Introduction to Microeconomics
Introduction to Microeconomics EC 201
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This 14 page Class Notes was uploaded by Kareem Larkin PhD on Saturday September 19, 2015. The Class Notes belongs to EC 201 at Michigan State University taught by B. Brown in Fall. Since its upload, it has received 17 views. For similar materials see /class/207656/ec-201-michigan-state-university in Economcs at Michigan State University.
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Date Created: 09/19/15
1 1 PRODUCTION AND COST IN THE SHORTRUN Purpose To illustrate the relationship between total product curves and total cost curves To show the relationship between changes in input prices and a rm s cost of production in the short run Computer le newtptc1xls Instructions and background information You own and operate an apartment cleaning service rm in Detroit Your business is to clean and repair apartments for landlords whose tenants have recently moved out The le graph in the computer display shows the total product curve for your rm The input is the number of workers you hire per day and the output is the number of apartments cleaned per day There are two baseline variables in this problem One is the wage rate you must pay your workers and the other is something called quotlabor ef ciencyquot Labor ef ciency is an index of how ef ciently labor services are used to clean apartments and is an aspect of the technology of production It doesn t have anything to do with whether you are a good manager or whether your workers goof off on the job The relationship between the numbers of employees you hire and the output produced is purely technical Labor ef ciency is 50 in this problem and you cannot change it that is reserved for the next problem set In the real world the labor ef ciency index might go up if you provide your workers with more equipment mops and brooms for example Workers for your business do not come free In fact you must hire workers and pay them at a rate of 10 per worker per day 10day is the market wage If you try to pay less than that workers simply will not work for you The data on the total product curve see the le graph shows the output you get for any amount of labor input you choose The data on the total cost curve show total cost for any output you choose given the wage rate You can pick any values you want for output and the wage rate and the total cost curve on the right displays the results The table also shows the amount of labor required for the output you choose The le and right graphs operate independently The input and output you see in the total product curve can be diiTerent from the output and cost you see on the total cost curve lll Here are some things to watch for and learn as you do the problems 1 Given the technology of production you can t get more output without using more labor input 2 Given the wage rate and the technology of production higher output is possible only with increased costs 3 Raising the wage rate the price of a variable input increases total average and marginal costs An increase in the wage causes total cost to increase more at higher outputs than lower outputs 4 In the shortrun xed costs are the lm s costs when output is zero Here are some hints to help you get the answers quicker 1 Average cost is total cost divided by output 2 Marginal cost is the change in total cost per unit change in output ACAQ Marginal cost is the cost of one more the extra cost of increasing output by one unit The marginal cost of the 25th unit of output is the di erence in total cost at 25 minus the total cost at 24 units of output MATH MAVEN39S CORNER The total product curve for the computer problems is Q ALe where the exponent e is the ef ciency index and A is a constant e in this case is also the elasticity of output with respect to changes in L The marginal product is the derivative of total product with respect to L or AeLe39l The total cost curve is TC FC pLQA1e where pL is the wage rate 1000 a day to start off with PRODUCTION AND COST IN THE SHORT RUN Questions Set all variables to their baseline values and set labor input to 10 1 How many apartments are cleaned per day with this amount of labor Set all variables to their baseline values and set labor input to 20 2 How many apartments are cleaned per day with this amount of labor Set all variables to their baseline values and set labor input to 20 Increase the wage rate to 12day 3 With labor at 20 what is the change in output Set the wage is 10day 4 If 15 apartments must be cleaned how many workers must be hired to get the job done Make sure the wage is set to 10day and set output at 15 apartments per day 5 What39s the TOTAL COST of cleaning 15 apartments Now set the wage to 12day 6 What39s the TOTAL COST of cleaning 15 apartments 7 When the wage rose from 10 to 12 per day did total cost INCREASE or DECREASE Set all variables to their baseline values and set output at 15 apartments per day 8 What39s the AVERAGE COST of cleaning 15 apartments Now set the wage to 12day 9 What39s the AVERAGE COST of cleaning 15 apartments 10 When the wage rose from 10 to 12 per day did average cost INCREASE or DECREASE Set the wage back to 10 day its baseline value 11 What39s the MARGINAL COST of cleaning the 15th apartment