ECONOMICS OF WORK AND PAY
ECONOMICS OF WORK AND PAY ECON 4960
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This 22 page Class Notes was uploaded by Amelia Reynolds on Monday September 21, 2015. The Class Notes belongs to ECON 4960 at Georgia State University taught by Rachana Bhatt in Fall. Since its upload, it has received 12 views. For similar materials see /class/209821/econ-4960-georgia-state-university in Economcs at Georgia State University.
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Date Created: 09/21/15
Homework Solutions 1 2 Indicate in each of the following instances whether the specified circumstances will cause a worker to want to work more or fewer hours a The wage rate increases and the substitution effect is greater than the income effect b The wage rate decreases and the income effect is greater than the substitution effect c The wage rate decreases and the substitution effect is greater than the income effect d The wage rate increases and the income effect is greater than the substitution effect a A wage rate increase will cause an income and substitution effect The income effect states that since an individual is wealthier he she will consume more goodsincluding leisure This implies a reduction in work hours The substitution effect states that because of the wage increase the price of leisure has become more expensive and a rational worker will respond by substituting away from expensive goods Consequently heshe will consume less leisure and work more When the substitution effect is greater than the income effect the net effect is for the worker to work more b A wage rate decrease will cause an income and substitution effect The income effect states that since an individual is less wealthy heshe will consume fewer goodsincluding leisure This implies a reduction in leisure and an increase in work hours The substitution effect states that because of the wage decrease the price of leisure has become cheaper and a rational worker will respond by consuming more of the cheaper good Consequently heshe will consume more leisure When the income effect is greater than the substitution effect the net effect is for the worker to work more c Net effect work less d Net effect work less 3 Employ a diagram similar to Figure 27 illustrates income and substitution effects of a wage increase to show an individual s leisureincome choices before and after a wage rate decrease Isolate the income and substitution effects indicate whether each increases or decreases hours of work and use the two effects to explain the overall impact of the wage decline on hours of work Is your worker on the forwardrising or backward bending portion of the labor supply curve The diagrams below illustrates a scenario where a worker initially has a wage rate represented by budget constraint W7old The worker maximizes utility by consuming L7l units of leisure at point U7l Then the worker s wage drops so that the new wage produces budget constraint W7new The new utility maximizing point is L73 units of leisure at point U73 This movement from U7l to U73 can be decomposed into two steps The income effect is illustrated by the movement from U7l to U72 and corresponding leisure consumption of L71 to L72 and the substitution effect is illustrated by the movement from U72 to U73 corresponding leisure consumption of L72 to L73 In both diagrams the income effect of a wage decrease reduces the amount of leisure consumed This is because when the wage drops the worker becomes less wealthy and a rational worker consumes fewer normal goods when heshe is less wealthy Leisure is a normal good so less leisure is consumed and consequently the worker works more We illustrate the income effect in the diagrams by shifting the in the original budget line in a parallel way until it is tangent to the new indifference curve Thus the wage has not decreased but the wealth of the worker has decreased On the other hand the substitution effect of a wage decrease increases the amount of leisure consumed This is because a lower wage reduces the relative price of leisure so leisure becomes a relatively less expensive good Rational workers consume more of a good when it is less expensive hence leisure consumption increases and work time decreases We illustrate the substitution effect in the diagrams by moving along the new indifference curve until we hit the tangency point of the new budget constraint to the new indifference curve By restricting the worker to be on the same indifference curve we ve essentially left the real income of the worker unchanged but have altered the wageand therefore the price of leisure In Diagram A the substitution effect is greater than the income effect so the worker consumes more leisure at U73 than heshe did at U7l ie L73 gt L7l In Diagram B the income effect is greater than the substitution effect so the worker consumes less leisure at U73 than heshe did at U7l ie L73 lt L7l In Diagram A the worker would be on the upward sloping portion of the labor supply curve wage decrease leads to less work and more leisure whereas in Diagram B the worker would be on the backward bending portion of