Part 1 Question 1 Dora lives in an island and her utility function is p U c 24 N where c denotes the number of apples she consumes and N denotes the number of hours she works in order to collect the apples She picks up 2 apples per each working hour Every morning before starting to pick up the apples Dora gets A 0 apples for free from the sky 1 Set up the maximization problem of Dora 2 Derive the first order condition 3 Which of the following statements is correct a If a 50 than Dora doesn t work at all b Dora s working decision does not depend on the size of a c Dora won t work more than 16 hours d Dora won t work more than 20 hours Answer 1 The maximization problem is given by max c p 24 l subject to c y 2l a 2 Substituting the budget constraint into the utility function you can get 2C 1 2 24 l 1 2 and then combining these two equation we can get c 96 4l 3 Use c 96 4l 2l a to get l 16 a 6 and thus the right answer is 3 Question 2 Dora lives in an island and her utility function is 1 2 U ln c ln 1 N 3 3 where N is the amount of hours put into collecting apples which she consumes denoted by c Dora s production function is c 2 N 1 Solve the optimal allocation of hours and consumption 11 points 1 Now assume that the government taxes Dora by 20 such that c 2 0 8 N i e for every hour worker Dora can now only consume 1 6 apples 2 Describe in words the income and substitution effect that the tax have 3 Resolve the optimal allocation of hours and consumption in the presence of the tax rate 4 Draw the budget constraint and preferences that corresponds to the before and after the tax On the X axis have hours worked and on the Y axis have consumption Answer The problem is max 31 ln c 23 ln 1 N s t c 2N We can write it as max 13 ln 2N 1 1 2 1 1 2 3 ln 1 N The FOC with respect to N is then 3 N 3 1 N 1 N 2N N 3 and thus consumption and output equal 32 In the case of a tax we rewrite the problem as max 13 ln c 23 ln 1 N s t c 2 0 8 N We can write it as max 13 ln 2 0 8 N 32 ln 1 N We get again N 13 but this time consumption equals c 2 0 8 13 1 6 3 The tax has an income and substitution effect The income effect is that the worker is poorer which will increase the amount of hours worked The substitution effect is that leisure is cheaper since working is now more expensive which will reduce the amount of hours worked In this example both effects cancel each other As such the indifference curve will intersect at the same working hours but at vertical lower consumption level Question 3 Mrs Robinson can use her labor in a production function of bananas Y N Assume that Mrs Robinson derives utility from her consumption of bananas and her leisure Mrs Robinson used to maximize her utility and work 16 hours a day which allowed her to consume four bananas per day i e she used to have 8 hours of leisure per day One day she was offered to get two bananas for free if she d adopt a different production function Y N 1 4 What can you say about her consumption of bananas and leisure if she accepts the new offer Will she accept the offer Answer Mrs Robinson used to enjoy eight hours of leisure and eat four bananas this was her optimal allocation of effort With the new production she can get the same allocation so she 2 cannot be worse of This implies that this change has no income effect but only a substitution effect since the MPL with the new production function is smaller than with the original one This implies Mrs Robinson is less efficient the price of a working hour is higher now since she gets less output for it Thus the optimal thing to do given the substitution effect is to work less consume more leisure and eat less bananas We know she will take the offer because she can always replicate exactly the same allocation of leisure and food she used to have Question 4 Suppose you used to get paid 10 per hour for the first 6 hours you work and 20 for each hour of overtime Given these you decided to work 8 hours Now your boss decided to change the wage structure and she will start paying you to pay a fixed wage of 12 5 per hour 1 How will this change the amount of hours you work Hint Use the concepts of income and substitution effects a You will work more then before b You will work less then before c You will work the same amount of hours d Unclear without more information Answer Note that you can keep on working the same amount of hours So the change has no income effect It only has a substitution effect that makes your last working hour less beneficial So you will work less The answer is B 2 Are you supportive of the change in the compensation policy a Yes b No c You will be indifferent d Unclear without more information Answer Yes You can always repeat the same working hours as before If you choose note to do so then you must be better off The answer is A Now suppose your boss decided to change the wage structure but not to 12 5 per hours Rather instead of paying you 10 per hour for the first 6 hours and 20 for each hour of overtime she will start paying you to pay a fixed wage of 25 per hour 3 How will this change the amount of hours you work Hint Use the concepts of income and substitution effects a You will work more then before b You will work less then before 3 c You will work the same amount of hours d Unclear without more information Answer Unclear At the same allocation of hours you are making more So the income effect make you less willing to work But the substitution effect makes you more willing to work So the answer is D 4 Are you supportive of the change in the compensation policy a Yes b No c You will be indifferent d Unclear without more information Answer Yes You can always repeat the same working hours as before If you choose note to do so then you must be better off The answer is A 4 Part 2 Question 1 Assume that a firm produces only with labor according to the …