Economics 102Spring 2009Homework 4Due 4/1/2009Directions: 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).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.) d. 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? (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?)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:W/P = 4000-(Lagriculture/3)2Industrial 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. 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 _____________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 ______________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 firm output. At the same time thatCarlos stops buying convenience store ice cream, he buys $200 worth of equipment,milk, butter, sugar, and cream and makes his own ice cream for the rest of the year.The change in GDP due to these actions by Carlos is ______________d. Laura, who lives in Nebraska, finds $50,000 in a garbage bag this year when shegoes to throw away her own garbage. Instead of reporting it to the authorities shedecides to start her own business. To do so she buys $32,000 worth of equipment from3Torcidos Ltd. of Venezuela and $18,000 from Tornado Ltd. from Washington, Kansas.Both purchases are made during this year and all the equipment was produced duringthis year.The change in GDP due to Laura’s actions is equal to ______________e. Econ Artists, Inc., located in Newton, Massachusetts produces 100,000 newMacroeconomic books this year and it prices each textbook at $115. These textbooksare basically the same book as last year’s textbook with the addition of some newgraphs and examples. 10,000 of these textbooks are sold abroad and 60,000 of thesetextbooks are sold in the US. The remainder of the textbooks produced this yearremain unsold on warehouse shelves.The contribution to this year’s GDP from Econ Artists, Inc. is equal to______________List of Notations for Next Two QuestionsC = Consumption SPrivate = Private SavingI = Investment SGovernment = Government SavingG = Government spending T = TaxX = Export TR = Government TransfersIM = Import KI = Capital InflowQuestion 3.
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