, and inframarginal consumers, who would have engaged in the incentivized behavior anyways. Label the two types of consumers on your graph. f) Recall from basic microeconomics that the elasticity of demand is the sensitivity of quantity demanded to price. How do the amounts of marginal and inframarginal con- sumers (and hence the overall response to a subsidy) depend on the elasticity of de- mand? 2. Temperatures and Test Scores (a) In Figure 3 Panel H, Carleton and Hsiang (2016) present one study that estimates the relationship between temperature and student test scores. There are now a number of these studies. One is Park, et al (2020) "Heat and Learning," available at https:// pubs-aeaweb-org.proxy-remote.galib.uga.edu/doi/pdfplus/10.1257/pol. 20180612 You don't need to read the whole paper for this problem, but it would be helpful to read the introduction. The dataset parketal_fig1b.xlsx provides the data used in creating Figure 1b. These are average standardized test scores, by county, for 3rd-8th graders in 2009-2013, as well as annual average temperatures in the county. Using Excel (or whatever program you like,) recreate the scatter plot in figure 1b. Note that the paper uses a "bin scatter" where temperatures are organized by bin, and each data point presents the average test score within a bin. This reduces the number of points in the scatter. You can try to make a bin scatter if you like, but a basic scatter using all 3000+ observations is fine.

1. In class we analyzed carbon taxes as a way to account for externalities arising from burning fossil fuels in cars. Another policy that has been implemented in the United States has been to subsidize electric vehicles. (a) Start by drawing a graph with the following, using price on the y-axis and quantity on the x-axis i. A demand (marginal private benefit) curve ii. A supply (marginal private cost) curve iii. Market equilibrium (b) Assume that consumers are choosing between electric cars and a higher-emitting form of transportation (e.g., gasoline-powered cars). In this case, choosing an electric car produces a positive externality from the amount of greenhouse gas emissions averted. Assume that this is a fixed amount per unit. i. On your graph, draw the marginal external benefit curve (or line), and the marginal social benefit curve. ii. Identify the deadweight loss from the market equilibrium in part (a) (c) The government wants to provide a per-unit subsidy on electric cars. i. Describe in words the economic rationale for the subsidy. ii. What will the optimal subsidy be? (d) On a new graph, display the following: i. Marginal private and social benefit curves ii. Marginal private cost curve iii. Equilibrium under the subsidy iv. Total amount of the subsidy (e) In this setup, we can classify two types of consumers: marginal consumers, whose behavior is changed by the incentive, and inframarginal consumers, who would have engaged in the incentivized behavior anyways. Label the two types of consumers on your graph. 1(f) Recall from basic microeconomics that the elasticity of demand is the sensitivity of quantity demanded to price. How do the amounts of marginal and inframarginal con- sumers (and hence the overall response to a subsidy) depend on the elasticity of de- mand? 2. Temperatures and Test Scores (a) In Figure 3 Panel H, Carleton and Hsiang (2016) present one study that estimates the relationship between temperature and student test scores. There are now a number of these studies. One is Park, et al (2020) "Heat and Learning," available at https:// pubs-aeaweb-org.proxy-remote.galib.uga.edu/doi/pdfplus/10.1257/pol. 20180612 You don't need to read the whole paper for this problem, but it would be helpful to read the introduction. The dataset parketal_fig1b.xlsx provides the data used in creating Figure 1b. These are average standardized test scores, by county, for 3rd-8th graders in 2009-2013, as well as annual average temperatures in the county. Using Excel (or whatever program you like,) recreate the scatter plot in figure 1b. Note that the paper uses a "bin scatter" where temperatures are organized by bin, and each data point presents the average test score within a bin. This reduces the number of points in the scatter. You can try to make a bin scatter if you like, but a basic scatter using all 3000+ observations is fine. (b) The figure includes coefficients from a regression of math scores on average tempera- ture. This uses the following model: math_meani = a + b tAvg_Fi + i In this equation, b is the incremental average math score change associated with a 1- degree change in average temperature. Run this regression. You should get the same coefficient that is presented in the figure. Interpret the magnitude of the coefficient. Is it statistically significant? (c) What does the graph tell you about the relationship between temperatures and test scores? Provide one reason why this relationship cannot be interpreted as causal. (d) Park, et al. use student-wise data from PSAT scores. They then restrict their data to students to take the test twice. Their strategy, formally called "student fixed effects," is conceptually similar to one that controls for a student's test score in the prior year. In 2other words, this holds prior test score fixed when looking at the relationship between temperature and test scores in a given year. Yet another way to think about this is that the relationship between temperature and test scores is examined only among students with similar prior-year test scores. How does this improve the causal interpretation of the effects of temperature relative to the analysis in part (a)? (e) What is the headline finding of the paper? Is it consistent with the correlational analysis form part (a)? 3. (From Harris and Roach, Environmental and Natural Resource Economics) Suppose that the annual consumption of an average American household is 1,000 gallons of gasoline and 200 Mcf (thousand cubic feet) of natural gas. Using the figures given in the below table on the effects of a carbon tax, calculate how much an average American household would pay per year with an added tax of $100 per ton of carbon dioxide if there was no initial change in quantity demanded. (Assume that the before-tax market prices remain unchanged.) Then, assuming a short-term demand elasticity of -0.1 and a long-term elasticity of -0.5, calculate the reductions in household quantity demanded for oil and gas in the short and long term. If there are 100 million households in the United States, what would be the revenue to the U.S. Treasury of such a carbon tax, in the short and long term? How might the government use such revenues? What would the impact be on the average family? Discuss the difference between the short-term and long-term impacts.

