Instruction to exam: Total points 40 points. To pass 24 points are required. To pass with distinction 30 points are required.

Transcription

1 Instruction to exam: Total points 40 points. To pass 24 points are required. To pass with distinction 30 points are required. Question 1: 4 points (=1+1+2). 1A. Over the past century, the productivity of farmers has risen substantially because of technological progress. According to the neoclassical theory (e.g., the Solow model) with the 1 standard production function: Yt A Kt Lt, where 0< <1, what should have happened to their real wage?? Has the real wage of barbers during this period stayed constant, increased or decreased or is it impossible to tell? 1B. Over the same period, the productivity of barbers has remained constant. Suppose workers can move freely between farmers and being barbers. What does this mobility imply for the development of the real wages of barbers during this period? In other words, has the real wage of barbers during this period stayed constant, increased or decreased or is it impossible to tell? 1C. What do your previous answers imply for the price of haircuts relative to the price of food? Question 2: 4 points (=2+2) 2. Briefly explain the Environmental Kuznets Curve (EKC)? In other words, explain how the level of pollution is related to real per capita income according to this theory. Explain also why the level of pollution and real per capita income are related, according to the theory behind the EKC. Question 3: 2 points 3. According to the OLG-model if the growth rate of the size of the young population (n) increases the steady state level of production per worker (y) increases/decreases/is unaffected/we cannot tell. Select one of the 4 underlined alternatives.

2 Question 4: 7 points 4. Assume an economy, which is described by the life-cycle model for a closed economy. To simplify assume that the growth rate of the technology is zero; that is, A/ A=0, and that the growth rate of the size of the young generation (n) is zero. Suppose that utility and production are described by the usual Cobb-Douglas functions, and that the following parameter values hold: Parameter Value A N 100 A. Calculate the steady-state capital-labor ratio (k), the level of output (Y) and level of output per worker (y). Note: N is the size of a generation. B. Suppose that the government decides to purchase 1 unit of output for government consumption (GC) each period. To pay for it, the government collects taxes equal to 1 from the old each period. What will the steady-state capital-labor ratio (k) and output per worker (y) be? Compare these answers to those calculated in a. Explain any differences or similarities. C. Now suppose that the government changes its policy and pays for its spending by collecting taxes equal to 1 from the young each period. How does the capital-labor ratio (k) and output per worker (y) compare to the answers in B). Give a qualitative answer: Higher/lower/the same? Explain any differences or similarities. D. If the old (due to altruism) compensate the young by a transfer of 1, what is the effect on capital-labor (k) and output per worker (y). Compare these answers to the steady state values calculated in part B. Explain any differences or similarities. E. Now disregard the possibility of voluntary transfers from old to young. Suppose that the government continues to collect taxes equal to 1 from the young each period. Now, however, the government uses the tax revenue to purchase 0.5 units of capital and 0.5 unit of consumption instead of 1 unit of consumption. What will be the impact of the policy change on the capital-labor ratio (k) and output per worker (y) level compared to the values in C. Higher, lower, the same..? Explain why!

3 Question 5: 10 points (4+2+4) 5. Voting Equilibrium of the provision of a public good Assume that the utility function of individual i is: U i 1 G Ci 1 where G is a public good and Ci the consumption of individual i of a private good. The number of individuals in the economy are n. The budget constraint of the individual i is: C ( 1 t) i Y i where t is the proportional tax rate and Yi is the income of the individual i which is assumed to be exogenously given. The budget constraint of the government is: G t n Y Where Y is average income (across individuals) in the economy. A) Derive an expression for the optimal choice of G of the individual i. This is a maximization problem: You can find the optimal G by including the budget constraints in the Utility-function and then find du/dg, which is set equal to 0. From the equation du/dg=0 you find the optimal G. B. In the voting equilibrium the median voter decides the outcome. What happens if the median voter becomes richer relative to the mean income (Y ) for the amount the public good? Explain your results! C. What is the optimal Level of G from a utilitarian point of view? Hint (=ledtråd): Maximize the sum of the individuals utilities (Maximera summan av individernas nyttor.)

