Part 1 Dora lives alone in an island Her production function is the usual cobb douglas we assumed in class The island is endowed with one constant unit of capital and the only thing Dora can adjust is her labor i e amount of hours she works Irrespective of the amount of capital and labor that she uses the amount of bananas that Dora gets depends on the weather Per each hour she works then on rainy days she gets half of the bananas she gets on sunny days For now assume that there is no way for Dora to save bananas across periods 1 Assuming as we did in class that the substitution e ect on the supply of hours is stronger than the income e ects then when comparing sunny days vs rainy days a Dora will produce more bananas and work more b Dora will produce more bananas without working more since the sun is like a positive TFP shock c Dora will produce the same amount of bananas without working more since the sun is like a positive TFP shock d Uncertain i The answer is a Since her labor supply is upward sloping and sun acts as a TFP shifter then the labor demand will move up and to the right 2 Assume now that a new unit of capital falls for free into the island Then how would your answer to the previous question change given that Dora has one extra unit of capital a My answer will be the same b My answer will change c Uncertain without further information i The answer is a Nothing changes 3 Assume now that Dora gets sick and cannot work and the unit of capital cannot be consumed Then she will have a Zero bananas b One banana c Uncertain i The answer is a Without production there will be no bananas 4 Assume now that Dora can save bananas across periods but she cannot borrow Specifically assume that Dora s utility from consumption is the one we discussed in class for example her utility is ln C ln C f Assume that 1 r 1 For simplicity assume that Dora works a fixed number of hours from now on Also after every sunny day there is a rainy day i e the wether alternates in a fixed predictable way then 1 a In sunny days Dora will consume less then what she produces b In sunny days Dora will consume exactly what she produces c In sunny days Dora will consume more then what she produces d Uncertain i The answer is a Since given the assumptions of the question she will produce more in sunny days then in rainy days then given the consumption smoothing desire she will save bananas in the sunny days 5 Continue to that the same setup of question 4 applies Then a In rainy days Dora will consume less then what she produces b In rainy days Dora will consume exactly what she produces c In rainy days Dora will consume more then what she produces d Uncertain i The answer is c Same logic as 4 6 Now assume that Diego arrives to the island He goes on a trip with Dora and they discover that there is another part to the island that has the opposite weather of the part where Dora lived so when it s rainy where Dora is then this new part of the island is sunny and vice versa Also bananas can be shipped costlessly across the di erent parts of the island Finally they discover that they don t need any capital to produce bananas and that each can collect bananas as a function of the amount of hours they work For simplicity assume they have no disutility from working but they cannot work more than 24 hours a day Then if Diego has the same utility of Dora i e as in question 4 we know that a Diego will go and live in the new part of the island b Diego will be indi erent where to be c Diego will live where Dora lives d Uncertain i If you assumed that there is no possibility of savings that the answer is a as this is the only way they can smooth consumption ii If you assumed that there is possibility of savings than the answer is d since they don t need to insure each other 7 Continue to that the same setup of question 6 applies but now shipping bananas across the di erent parts of the island is costly Then how would your answer to the previous question change a My answer will be the same b My answer will change for sure 2 c Uncertain without further information i If you assumed that there is no possibility of savings that the answer is c as we don t know how the smoothing channel compares to the cost of shipping bananas ii If you assumed that there is possibility of savings than the answer is a since the situation is still uncertain 8 Now assume that when Diego and Dora live in the same part of the island they also derive a utility from being together and talk about their lives Then how would your answer to question 6 change a My answer will be the same b My answer will change for sure c Uncertain without further information i If you assumed that there is no possibility of savings than the answer is c since the smoothing argument has a tradeo form the utility that they derive of being together ii If you assumed that there is possibility of savings than the answer is b since now for sure they want to be on the same part 9 Now assume that Diego and Dora cannot stand each other anymore so when they are in the same part of the island they derive a negative utility from being together Then how would your answer to question 6 change a My answer will be the same b My answer will change for sure c Uncertain without further information i If you assumed that there is no possibility of savings than the answer is a since both channels work in the same direction ii If you assumed that there is possibility of savings than the answer is b since now for sure they want to be on di erent parts 10 Now assume that the weather has changed such that it s always sunny Also assume that Dora and Diego don t derive a utility or disutility if they live in the same part of the island they don t communicate as they just look at their iPhones The rest of the assumptions are as in question 6 Then a They are indi erent where each one of them lives b They want to live in separate parts of the island c They want to live in the same part of the island i If you assumed that there is no possibility of savings than the answer is a since it s all the same ii If you assumed …