DATA:

fips	urban	totenrl	state	year	ela_mean	math_mean	tAvg_F
1001	0	769	2	2011	0.25	0.36	64.00
1003	0	2175	2	2011	0.20	0.22	66.79
1005	0	143	2	2011	-0.51	-0.55	64.43
1007	0	279	2	2011	-0.16	-0.26	63.07
1009	0	393	2	2011	0.14	0.00	61.06
1011	0	118	2	2011	-0.52	-0.63	63.69
1013	0	257	2	2011	-0.29	-0.10	64.74
1015	1	293	2	2011	0.02	-0.06	61.08
1017	0	187	2	2011	-0.39	-0.52	62.25
1019	0	325	2	2011	-0.13	-0.09	60.52
1021	0	615	2	2011	-0.10	-0.09	63.01
1023	0	143	2	2011	-0.31	-0.22	64.51
1025	0	186	2	2011	-0.18	-0.28	65.10
1027	0	173	2	2011	-0.23	-0.21	60.78
1029	0	201	2	2011	0.08	0.12	60.18
1031	0	240	2	2011	0.00	0.05	65.40
1033	0	162	2	2011	0.04	0.03	60.66
1035	0	126	2	2011	-0.28	0.08	64.91
1037	0	98	2	2011	-0.25	-0.31	62.33
1039	0	155	2	2011	0.08	0.14	65.12
1041	0	177	2	2011	-0.16	-0.08	64.29
1043	0	498	2	2011	0.47	0.50	60.73
1045	0	172	2	2011	-0.12	-0.11	65.73
1047	0	300	2	2011	-0.44	-0.33	64.31
1049	0	465	2	2011	-0.17	-0.17	58.90
1051	0	494	2	2011	-0.05	-0.15	63.39
1053	0	229	2	2011	0.05	0.09	65.38
1055	0	423	2	2011	-0.07	-0.16	61.03
1057	0	191	2	2011	0.03	0.03	61.37
1059	0	220	2	2011	0.04	0.15	60.56
1061	0	158	2	2011	-0.09	0.00	65.78
1063	0	106	2	2011	-0.47	-0.53	63.74
1065	0	218	2	2011	-0.27	-0.09	64.08
1067	0	220	2	2011	-0.27	-0.29	65.65
1069	1	614	2	2011	0.04	0.12	66.30
1071	0	335	2	2011	0.09	0.05	59.22
1073	0	660	2	2011	0.10	0.10	62.50
1075	0	189	2	2011	-0.15	-0.15	61.36
1077	1	499	2	2011	0.11	0.13	60.32
1079	0	391	2	2011	0.01	-0.06	61.10
1081	1	532	2	2011	0.09	0.09	63.20
1083	0	468	2	2011	0.07	-0.07	60.30
1085	0	143	2	2011	-0.64	-0.54	64.46
1087	0	197	2	2011	-0.43	-0.55	63.68
1089	0	1289	2	2011	0.34	0.26	60.02
1091	0	112	2	2011	-0.33	-0.31	64.36
1093	0	196	2	2011	0.27	0.34	60.63
1095	0	252	2	2011	0.21	0.29	60.71
1097	1	2406	2	2011	0.13	0.20	66.72
1099	0	307	2	2011	-0.29	-0.26	64.98
1101	1	2554	2	2011	-0.32	-0.34	64.50
1103	0	511	2	2011	0.15	0.13	60.68
1105	0	145	2	2011	-0.39	-0.30	63.69
1107	0	229	2	2011	-0.24	-0.26	62.87
1109	0	175	2	2011	-0.07	0.04	64.50
1111	0	151	2	2011	-0.25	-0.31	61.14
1113	0	387	2	2011	-0.24	-0.27	63.82
1115	0	485	2	2011	0.07	-0.05	61.10
1117	0	2209	2	2011	0.20	0.16	62.77
1119	0	154	2	2011	-0.68	-0.64	63.85
1121	0	328	2	2011	-0.16	-0.11	61.84
1123	0	242	2	2011	-0.12	-0.07	62.18
1125	1	1078	2	2011	-0.15	-0.18	63.02
1127	0	428	2	2011	0.13	0.12	61.61
1129	0	263	2	2011	-0.20	-0.28	65.21
1131	0	150	2	2011	-0.50	-0.50	64.34
1133	0	171	2	2011	0.03	-0.06	60.70
4001	0	131	4	2011	-0.42	-0.44	50.75
4003	0	149	4	2011	-0.11	-0.18	61.37
4005	0	247	4	2011	-0.31	-0.35	52.78
4007	0	118	4	2011	-0.42	-0.51	58.89
4009	0	112	4	2011	-0.05	-0.13	59.88
4011	0	63	4	2011	-0.08	-0.07	55.41
4012	0	85	4	2011	-0.33	-0.37	71.61
4013	1	1172	4	2011	-0.09	-0.07	70.99
4015	0	311	4	2011	-0.07	-0.10	61.89
4017	0	133	4	2011	-0.25	-0.24	52.84
4019	0	855	4	2011	0.01	-0.01	68.42
4021	0	275	4	2011	-0.23	-0.26	68.89
4023	0	261	4	2011	0.00	0.00	61.04
4025	0	180	4	2011	-0.02	-0.10	59.01
4027	1	534	4	2011	-0.29	-0.23	72.95
5001	0	124	3	2011	-0.14	-0.16	62.83
5003	0	150	3	2011	-0.13	-0.10	63.50
5005	0	130

