Part 1Dora lives alone in an island. Her production function is the usual cobb-douglaswe assumed in class. The island is endowed with one constant unit of capital andthe 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 u ses the amount ofbananas that Dora gets depends on the weather. Per each hour she works thenon rainy days she gets half of the bananas she gets on sunny days. For nowassume that there is no way for Dora to “save bananas” across periods.1. Assuming as we did in class th at the substitution effect on the supplyof hours is stronger than the income effects, then when comp aring sunnydays vs. rainy days:(a) Dora will “produce” more bananas and work more.(b) Dora will “produce” more bananas without working more since thesun is like a positive TFP shock.(c) Dora will “produce” the same amount of bananas without workingmore since the sun is like a positive TFP shock.(d) Uncertain.i. The answer is (a): Since her labor supply is upward sloping andsun acts as a TFP shifter then the labor demand will move upand 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 thatDora has one extra unit of capital?(a) My answer will be the same(b) My answer will change(c) Uncertain without further informationi. The answer is (a): Nothing changes.3. Assume now that Dora gets sick and cannot work and the unit of capitalcannot be consumed. Then she will have(a) Zero bananas(b) One banana(c) Uncertaini. The an s wer 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 isthe one we discussed in class (for example her utility is ln(C)+ln(Cf)).Assume that  ⇥ (1 + r)=1. For simplicity assume that Dora works afixed number of hours from now on. Also, after every sunny day there isarainyday(i.e. thewetheralternatesinafixed,predictableway)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 questionshe will produce more in sunny days then in rainy days thengiven the consumption smoothing desire she will save bananas inthe 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 sh e 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 Doraand they discover that there is another part to the island that has theopposite weather of the part where Dora lived (so when it’s rainy whereDora is then this new part of the island is sunny and vice versa). Alsobananas can be shipped costlessly across the different parts of the island.Finally, they discover that they don’t need any capital to produc e bananasand that each can collect bananas as a function of the amount of hoursthey work. For simplicity assume they have no disutility from workingbut they cannot work more than 24 hours a day. Then, if Diego has thesame 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 indifferent where to be(c) Diego will live where Dora lives(d) Uncertaini. If you assumed that there is no possibility of savings that the an-swer is (a) as this is the only way they can smooth consumption.ii. If you assumed that there is possibility of savings than the answeris (d) since they don’t need to “insure” each other.7. Continue to that the same setup of question 6 applies but now shippingbananas across the different parts of the island is costly. Then, how wouldyour answer to the previous question change?(a) My answer will be the same(b) My answer will change for sure2(c) Uncertain without further informationi. If you assumed that there is no possibility of savings that theanswer is (c) as we don’t know how the smoothing channel com-pares to the cost of shipping bananas.ii. If you assumed that there is possibility of savings than the answeris (a) since the situation is still uncertain8. Now assume that when Diego and Dora live in the same part of the islandthey also derive a utility from being together and talk abou t 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 informationi. If you assumed that there is no possibility of savings than theanswer is (c) since the smoothing argument has a tradeoff formthe utility that they derive of being together.ii. If you assumed that there is possibility of savings than the answeris (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 sowhen they are in the same part of the island they derive a negative utilityfrom 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 informationi. If you assumed that there is no possibility of savings than theanswer is (a) since both channels work in the same direction.ii. If you assumed that there is possibility of savings than the answeris (b) since now for sure they want to be on different 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 ifthey live in the same part of the island (they don’t communicate as theyjust look at their iPhones). The rest of the assumptions are as in question6. Then:(a) They are indifferent 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 islandi. If you assumed that there is no possibility of savings than theanswer is (a) since it’s all the same.ii. If you assumed that there is possibility of savings than the answeris (a) since it’s all the same.311. Continue to that the same setup of question 10 ap plies but now shippingbananas across the different parts of the