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homework_4_neil_solution - E nvironmental economics...

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Environmental economics Homework 4: Due Monday 10 May in class (work alone or in groups of 2-4) Question 1: Beer and taxes There are 24 hours in a day. Neil needs 14 of these hours for beauty sleep. He can split the remaining 10 hours between labor (L) and leisure (l). Neil enjoys leisure, but can use the money he earns as a laborer to pay for beer (b), which Neil also enjoys. Laboring as a TA Neil earns minimum wage of $3 an hour. Beers cost $2 each. a) Write down the amount of labor Neil works in terms of leisure (i.e. L=…) L=10-l b) If Neil gets all of his income from TAing, what is his income (M) as a function of leisure. M=3*L=3*(10-l)=30-3l c) What is the opportunity cost of one unit of leisure? Therefore, what is the price of leisure? Every unit of leisure means one hour less working. Thus leisure costs $3 (the wage) d) Write down the amount of beer (b) Neil can buy in terms of leisure if he uses all of his income for beer (i.e. b=…) b=M/P b =(30-3l)/2=15-(3/2)l The table below shows the utility Neil gets from different amounts of beer and leisure Beer Leisure Total Utility Marginal Utility Marginal utility per dollar Total Utility Marginal Utility Marginal utility per dollar 1 Ignore 16 20
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2 26 15 17 3 40 16 4 53 65 5 12 11 6 10.5 9 7 9.5 93 8 94 99 9 102 3 10 7 2 11 6 0 12 120 101 13 124 91 14 -3 -21 15 121 -30 16 -10 7 e) Fill out the table, given the prices above (since we will redo this question with different prices, we suggest you do the table in Excel) See excel f) What is the bundle that will maximize Neil’s utility and satisfy his budget constraint (hint choose the item that gives the highest marginal utility per dollar, until he runs out of money) Neil should buy 9 beers and have 4 hours of leisure. This means that his income will be $18
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