the labor supply curve wage decrease leads to less leisure and more work Note A third possibility is when the income and substitution effects cancel each other out completely In this case there is no change in the workers consumption of leisure after the wage decrease compared to before the wage decrease although overall utility has been lowered lower indifference curve Dia ram A Income W 01d Leisure 7 L73 L72 L1 Diagram B Income Wield Winew Leisure 5 Suppose Lauren is given two options by her employer First option She may choose her own hours of work and will be paid relatively low wage rate implied by budget line HWil shown in the accompanying diagram Second option She can work exactly HR hours and will be paid the relatively high wage rate implied by budget line HW72 Which option will she choose Justify your answer Lauren will choose the highwage option HW72 and work HR hours Although she will feel underemployed at HR hours at HR her MRS of L for Y is less than the wage rate this option will allow her to reach a higher indifference curve a higher level of utility 7 Note Modi cation to text question What generalizations can you formulate on the basis of a education b the presence of preschool children c level of spouse s income and d location of a household urban or rural on the probability that a married woman will be a labor force participant a A married woman with more education is more likely to work than another married woman with a lower level of education This is because the wage of the higher education woman say she has a college education is generally higher than that of the lower educated woman say she has a high school degree but no college The higher the wage the steeper the budget constraint Assuming both women have identical workleisure preferences ie indifference curves have same shape the college educated woman is more likely to participate in the labor market b If a married woman has preschool aged children she is less likely to be a labor force participant This is because she likely attaches a greater deal of utility to her non market time in which she would be caring for children In technical terms her indifference curves will be steeply drawn illustrating the point that in order to give up 1 unit of leisure nonmarket time she would have to be compensated by a large increase in income c When a married woman s spouse has a high income she is less likely to participate in the labor market A high spousal income basically raises the own nonwage income of the married woman ie at 24 hours of leisure she still has some income hence she is less likely to participate d When a married woman or anyone lives in a rural setting as compared to a more urban setting she is less likely to participate in the labor market assuming that most jobs are located in urban areas This is because commuting and travel costs essentially eat away at the wages that individual is receiving implying a atter budget constraint and lower earnings For instance compare two individuals with the same wageoccupationpersonal characteristics One lives 1 mile away from work the other lives 5 miles away The latter will spend a substantial amount of time commuting and more directly may have to pay more in terms of transportation costs to go to work We can visualize these costs as a xed cost that are deducted each day from the workers actual wage This lower wage decreases the lower probability that she will work 11 If an income maintenance program entails a 3000 basic benefit and a benefit reduction rate of 030 what will be the size of the subsidy received by a family that earns 2000 per year What will be the family s total income What breakeven level of income does this program imply Recall that the formula for the subsidy payment is SBtY When S3000 t030 and Y2000 we have a subsidy payment S3000030 2000 2400 The individualfamily s total income is given by the subsidy payment plus the income earned from work 2400 2000 4400 The break even level of income is the level of earned income at which the individualfamily receives no bene t from the program At this level 80 so Y7bBt where Y7b is the breakeven level of income Y7b 3000030 10000 Ifthe individualfamily earns 10000 or more from work they are no longer eligible for participation in the subsidy program Income Wage W7old ineligible for subsidy Wage W7old1 7 030 W7old 10000 3000 Bene t 3000 L71 L 2 L73 Leisure The diagram above illustrates the impact of this income maintenance program Before the program worker earned wage rate W7old and had the corresponding budget constraint Utility was maximized at point U71 with leisure consumption L71 The income maintenance program shifts the budget line up at 24 hours of leisure by the total benefit amount 3000 The next part of the budget constraint has slope W7old1030 since the bene t reduction rate is 030 Finally at an income level of 10000 the worker is no longer eligible for the subsidy so the budget constraint returns to having the original slope of W7old With the program the worker maximizes utility at point U73 where he she consumes L73 units of leisure The diagram breaks the shift from L71 to L73 or in terms of