Hint What39s the total cost of cleaning 15compared to 14 Now set the wage to 12 per day 12 What39s the MARGINAL COST of cleaning the 15th apartment at the higher wage INTERNAL RATE OF RETURN Purpose To illustrate how to compute the intemal rate of return on an investment or series of lture payments and costs To show how to use the internal rate of return to make investment decisions Computer les newirrxls Instructions and background information The rst two spreadsheet columns show information on payments and costs associated with an asset in several years Column A lists the years payments are received or costs incurred Year 0 is today year 1 is one year from today etc Column B shows the dollar payments received or costs incurred on a hypothetical asset in respective years On quotwake upquot this column has 9500 500 500 and 10500 in the topmost cells Costs are entered as negative numbers so the asset represented is one that costs 9500 today and pays 500 500 and 10500 in each ofthe next 3 years successively Cell D58 shows the internal rate of return IRR on the asset whose cash ow values are listed in the cells in column B The IRR is the interest rate that makes the mi of the present values of the payments equal to zero If 139 is a rate of interest the IRR is the value of 139 that makes this equation true 0 R0 Rl1z39 R21z392 RT1z39T where Rt is the dollar return t years from now Another way to de ne the internal rate of return is as the interest rate that makes the net discounted present value of an asset equal to zero Or equivalently as the interest rate that makes the discounted present value of the costs equal to the discounted present value of the returns All of these ways of saying it come down to the same thing Of course solving the equation for the intemal rate of return may not be an easy task In fact for T larger than 5 there is in general no way to do it using the ordinary methods of algebra so various methods of approximation are used Excel nds the IRR by trial and error and the way the computer you are working on is set up it gives up if it doesn t get close to the answer a er 20 tries To help Excel out you can choose a value in cell F58 labeled BEST GUESS It is the interest rate Excel starts with as it tries to nd the IRR by trial and error When the spreadsheet wakes up the BEST GUESS for the intemal rate of return is 10 You can change BEST GUESS and all of the values in column B to answer the questions All other cells in the sheet are locked The graph shows the net discounted present value of the asset you are working with at interest rates from 0 to 100 percent in 1 percent intervals The intemal rate of return can be estimated by seeing where the graph crosses zero on the vertical axis You can use the graph to make a good BEST GUESS Experiment with some diiTerent values for returns and costs in diiTerent years and see what happens to the intemal rate of return NOTE The numbers in column B must contain at least one positive value and one negative value for the procedure to work In addition Excel has a quirk in the IRR computation that makes it treat blanks and zeros diiTerently If you want a zero payment or cost in an intermediate year of your asset be sure to enter quot0quot in the cell don t just leave it blank Here are some things to watch for and learn as you do the problems 1 The answers to questions 1 3 4 and 8 are percentages rates of return Enter your answer in the answer sheet either as a decimal or with a percent sign For example ifyour answer is 752 percent enter either 0752 or 752 2 The IRR is the average annual rate of return on an asset 3 Generally you can pro t by buying assets that have an IRR greater than the rate of interest you have to pay to borrow money The idea is that if IRR exceeds the rate of interest you can use the income from the asset to pay off both principal and interest from the loan and still have something le over 4 Higher intemal rates of return occur when costs go down or returns rise Here are some hints to help you get the answers quicker 1 In question 3 remember to deduct the 3000 down payment from the cost of the car Enter the loan amount as a negative number in cell B58 Then enter the 5 payments you must make in succeeding years 2 Question 4 is very much like Question 7 in the problem set on discounted present value Remember to add the scrap value of the machine to the last return that you enter in year 7 3 In Question 8 on the lottery you sell the winning ticket to someone else That means the buyer s return in period zero is a negative amount that is the payment to you plus the immediate payment when the ticket is cashed The remaining 9 payments are entered as positive numbers Try this exercise to get an idea how economists use the IRR to measure the value of a college education Suppose your sister or brother is about to nish high school and is considering buying a college education majoring in Economics which heshe expects to yield considerably higher incomes in lture years than ifheshe had just a high school education Income will be 18000 per year higher with the college education If your sibling goes to college hisher working life will start 5 years from now say and last for 40 years Suppose the costs in each of the 4 years of college are 12000 The rst year of costs