(b) The figure includes coefficients from a regression of math scores on average tempera- ture. This uses the following model: math_meani = a + b tAvg_Fi + i In this equation, b is the incremental average math score change associated with a 1- degree change in average temperature. Run this regression. You should get the same coefficient that is presented in the figure. Interpret the magnitude of the coefficient. Is it statistically significant? (c) What does the graph tell you about the relationship between temperatures and test scores? Provide one reason why this relationship cannot be interpreted as causal. (d) Park, et al. use student-wise data from PSAT scores. They then restrict their data to students to take the test twice. Their strategy, formally called "student fixed effects," is conceptually similar to one that controls for a student's test score in the prior year. In other words, this holds prior test score fixed when looking at the relationship between temperature and test scores in a given year. Yet another way to think about this is that the relationship between temperature and test scores is examined only among students with similar prior-year test scores. How does this improve the causal interpretation of the effects of temperature relative to the analysis in part (a)? (e) What is the headline finding of the paper? Is it consistent with the correlational analysis form part (a)? 3. (From Harris and Roach, Environmental and Natural Resource Economics) Suppose that the annual consumption of an average American household is 1,000 gallons of gasoline and 200 Mcf (thousand cubic feet) of natural gas. Using the figures given in the below table on the effects of a carbon tax, calculate how much an average American household would pay per year with an added tax of $100 per ton of carbon dioxide if there was no initial change in quantity demanded. (Assume that the before-tax market prices remain unchanged.) Then, assuming a short-term demand elasticity of -0.1 and a long-term elasticity of -0.5, calculate the reductions in household quantity demanded for oil and gas in the short and long term. If there are 100 million households in the United States, what would be the revenue to the U.S. Treasury of such a carbon tax, in the short and long term? How might the government use such revenues? What would the impact be on the average family? Discuss the difference between the short-term and long-term impacts.

Impact of Carbon Tax on Retail Price of Gasoline kg CO, per gallon 8.89 Tonnes CO, per gallon 0.00889 $/gal., $50/tonne tax $0.45 $/gal., $100/tonne tax $0.89 Retail price (2021) per gallon $2.20 % increase, $50/tonne tax 20.5% % 1ncrease, S100/tonne tax 41% Impact of Carbon Tax on Retail Price of Coal kg CO, per short ton 2100 Tonnes CO, per short ton 2 S/short ton, $50/tonne tax $105 S/short ton, $100/tonne tax $210 Retail price (2021) per short ton $40 % increase, $50/tonne tax 220% % increase, $100/tonne tax 440% Impact of Carbon Tax on Retail Price of Natural Gas kg CO, per 1,000 cu. ft. 53.12 Tonnes CO, per 1.000 cu. ft. 0.05312 $/1,000 cu. ft., $50/tonne tax $2.66 $/1.000 cu. ft.. S100/tonne tax $5.31 Retail price (2020) $12 % increase from $50/tonne tax 22.2% % increase from $100/tonne tax 44.4% Source: Carbon emissions calculated from carbon coefficients and thermal conversion factors available from the U.S. Department of Energy. All price data from the U.S. Energy Information Administration. Nore: tonne = metfric ton, equal to 1.1 U.S. short tons