Economics 302 4 Week Summer Session 2006 Homework 2 Due Monday June 5 2006 5 31 06 Homework will be graded for content as well as neatness Sloppy or illegible work will not receive full credit This homework requires the use of Excel which is a spreadsheet program 1 2 points Suppose that the production function for an economy is given by Y F K N A AK1 2N1 2 where Y is output K is capital N is labor and A is the level of technology a Suppose that the value of A is equal to 1 Fill in the table below based on this information and the given production function Labor Capital Output MPN Using a MPN using the change in Derivative output change in labor 0 25 4 25 9 25 16 25 25 25 36 25 Labor 0 4 9 16 25 36 b Suppose that the value of A increases to 10 Fill in the table below based on this information and the given production function Capital Output MPN Using a MPN using the change in Derivative output change in labor 25 25 25 25 25 25 c Draw a picture of the two production function relationships you computed in parts a and b placing output on the vertical axis and labor on the horizontal axis Verbally explain the effects of a change in technology on the aggregate production function d In the tables you computed the MPN using a derivative and the MPN using a formula for discrete data the change in output the change in labor Provide an explanation for why these two measures would not be equivalent and use a graphical explanation to explore what would make these two measures numerically closer to one another 1 2 5 points Suppose that the production function for an economy is given by Y F K N A K1 2N1 2A where Y is output K is capital N is labor and A is the level of technology a If K equals 100 N equals 400 and technology equals 1 what is output Y and output per worker Y N b What is the value of the marginal product of capital using the information in a Show your work c What does it mean to say that the marginal product of capital is proportional to output per unit of capital d What is the value of the marginal product of labor using the information in a Show your work e What does it mean to say that the marginal product of labor is proportional to output per worker f What is the total wage bill in the economy described in a g What is the total return to capital in the economy described in a h What is the ratio of labor income to capital income in the economy described in a i If capital and labor both increase by 100 while technology is constant what will the new levels of output and output per worker be in this economy Round your answer to the nearest whole number Hint you really don t need to round at all with this one just be alert to what s happening in this question j If capital increases by 50 from its initial level labor increases by 25 from its initial level and technology is constant what will the new levels of output and output per worker be in this economy Round your answer to the nearest whole number 3 1 points You are given the following information for this set of questions Year Price of Pizzas 2000 10 2001 12 2002 15 Quantity of Pizzas 100 110 110 Price of Coke 1 1 2 Quantity of Coke 30 40 35 Price of Salad 2 2 3 Quantity of Salad 40 40 30 Furthermore you are told that the market basket for purposes of computing the CPU is defined as 100 Pizzas 30 cokes and 40 salads a Calculate the CPI and for this economy and put your answer in the table below Year 2000 2001 2002 CPI 100 b From the information you found in part a calculate the rate of inflation for the following periods 2 Period 2000 2001 2001 2002 Inflation Rate 4 2 points Suppose you are told that government spending equals 100 and net taxes equal 50 You are also told that the level of government spending and the net taxes is independent of the level of the real interest rate Furthermore you are told that when the real interest rate is 20 private saving SP equals 200 and when the real interest rate falls to 10 private saving SP is equal to 100 You also know that the relationship between private saving and the real interest rate is linear a Draw three graphs that are horizontally aligned and then use these graphs to depict government saving SG in the first graph private saving SP in the second graph and national saving NS is the third graph b Write an equation for NS using the information provided c Suppose I 300 750r Graph this investment function on a graph along with the NS you found in part a d What is the equilibrium level of investment and real interest rate in this economy 5 2 5 points This question is from Chapter 6 in your text you should be able to do this question from the information that is provided to you in the question But you may find the text helpful We can define the Labor Force L as the sum of employed workers E plus unemployed workers U For this problem assume the labor force is a constant Suppose initially there are 80 000 employed workers and 20 000 unemployed workers a What is the labor force equal to in this economy and the initial unemployment rate Now suppose that the rate of job separation each month s changes and is now equal to 1 of the previous month s employment Furthermore suppose that the rate of job finding each month f changes and is now equal to 3 of the previous month s unemployment Use this information to answer the following questions Note your labor force is constant and should always sum to the answer you provide din part a If necessary round to the nearest whole number 3 b Calculate the following values for the end of the first month after these changes to s and f Unemployment Employment Total Labor Force Initial Levels at beginning of month Change Due to XXX Job Separation Sub Total Change due to Job XXX Finding Total Unemployment Rate at the end of the first month Calculate the following values for the end of the second month after these changes to s and f Unemployment Employment Initial Levels at beginning of month Change Due to Job Separation Sub Total Change due to Job Finding Total Total Labor Force XXX XXX Unemployment Rate at the end of the second month Calculate the following values for the end of the third month after these changes to s and f Unemployment Employment Initial Levels at beginning of month Change Due to Job Separation Sub Total Change …