Conference 3Intermediate Microeconomics - Fall 2018September 10, 2018Problem 1: Efficient Allocation.I own a plot of land in southern France, on which I vacation. My next-door neighbor wantsmy land as well, to expand his own house. The value of the land to me is$150,000. (That is,I would be indifferent between keeping the house, and losing the house but having$150,000.)The value of the land to my neighbor is$275,000.Which of the following are Kaldor-Hicks improvements?1. My neighbor buys my land for$200,0002. My neighbor buys my land for$275,0003. My neighbor pressures the town council to force me to sell him the land for$125,0004. My neighbor, while drunk, buys my land for$350,000All of these are Kaldor-Hicks improvements: my land ends up in the hands of my neighbor whovalues it more than me. The distributive effects of the different solutions differ however, and,while (a) and (b) are Pareto improvements over the initial situation, (c) and (d) are not.Problem 2: Efficient Production.Upon graduation, you realize you have three options: you can take a job as a computer pro-grammer, take a job as a coal miner, or remain unemployed and play video games all day.As a computer programmer, you would create value of$2,000 per week for your employer, andreceive disutility of$1,000 per week relative to playing video games. (To put it another way,at a wage of$1,000 a week, you would be exactly indifferent between taking the programmingjob and staying home.)As a coal miner, you would create value of$3,000 per week, and receive disutility of$1,800 aweek (mining coal is less fun than an office job, which is still less fun than playing video games).1. What is the efficient use of your time?The efficient use of your time is to pick the activity that creates the highest social value. Inthis case, you add$2,000 (employer)-$1,000 (you) =$1,000 more if you choose computerprogramming relative to staying home, and$3,000-$1,800=$1,200 more if you chose mining.So mining is the efficient choice2. Assume that both the programming and coal mining industries are perfectly competitivewhen it comes to hiring, so either firm would offer you a wage equal to the value they getfrom you. Which job would you end up taking?You get a wage of$2,000 in programming and$3,000 in mining, so your incentives arealigned with society and you pick mining.1Now suppose that mining coal also creates an externality. If you work as a coal miner, morecoal gets dug up and eventually burned, leading to more pollution. Suppose that the totalexternality associated with you working as a coal miner is$400 per week, and is spread over alarge number of people. (In particular, the coal company does not have to pay for it.)3. What is the efficient use of your time?With the externality, the social value created by mining is now$1,200-$400=$800, soprogramming is more efficient.4. If you are perfectly rational and selfish, which job will you end up taking?The mining company still gives you a wage of$3,000, and you are selfish, so both you andthe firm fail to internalize the externality your mining generates. You still chose mining.Problem 3: Pareto efficiency and externalities.Consider two individuals i = 1, 2 and two goods x and y (coffee and cigarettes). x1and y1(resp. x2and y2) are the quantities of coffee and cigarettes consumed by individual 1 (resp.individual 2).Individual 1 likes coffee and cigarettes: her utility is U1(x1, y1) = log(x1) + log(y1)Individual 2 likes coffee but strongly dislikes when individual 1 smokes next to him: hisutility is U2(x2, y1) = log(x2) − y1Individual 1 and 2 each have a budget of 10.A coffee costs 1 and a cigarette costs 21. Assume coffee and cigarettes are bought only in units (for instance individuals cannot buyhalf a coffee). What are all the possible bundles individual 1 and 2 can get given the goods’price and their budget constraint?The possible bundles are (xi, yi) = {(10, 0), (8, 1), (6, 2), (4, 3), (2, 4), (0, 5)}2. Consider only individual 1. Among the bundles listed above, which bundle(s) give her thehighest utility? (Use a calculator to compute the log if need be).Try all the bundles described above to find individual 1’s highest utility:U1(8, 1) = log(8) + log(1)= log(8 × 1)= log(8)U1(6, 2) = log(12)U1(4, 3) = log(12)U1(2, 4) = log(8)Note that limx→0log(x) = −∞ so that individual 1 will never choose a bundle with 0 coffeesor cigarettes.Since x → log(x) is increasing in x, individual 1’s favorite bundles are (6, 2) and (4, 3)23. What about individual 2? (Remember: each individual can only choose their own con-sumption)Since individual 2 does not smoke (y2does not impact his utility function), he spends allhis budget on coffee and buys 10 cups.4. Individuals chose their favorite bundle(s). Compute their corresponding utility. How wouldtheir utilities change if individual 1 accepted to give up half a cigarette, in exchange fora coffee individual 2 would give her? Is this a Pareto improvement? (If individuals haveseveral favorite bundles, describe each case)Individual 1 is indifferent between bundle (6, 2) and (4, 3). Let’s detail both cases:If individual 1 choses (6, 2), she gets utility U1(6, 2) = log(12) ∼ 2.485. Then individual2 obtains U2(10, 2) = log(10) − 2 = 0.303If individual 1 choses (4, 3), she gets utility U1(4, 3) = log(12) ∼ 2.485. Then individual2 obtains U2(10, 3) = log(10) − 3 = −0.687If individuals 1 and 2 make their exchange, they get either:Bundle (7, 1.5) and (9, 0) for individuals 1 and 2 (respectively). Individual 1 gets utilityU1(7, 1.5) = log(10.5) ∼ 2.351 and individual 2 obtains U2(9, 1.5) = log(10) − 2 ∼0.697.Bundle (5, 2.5) and (9, 0) for individuals 1 and 2 (respectively). Individual 1 gets utilityU1(5, 2.5) = log(12.5) ∼ 2.526 and individual 2 obtains U2(9, 2.5) = log(10) − 2 ∼−0.303.5. What do these utility change say about Pareto efficiencies and externalities?Individual 2 sees his utility improve in both cases, while individual 1 sees her utility im-prove in the second case. Therefore making the exchange in the second case is a Paretoimprovement. The takeaway is that rational optimization is not always Pareto-efficient inthe presence of