utility U71 to U73 into two parts U71 to U72 illustrates the income effect and U72 to U73 illustrates the substitution effect In the case of an income maintenance program the income effect induces the individual to consume more leisuresince the program makes the worker wealthier The substitution effect also encourages the worker to consume more leisurebecause the program alters the price of leisure from W7old to W7old1030 Now that the price of leisure has become less expensive the individual will want to consume more of it Homework 4 Solutions Chapter 6 4 Predict the impact of each of the following on the equilibrium wage rate and level of employment in labor market A a An increase in labor demand and supply in labor market A An increase in labor demand will shift the labor demand curve to the right thus increasing the equilibrium wage rate and quantity of labor hired An increase in the supply of labor will shift the supply curve to the right thus decreasing the equilibrium wage rate and increasing the quantity of labor hired Consequently if both demand and supply for labor increase there is an increase in the quantity of labor hired but an indeterminate change in the equilibrium wage rate b The transformation of labor market A from a competitive to a monopsonistic market If the market transformed from a competitive to monopsonistic in labor this would decrease the wage rate Both a competitive and monopsonistic hirer of labor would maximize profit by equating MWC to MRP For a competitive rm MWCwage however for a monopsonist MWCgtwage Consequently the wage paid by a monoposonist is lower than what would be paid by a perfectly competitive firm 5 Assume a surplus of doctors exists Use the labor market supply and demand graphics to depict this outcome How would the market remedy this situation in the short run and long run Supplyis R71 SupplyisRio SupplyiLR w0 w1 w2 Demand 0 Demand 1 El E0 The above diagram illustrates the market supply and demand for doctors Assume we are in an initial long run equilibrium which occurs at the intersection of Demand 0 and Supply iLR E0 w0 There is a decrease in demand Demand 1 and as a result the demand decrease should move the the new equilibrium to El There are however a fixed number of doctors in the short run illustrated by SupplyisRio thus this leads the wage rate to be set at w2 rather than wl As a result of the lower wage fewer individuals are attracted to the medical profession and so over time there are fewer doctors SupplyiSRil thus increasing the wage again Chapter 4 3 In order to determine if Floyd should make the investment in the automobile mechanics course we need to calculate the net present value of this decision Since the cost of the course is incurred at a different point in time than the payoffs we must put all monetary costs in present value terms to make them comparable Cost of Course l000 incurred now year 0 Forgone Income 8000 incurred now year 0 Incremental gain in earnings from course 130008000 5000 received in years l2 3 Since the costs direct and indirect are incurred in the present they are already in present value terms However the future payoffs need to be placed in present value terms using the given interest rate of 10 and the formula futurenowliAn Payoffin year 1 5000 now7yearll01001 now7yearl5000l l Payoff in year 2 5000now7year2l010A2 nOWJear25000ll 2 Payoffin year 3 5000now7year3l010A3 now7year35000ll 3 Net present value of investment l00080005000ll 5000l2l 5000l33l 343426 Since the net present value is positive Floyd should invest in the automobile mechanics course 7 General training is training that is usable at all firms and industries It enhances the productivity of workers to all firms Employees usually pay for general training by accepting lower wages during the training period compared to what they would earn if they were not being trained Specific training is training that is usable only at the firm that provides the training Employers usually pay for specific training since it is valuable only at that fum 9 Scholarships based on ability will likely increase the dispersion of earnings If high ability individuals are able to finance their education at a lower cost this will increase the amount of education they obtain and hence increase their earnings compared to those who were not eligible for the scholarship Consider the figure below The demands for education rate of return of three individuals with different ability levels are depicted a b c Individual a has the highest ability since he has a higher return to education at each level of schooling compared to the other individuals Individual c has the lowest ability and b is in the middle Individuals a b and c initially face the same costs of nancing their education iil At this interest rate they obtain education levels eiail eibil and eicil respectively and it is assumed that the higher the education level the higher the eamings Ifa scholarship became available that lowers the cost of nancing school only for the highest ability individual to i72 the new education level obtained by individual a is e7a72 while everyone else remains at eibil eicil The