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UW-Madison ECON 102 - Answers to Homework 4

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Economics 102Spring 2009Answers to Homework 4Due 4/1/09Directions: The homework will be collected by your TA in a box before the lecture. Please makesure you know your TA name so that you can place your homework in the correct box. Pleaseplace your name, TA name and section number on top of the homework (legibly). Make sure you writeyour name as it appears on your ID so that you can receive the correct grade. Please remember thesection number for the section you are registered, because you will need that number when yousubmit exams and homework. Late homework will not be accepted so make plans ahead of time.Good luck!Question 1.The economy of country A is described by the production function:Y KL=In this equation the symbol Y stands for real GDP, K for capital and L for theemployed individuals in this economy. The labor force at the beginning of time,period 0, is 100 individuals. Capital in each period is constant and equal to 120 units.Every period the labor force increases by 100 individuals and the unemployment ratestays constant at 10% of the labor force. (Suggestion: Use Microsoft Excel or someother computer program to do the calculations and the graphs of the questionsposed below rather than a regular calculator. On the homework page of the classwebsite is a link to some helpful guidelines for using Excel. )a. Complete the following chart using the above information. Calculate real GDP withat least 3 decimal places. Hint: this will be far easier if you use Excel to do thesecalculations and you may present your own Excel Chart as the answer to thisquestion.1b. Graph Real GDP and the employment level for this economy. Please measure realGDP on the y-axis and employment on the x-axis. For this question it is fine topresent your answer as an Excel Graph (hint: this is much easier to do with a programlike Excel). Note: Period zero is depicted as period 1.c. Suppose now that instead of capital being constant at 120 units during the periodsof our analysis capital is instead equal to 240 units. Nothing else changes about thisproblem (e.g., the labor force still increases as described earlier in the problem). Inone graph present real GDP under both situations: situation one, where capital is equalto 120 units and situation two, where capital is equal to 240 units. On your graphmeasure real GDP on the y-axis and employment on the x-axis. (Hint: once again, thiswill be easier to do if you use Excel to calculate the necessary values and then useExcel to graph the two situations.) 2d. Suppose the level of employment is equal to 180 people. What is the percentagechange in the productivity of labor from the first situation when capital is equal to 120units to the second situation when capital is equal to 240 units? It generates a 41 percent increase in productivity. This is the result of an increasefrom 146.97 to 207.85(Extra Fun. This is NOT mandatory. For a constant level of labor calculate thederivative of Y with respect to capital and take the limit when capital tends to zero ofthis expression. What does this tell us of the benefits of increasing capital whencapital levels in an economy are extremely low?)ANS: 02lim2KY LKKLK��=�=+�This implies that for very low levels of capital the gains obtained in production byincreasing the level of capital are gargantuan.e. Using the previous information assume that for period 0 we know that thiseconomy consists of two types of firms, agricultural and industrial firms. Agricultural firms have a labor demand given by:3W/P = 4000-(Lagriculture/3)Industrial firms have a labor demand given by:Lindustry=3000-(W/P)*(7/8)where W/P is the real wage rate and L refers to labor demand (thus Lagriculture is the demand for workers by the agricultural firms). Assume that in period 0 the aggregate price level P is equal to 1, and therefore the real wage (W/P) is equal to the nominal wage (W). Find the aggregate labor demand in this economy and then calculate the real wage in this economy for period 0. ANS:The labor demand is:2400012000 3 if 4000731 2400015000 if 08 7W WLP PW WLP P= - � >= - � >The real wage is 3970.For a fixed labor supply of 90 individuals real wages are 3847.74 if you plug thisnumber into the segment of the market that includes both the agricultural and theindustrial demand for labor. But, if you do this you get a value for the equilibriumreal wage that is greater than the maximum possible real wage for this segment of thelabor demand curve (the value you get is 3428.57 or (24000/7)) . Thus, the onlysegment of the market that matters is the one comprised of the agricultural demandfor labor. For this segment of the market demand curve for labor the real wage istherefore 3970.Question 2.Each of the following questions involves calculating some aspect of real GDP.a. A day before his birthday (June 6, 2009) Bruno sells his hair salon for $100,000. Inaddition he sells his car (produced in 2002) for $25,000. That same day he provides 5hair cuts for $15 per haircut. On his birthday he dies leaving an inheritance of$125,000 to his best friend.The change in GDP due to these events is _____$75________4The only real good or service being provided in this example is the service of ahaircut. The other pieces of information refer to old production or the receipt of aninheritance that does not represent current production.b. Bakery A annually uses $10 million worth of sugar, flour, and eggs (assume allthree of these ingredients are produced in the same year that the bread is produced) toproduce its bread. Wages and salaries in Bakery A for the year are equal to $40million; the bakery's only other annual expense is $15 million in interest that it payson its bonds. The annual profits for the owner of the bakery are $ 10 million. The bakery’s annual effect on GDP equals _____$75 million_________Here all of the information is added because all the monetary amounts refer to factorpayments made during the year of interest in the GDP calculation. This includes theprofits of the owner of the bakery and, more importantly, of the industries where theintermediate goods where produced. c. On April 30, Carlos decides to stop throwing away $60 a month on conveniencestore ice cream. In the economy where Carlos lives, supply=demand at every momentin time: thus, Carlos’ decisions immediately affect


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UW-Madison ECON 102 - Answers to Homework 4

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