occurs one year from now so enter it next to Year 1 And remember to put a minus sign in front of the costs Then enter the remaining costs and bene ts next to the correct years The last income payment should be entered in year 44 What is the intemal rate of return on a college education for your sibling In the computer exercise on discounted present value you gave an estimate of your real life estimated costs of your college education Divide that total cost by 4 to get the estimated annual cost and enter the costs in the spreadsheet What is the expected intemal rate of return on your investment if the annual income gain estimates of15000 per year for 40 years are correct 253 INTERNAL RATE OF RETURN Questions Note The values of payments and costs you need to answer the questions are generated randomly by the spreadsheet when you open it You will need to look at the questions in the spreadsheet to obtain the values 1A A government bond costs today and will pay you in interest in each ofthe next 3 years The rst payment occurs one year from now Go on to 1B At the time you receive the last interest payment you also receive the bonds principal or face value of10000 1B What39s the internal rate of return on the bond Continuing on from the last question 2 If you can borrow money at 4 should you buy the bond Yes or No 3A You are considering buying a car for and need to borrow the entire amount less a down payment of 3000 You take out a loan that you will pay back in ve annual installments of Go on to 3B 3B The rst loan payment is due one year from the time you get the car the second two years hence etc The salesman tells you that the loan payments include both principal and interest Go on to 3C You will own the car a er you make the last payment 3C What rate of interest are you paying on the loan 4A You are in the pizza business and want to buy a new pizza making machine The machine costs today At the end of each year you own the machine it will give you returns of a er paying for maintenance and repairs Go on to 4B A er you have owned the machine for 6 years you expect to sell it for scrap for 1000 You scrap it at the same time you get the last return 4B What is the internal rate of return on the machine Consider again the pizza machine in the last question Would you buy the machine if you could borrow money at the following rates Answer Yes or No 5 5 6 12 7 20 5 LABOR MARKETS Purpose To show the determinants of wages in a simple market for labor To show the effects of imposing an effective minimum wage in a labor market To show how equilibrium wages change in response to changes in output prices and labor productivity Computer le lab01 98xls Instructions and background information The previous exercise showed how equilibrium price was determined in the market for a good Economists claim that the markets for labor can also be described using a model of supply and demand In particular the equilibrium wage rate which is the price of labor services is determined in a labor market But there are important diiferences between the markets for goods such as spaghetti and the markets for inputs such as labor One is that the roles of consumers and firms in input markets are reversed from what we saw in goods markets This is because consumers are at the same time both the suppliers of labor and the demanders of goods while firms have the dual role of suppliers of goods and demanders of labor Open the Excel le lab01 98xls What you see are some data on the market for unskilled labor in Flint Michigan including the wage rate for that labor the price of bread the food of the working classes the price firms must pay for capital inputs an index of labor productivity quantity supplied quantity demanded and excess demand at the currently selected wage Quantities of labor are measured as the number of workers employed assuming each worker labors for 8 hours a day The wage rate is the hourly wage To find the daily wage just multiply the wage rate by 8 Firms produce automobiles that sell for 18000 each On the labor supply side the workers have the chance to be employed either in the automobile industry at the going wage or join the army and receive on average the wage of a corporal You should experiment by trying some diiferent values for the selected wage and each of the demand and supply variables The factors listed under DEMAND DATA and SUPPLY DATA cause the respective curve to shi Be sure you understand the reasoning behind the shi s For example an increase in the index of labor productivity perhaps because workers get extra training results in an increase in labor demand Be sure you can explain why labor demand changes at all in this case and why the change in demand for labor is an increase and not a decrease Why does it cause the demand curve to shi compared to moving along the curve 51 In questions 710 you re asked to explore the effects on labor markets of increases in the prices of goods that consumers buy To understand these questions you need to know the diiTerence between the money wage and the real wage workers are paid The money wage is simply the number of dollars per hour that workers get paid The real wage is the wage in terms of goods the amount of goods workers earn per hour For example the real wage of unskilled workers in terms of