scholarship increases the educational attainment of individual a compared to before and heshe earns higher eamings thus increasing the dispersion of earnings Scholarships based on ability Years of Schooling A scholarship based on need will likely reduce the dispersion of earnings by reducing the dispersion in the cost of nancing education interest rate For instance consider the gure below where there are three different individuals each of which faces a different cost of nancing education Individual a achieves education level eiail individual b achieves eibil and individual c achieves eicil Suppose all three individuals are eligible for need based assistance and are offered the same cost of education i72 The new levels of education are e7a72 e7b72e7bil and e7c72 for individuals a b and c respectively The individuals now receive more similar amounts of education compared to before and this implies their ea1nings are now more similar Scholarships based on need Years of Schooling eal a The screening hypothesis states that schooling increases earnings not by 39 39 I 39 quot y but b 39J39 g rms with a way to identify high quality workers The private rate of return will be unbiased because workers still get higher earnings but the social rate of return to education will be overstated since education has not actually increase productivity b Some economists argue that some expenditure on education should be considered consumption and not expenditure By ignoring the consumption bene ts of education researchers overstate the costs of education and understate the return c If individuals with more ability are more likely to go to college then presumably even without a college degree they would earn more than those who decided not to go If the higher earnings re ects greater ability rather than the outcome of schooling the rate of return is overstated d The jobs of college graduates generally include greater fringe bene ts as a percent of pay than in the jobs of high school graduates Ignoring these fringe bene ts pleasant working conditions etc will understate the rate of return to getting a college education Homework 3 Solutions Chapter 5 4 Note Changes made from book question in question and in table values Given the data in Table A calculate MP AP TR MR and MRP of labor assume capital is xed for this rm Then complete the labor demand schedule shown in Table B Calculate the value of marginal product VMP for this schedule Explain why the labor demand and VMP schedules differ Inputs Wage Rate Demanded 0 0 8 1 4 The following table displays the MP AP MR and MRP for the rm Each column is calculated using the formulas MPdelta TPdelta L APTP L TRTP P MRde1taTIUdeltaTP MRPMR MP Inputs T Labor Product Price We know a rm will hire a quantity of labor where MRPgtMWC ie the revenue to the rm from the hire of an additional worker is greater than the wage cost of hiring that worker The lm will try to get as close to equality of this equation as possible Given the wage rates in the table and the above calculated MRP we can ll in the demand schedule Demanded Finally we can calculate the VMPPMP Labor The VMP differs from the MRP for this firm because it operates in an imperfectly competitive product market That means the firm has some market power and in order to sell extra units of output it must lower the price on all units This implies that in addition to having diminishing marginal returns to production which occurs for firms that operate in perfectly competitive firms too which lead to decreasing MP it also has this market power effect which leads to a decreasing MR whereas for competitive firms MR is constant For a competitive firm MRP but for an imperfectly competitive firm MRltP That implies that firms don t value the output of each additional worker as highly as society does and hence the MRP and VMP curves differ 5 Explain how each of the following would affect the demand schedule you derived in Question 4 previous question a an increase in the price of a gross substitute for labor b a decrease in the price of a pure complement in production with labor and c a decrease in the demand for the product that labor helps produce Note The answers to this question do not depend on whether or not you got the previous question right The demand curve for each of the following is assumed to be a downward sloping curve as the wage rate increases quantity demanded of labor decreases a An increase in the price of a gross substitute for labor will increase the demand for labor Consequently the demand curve shifts to the right Reason When the price of the gross substitute say capital increases this increases the marginal cost of producing the good which decreases output and lowers the demand for both labor and capital called output effect The increased price of capital causes rms to substitute towards the relatively less expensive inputlabor and this increases the demand for labor called substitution effect When the capital and labor are gross substitutes the substitution effect outweighs the output effect so overall demand for labor increases b A decrease in the price of a pure complement will increase the demand for