4 Question 6: 13 points (= ) 6. Suppose that the world consists of only two countries. Savum and Spendum. The following values apply to the cobb-douglas production functions and utility functions of each country. Use the values in the table to answer the questions below. Parameter Savum Spendum A N a. calculate the steady state values for capital per worker (k=k/l), production per worker (y=y/l), the real wage per worker (w), and the real return on capital (r) for the two countries: Savum and Spendum under autarky; that is, when the countries are closed with respect to each other (=autarky). b. calculate steady state values of utilities (U) for Savum and Spendum (which depend upon the steady state value of consumption when young ( c ), and on the steady state value of consumption when old ( c o )). c. Calculate the steady state values of y, k, w, and r for each country under free trade; that is, when capital mobility is allowed for. Help: The world-wide value of equals N N savum spendum savum spendum N N N N savum spendum savum spendum d. From what country will capital move? In other words, which of the countries will end up owning assets (=capital) in the other country? E. calculate steady state values of Utility for the two countries under free trade. E1. Compare the steady-state utility of a young person in Spendum under autarky with the steady-state utility of a young person in Spendum under free trade. Is it higher or lower or unchanged? E2. Compare the steady-state utility of a young person in Savum under autarky with the steady-state utility of a young person in SAVUM under free trade. Is it higher or lower or unchanged? f. During the transition to the new steady state which group (current young and current old) gain or loose in the two countries? If you cannot answer with numbers, explain in words which country has higher or lower values on the variables asked for, for partial credit. y

5 Answers:1. A. Their real wage should have increased. B. The real wages measured in the same units will be the same in the two sectors. Everyone benefits from technological progress in the farm sector. C. The price of food products fall relative to the price of haircuts when there is technological progress in the agricultural sector. Answer2: An EKC exists if the level of pollution first is increasing with per capita income and later decreases when per capita income increases. Pollution increases at first because production pollutes. Later pollution may decrease because as people become richer they want to improve the environment. In other words, the environment is a normal good. Answer3: Decreases Answers4: A. 1/(1 ) 2 k (1 ) A 2 4, y=4*2=8. Y=800. B. Same. C. Lower because the young generation saves. D. Same as in b. E. They will be Higher in e. compared to c. Answer5: A. 1 G Ui Ci = 1 1 G G (1 ) Yi ny 1 FOC: Yi (1 ) G 0 ny 1 Y i ny 1 G 1 ny G Yi B. Less. C. Maximera summan av individernas nytta: 1 G G (1 ) Yi ny 1 = G ng (1 ) ny ny ng 0

6 G 1 n Answers6: A+B SAVUM SPENDUM k=((1-a)*(1-b)a)^(1/1-b) 1 (0.4*0.5*4) )^2=0.64 y=ak^ w=(1-b)*y=0.5*y r=a*b*k^ Y=y*N 4* Cy=a*w Co=(1+r)(1-a)w 3 3.5*0.4*1.6=2.24 U=cy^a*co^(1-a) 3^0.5=1.73 U=0.96^0.6*2.24^0.4=0.98*1.38= Answers6: C.-e. WORLD K=((1-a)*(1-b)A)^(1/1-b) (0.45*0.5*4) )^2=0.81 Y=Ak^ W=(1-b)*y=0.5*y 1.8 r=a*b*k^ Y=y*N 720 Cy=a*w: spendum 0.5*1.8=0.9 Co=(1+r)(1-a)w: spendum 3.222*0.5*1.8=2.9 U=cy^a*co^(1-a): spend. U=0.9^0.5*2.9^0.5=0.95*1.70=1.615 Cy=a*w: spendum 0.6*1.8=1.08 Co=(1+r)(1-a)w: spendum 3.222*0.4*1.8=2.32 U=cy^a*co^(1-a): spend. U=1.08^0.6*2.32^0.4=1.05*1.40=1.47 d. Savum will end up owning capita in spendum e. Steady state utility goes down in savum and up in spendum. f.during the transition: in savum: workers loose and old people gain. In spendum: workers gain and old people loose.

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