Overview This assignment has multiple parts: 1) you will extend your Excel model to include the impacts from climate change and 2) analyze the costs and benefits of a number of specific policy proposals. Then, 3) you will adjust the model such that the impacts from climate change are related in a more interesting way to the level of economic development, and finally 4) investigate the effect of different income elasticities on damages. Section 1: Impacts from Climate Change Part I: Modeling Overview You will add a component for the impacts of climate change to your model this week. You will also modify the growth model to pick up the estimate of climate impacts. With that component, you will have a model that provides estimates of everything needed to do a cost-benefit analysis of climate change policy. Impact model The impact model is extremely simple. We assume that the harm done from rising temperatures in a given year as a share of gross output is: Dt = VT2 (1) So Dt is damage as a share of gross output in year t, y is a parameter that you should set to 0.003 and Tt is global average temperature in °C above pre-industrial levels at time t. You should pick up the temperature from the climate dynamics component you have built previously. Growth model To close the loop, you should modify the equation for net output in the growth model to not only subtract the costs of abatement from gross output, but also the damages from climate change that you just added to the model. You must figure out the precise new equation for net output yourself. Have a look at how abatement costs were subtracted from gross output and try to do the same for the impacts of climate change. 1 The last addition to our model is two variables: consumption (in trillion dollar) and per capita consumption (in dollar per person). The equation for consumption is straightforward: whatever is left of gross output once the costs of abatement, the damages from climate change and investment in the capital stock are subtracted can be consumed and thus equals consumption. To compute per capita consumption you divide consumption by population. Be careful with the units, though! Part II: Policy Analysis Question 1: Find out in which year the net change in per capita consumption from four different policies turns beneficial. All the policies you should analyze are characterized by a constant reduction in emissions, i.e. the same percentage reduction in each year. The four policies you should analyze are a 10%, 20%, 30% and 40% emission reduction. For each policy, compute how the per capita consumption in each year changes compared to the no-policy scenario. For each policy, find the first year in which per capita consumption is higher with policy compared to the no-policy case. Question 2: Create a graph that plots the change in per capita consumption for all four policies, one that plots abatement costs as percent of output and one that plots damages as percent of output. The horizontal axis should be years in all three figures. The vertical axes should be percentage change in per capita consumption for the first figure, and percent of output for the second and third figure. Each policy should be one line in each figure. Section 2: Income Elasticity Part I: Modeling Now, we will add a slight twist to the damage function. Above, we had assumed that a given temperature increase would always cause the same loss as a share of income, independently of the level of income. So whether we assumed a high income or a low income, a 3º warming would always cause the same loss as a percent of income. You will replace that damage function with one that has an additional parameter, namely an income elasticity of impacts. We can specify a more nuanced relationship between economic impacts and income levels with this new parameter. You should change the damage function equation from last week to the following format (the new term is marked in the equation): € Dt = VT2 new (1) 2 Yo should be set to gross income in the base year of the model, i.e. GDP in the year 2010. Yt is gross income in year t, and e is called an income elasticity, which you should set to 0 for the base case. e is the parameter you will vary in the second part of the exercise. Part II: Policy Analysis Question 1:How do damages in dollar terms change compared to the model that does not include income elasticity if you set the income elasticity to -0.25, 0.0 and 0.25? You should create a new copy of your model for each of these three cases (one Excel sheet for each). You should then add as another sheet the model from above. Finally, on a new sheet, create a graph that plots damages in dollars for each of these four cases over time (section one's model, and the three models with different income elasticities you created in section two). Write one short sentence (in Excel) for each of the three income elasticity cases that describes how damages differ from the damages in the section one of this assignment. 3 C104 X V fx =$B$96*C100^2 *(C101/$B$101) A Formula Bar D E F G H 1 K L 1 2 Year 2011 2012 2013 5.854 2014 5.808 2015 5.760 2016 2017 2018 5.606 5.551 5. 3 Variable Name 2010 5.980 5.940 5.898 5.711 5.660 18.620 18.602 18.584 18.568 18.553 18.538 18.524 18.511 18.499 18.487 18 67 Energy Intensity (EJ/trillion $ of output) 68 69 Carbon Intensity (MtC/EJ) Gross Output ($ trillion) 190.025 195.260 200.465 205.638 210.783 215.901 220.997 226.073 231.133 236.180 241. 70 Kaya Emissions (Mt C) 71 Total Emissions (Mt C) Emissions with policy (Mt C) Abatement cost (% of output) Abatement cost ($ tillion) 2019 2 6530.537 6619.145 6706.909 7842.909 7842.909 7640.537 7742.145 7742.145 6793.616 6879.054 8041.054 8041.054 7942.616 7942.616 6963.008 8138.008 8138.008 0% 8233.267 8233.267 0% 7045.267 7125.618 7203.853 7279.765 7353. 8593. 8326.618 8417.853 8506.765 8326.618 8417.853 8506.765 8593. 72 73 74 75 7640.53674 0% 0% 0% 0% 0% 0 0 0 0 0 0 0 0% 0 0% 0 0% 0 76 Solow Growth Model 77 Parameters Capital Share Depreciation Rate Savings Rate 30% 10% 22% 78 79 80 81 82 Forcings Total Factor Productivity 0.0275 0.0279 0.0283 83 84 0.0287 0.0291 0.0294 0.0298 0.0301 0.0304 0.0307 0.0 85 Variables 86 Investment (trillion S) 41.7252 139.6500 167.4102 190.0246 195.2605 200.4645 195.2605 205.6380 210.7827 -30.9870 27.8503 200.4645 6.8381 -12.7280 -1.776446 -4.272608 42.9573 44.1022 193.6264 45.2404 218.3660 205.6380 46.3722 241.7698 210.7827 47.4983 263.9650 215.9013 285.0668 220.9969 226.0728 231.1327 236.1804 87 Capital Stock (trillion $) Gross Output (trillion $) 89 Net Output (trillion) 90 Consumption ($ tril) 91 Consumption per capita ($ per person) 48.6193 49.7360 50.8492 51.9597 53.0 305.1794 324.3975 342.8069 360.41 241.2 189.6598 50.0098 215.9013 220.9969 -64.0699 48.0637 -6.548475 -8.627344 226.0728 -79.1066 -10.52993 231.1327 -93.2648 -12.27471 236.1804 241.2 -119.21 -13.87813 -15.35 92 -106.6265 7.24779639 3.985116 0.966258 93 Impact component 94 95 Parameters coefficient on temp squared (psi) Income Elasticity 0.003 0 96 97 98 99 Forcings 100 global average temperature in ℃ above pre-industrial levels 101 Gross Output ($ Tril) 0.8 190.0246 0.819071 195.2605 0.83813 200.4645 0.857177 205.6380 0.876215 210.7827 0.895244 215.9013 0.914266 220.9969 0.933281 226.0728 0.95229 231.1327 0.971294 236.1804 241.2 0.00192 0.36484731 0.002068 0.403816 0.002223 0.445666 0.002385 0.490523 0.002303 0.990 102 103 Variables 104 Damages (% of Output) 105 Damages ($ Trill) 106 107 108 109 0.002404 85487 0.51911 0.002508 0.554182 0.002613 0.590737 0.002721 0.628813 0.00283 0.668446 0.002 0.709