bread is the number of loaves of bread the worker earns per hour You compute the real wage by dividing the money wage by the price of goods In this example the real wage is the money wage divided by the price of bread Here are some things to watch for and learn as you do the problems 1 Labor markets can achieve equilibrium through changes in the money wage 2 An effective minimum wage will cause some unemployment but may also raise the incomes of employed workers as a group The effect on incomes depends on the elasticity of demand for labor 3 An increase in the price of the output sold by the rm will ultimately increase the money and real wages of workers 4 Higher wages in other occupations such as the army have effects on the wages of unskilled labor Here are some hints l The spreadsheet is not sensitive to the units of measurement such a dollars when you enter answers You can always omit dollar signs for example and still get the right answer But the spreadsheet is sensitive to sign or so be care ll on that account 2 If you use trial and error rather than Goal Seek to get an answer remember that you usually have to be accurate to within about onetenth of one percent of the exact answer Sometimes however being accurate within ve percent plus or minus will be ok MATH MAVEN39S CORNER The demand lnction for labor is given by DL Aw Tb p where w is the money wage for unskilled labor pc is the price of capital and T is the technology index for labor The supply lnction for labor is given by S L M w tquot p15 wcf where w is the wage rate pbread is the price of bread W0 is the corporal s wage and t is a tax per hour of labor The values of all of the parameters are randomly assigned LABOR MARKETS Questions Set all variables to their baseline values 1 What is the equilibrium hourly wage for unskilled labor in this market 2 What is the equilibrium level of employment Set all variables to their baseline values and set the wage to its equilibrium level The price of output automobiles rises to 23000 3 What39s the new equilibrium wage 4 What39s the new level of equilibrium employment level Set all variables at their baseline values including the price of automobiles You are a consultant to the auto industry in Flint Michigan and have been asked by your bosses to advise them on the effects of a recent Pentagon proposal The proposal is to change the military pay scale so the average wage for a corporal in the army will rise to 12 per hour 5 What39s the new equilibrium wage in the unskilled labor market For the proposal in the last question to raise corporals39 wages to 12 per hour 6 What39s the new level of employment in the market for unskilled labor Set all variables to their baseline values The price of bread rises to 400 per loaf 7 What39s the new equilibrium wage rate 8 What39s the new equilibrium level of employment Set all variables to their baseline values 9 What39s the real wage in terms of bread of unskilled labor in the baseline equilibrium When the price of bread rises to 4 per loaf and the market for unskilled labor adjusts to its new equilibrium 10 What39s the new real wage of unskilled labor 11 With all variables at their baseline values and the labor market in equilibrium what39s the TOTAL HOURLY INCOME FROM WAGES of unskilled workers as a group Set all variables to their baseline values Your task is to pick a value for an effective minimum wage Choose a wage less than 20 so it shows on the graph 12 What wage rate do you choose 13 For the minimum wage you chose in the last question did the incomes of unskilled workers increase or decrease compared to the market equilibrium wage 53 3 3 DISCOUNTED PRESENT VALUE Purpose To illustrate the idea of discounted present value with computations of the value of payments to be received in the lture at diiTerent rates of interest To use discounted present value to determine the pro tability of investments Computer le pv98xls Instructions and background information The spreadsheet for this problem set is a kind of calculator that will help you compute the discounted present value of a series of payments and costs The rst three spreadsheet columns show information on payments and costs associated with an asset in several years The relationship upon which all the calculations are based is that the present value of Pt dollars to be received t years hence is equal to Pt1z39t where 139 is the rate of interest expressed as a decimal Column A lists the years payments are to be received or costs incurred Year 0 is today year 1 is one year from today one year hence in economist39s jargon etc Column B shows the amounts of payments in dollars received by the owner of a hypothetical asset in respective years On quotwake upquot this column has 100 in rows 3 through 7 You can enter any numbers you wish in this column Hitting the Reset to Baseline button will clear the values from this column Each entry in column C shows the discounted present value DPV of the payment just to the le in column B Eg the DPV of 10000 to be received 4 years in the lture ifthe interest rate is 6 is 7921 cell C7 7921 1001 062 In economist39s lingo this is called quotThe present value of 100 four years hence at 6 percentquot Cell E3 shows the current interest rate On quotwake upquot 139 06 or 6 To change the interest rate select cell E3 and enter the rate of interest either as a percent or a decimal For example to change the interest rate to 10 percent enter either 10 g 10 Many assets and the one shown is an example give the owner a series of payments in many years in the lture not just a single payment Cell F3 shows the discounted present value of the series of payments in column B That is it is the sum of the values in column C The value in cell F3 is the present value of the asset The graph is a bar chart showing the present value of each of the payments in the respective years You should experiment by choosing some diiTerent values for the payments andor inserting new ones and seeing what happens to the present values in the graph You should also experiment by choosing some diiTerent values for the rate of interest Be sure you understand m an increase in the rate of interest must decrease the present value of a payment to be received in the lture Here are some things to watch for and learn as you do the problems 1 For a payment to be received in the lture there is an inverse relationship between the rate of interest and the present value of the payment Higher interest rates always lead to lower discounted values 2 You should buy an asset if the discounted present value of the bene ts payments is greater than the discounted present value of the costs 3 The DPV of an asset is the amount of money you would have to put on deposit lend today at the current interest rate to be able to withdraw receive the payments in the lture Here are some hints to help you get the answers quicker 1 In these problems all lture payments and costs are assumed to take place at the end of the period in question For example in question 1 enter the value of the payment in cell B6 next to year 3 In question 5 enter the rst interest payment from the bond next to year 1 The payment for year 0 should be blank 2 In question 5 enter the rst interest payment from the bond next to year 1 The payment for year 0 should be blank 3 In question 7 the rst return from owning the machine occurs in year 1 that is after one year However the cost of the machine occurs today year 0 In all you get 6 years of returns from owning the machine Remember to add the scrap value of the machine to the returns in last year 4 In question 17 you get the payolT from the rst year of energy saving in year 1 Year 0 should be blank or zero Then enter 40 through year 10 Try this exercise to get some insight into the value of your college education Suppose you are considering buying a college education majoring in Economics which you expect to give you considerably higher incomes in lture years than if you had just a high school education Your income is expected to be 332 15000 per year higher with the college education Your working life will start 3 years from now say and last for 40 years What is the value of the returns to the college education if interest rates are 3 6 and 10 What39s your own personal estimate of the cost of your college education Assume a 4 year college career Add a and b together discounting the lture costs if you wish to get the total cost a Opportunity cost in lost wages b Out of pocket costs of tuition books supplies etc but not housing or meals Is the investment going to be worth it DISCOUNTED PRESENT VALUE Questions Note The values of payments and costs you need to answer the questions are generated randomly by the spreadsheet when you open it You will need to look at the questions in the spreadsheet to obtain the values Your Uncle Harry says he will give you three years from now to help you pay for a new car 1 When the interest rate is 6 what39s the present value of his gi to you 2 What39s the present value if the rate of interest is 3 3A Some people set up trusts or make other nancial arrangements to pay for their kids college education Martha Klutz knows that when her daughter goes to college the expenses will be per year for four years Go on to 3B Her daughter is now a high school sophomore so the rst bill will arrive 3 years from now The rate of interest is 8 3B How large a trust must Klutz set up today so that her daughter39s college education is just paid for in the lture 4 How large would the trust have to be if the rate of interest was 3 instead of 8 5A A bond is a promise to pay its holder xed amounts of money at speci ed times in the lture Suppose you have a chance to buy a bond that pays the following amounts in interest and principal Go on to 5B 5B A er one year you will receive a series of annual interest payments of for 10 years At the time you receive the last interest payment you will receive the principal value ofthe bond of 20000 Go on to SC 5C If the rate of interest is 7 what39s the maximum amount you would be willing to pay for the bond 6 If the rate of interest were 10 what would be the price of the bond 7A You are in the pizza business and want to buy a new pizza making machine The machine costs today At the end of each year you own the machine it will give you returns of a er paying for maintenance and repairs Go on to Alter you have owned the machine for 6 years you expect to sell it for scrap for 1000 You scrap it at the same time you get the last return What is the present value of the RETURNS at 33 4
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