labor Consequently the demand curve shifts to the right Reason When the price of a pure complement say capital decreases this decreases the marginal cost of producing the good which increases the output of the firm This increased output increases the demand for both labor and capital Although capital has gotten relatively less expensive firms must use capital and labor in direct proportion with one another and so there is no substitution away from labor towards the relatively less expensive capital Since there is only an output effect the demand for labor increases c When the demand for a final product that uses labor as an input decreases the demand for labor will decrease Consequently the demand curve shifts to the left Reason When the demand for a good increases ceteris paribus the price of the good will increase Suppliers will be willing to produce more output because they can charge a higher price and so they will demand more labor in order to make more output 6 Referring to the output and substitution effects explain why an increase in the wage rate for autoworkers will generate more of a negative employment response in the long run than in the short run Assume there is no productivity increase and no change in the price of nonlabor services If the wage for autoworkers increases this will increase the marginal cost of production and firms will consequently supply less output This lower output level means that less labor is demanded by firms and so demand for labor decreases This is called the output effect and this occurs in the shortrun for a firm Over a longer time frame the firm can substitute the expensive labor for the relatively cheaper capital and so the demand for labor drops even more This attens the demand curve in the long run As a consequence the long run demand curve for labor is more elastic than the short run demand curve for labor This is illustrated in the graph below Quantity of Labor Additional Problem 2 Calculate the wage elasticity of labor demand in the following scenario Wage increases from 3 to 7 and as a consequence labor demand decreases from 100 to 65 Is wage elasticity of labor demand elastic inelastic or unitary elastic Using the first method taught in class the wage elasticity of demand is change in Quantity Labor Demanded Change in Wage change in Quantity Labor Demanded 65100100 100 35 change in Wage 733 133 Elasticity 35l33 026 taking absolute value 026 This implies when wage changes by 1 unit labor demanded will change by 026 units Since elasticityltl we consider labor demand to be inelastic Using the midpoint method taught in class the wage elasticity of demand is change in Quantity Labor Demanded Change in Wage change in Quantity Labor Demanded 65100100652 100 4242 change in Wage 73732 80 Elasticity 424280 053 taking absolute value 053 This implies when wage changes by 1 unit labor demanded will change by 053 units Since elasticityltl we consider labor demand to be inelastic Although the two estimates themselves differ 026 vs 053 the classification of inelastic remains Chapter 6 3 What effect will each of the following have on the market labor demand for a specific type of labor a An increase in product demand that increases product price Increase since more labor is needed to meet the increased demand for the product b A decline in productivity of this type of labor Decrease because labor is less productive assuming there s no change in the price of the product c An increase in the price of a gross substitute for labor Increase since output effect decrease demandltsubstitution effect increase demand d A decline in the price ofa gross complement for labor Increase since output H 39 ease demand 39 39 39 H ease demand e The demise of several rms that hire this labor Decrease since this type of labor is no longer used in production f A decline in the market wage rate for this labor Increase since this labor is now cheaper to use g A series of mergers that transforms the product market into a monopoly Decrease since for a monopoly MRPMP MR and MRltP Homework 5 Solutions Chapter 8 2 Analyze why college professors generally earn less than their professional PhD counterparts who are employed by corporations College professors generally earn less than their professional counterparts because of compensating wage differentials Compensating differentials are defined as the extra pay that an employer must provide to compensate a worker for some undesirable job characteristics that do not exist in alternative employment College professors generally have more exible work schedules and fewer bureaucratic interferences as compared to their private sector workers In order to put up with these undesirable nonwage amenities corporations must pay private sector workers more to attract workers 3 Many of the lowestpaid people in societyfor example shortorder cooksalso have relatively poor working conditions Hence the theory of compensating wage differentials is disproved The theory is not disproved The lower wages paid for unskilled work ie shortorder cook may outweigh the relatively high wages that are necessary to draw these unskilled workers into jobs with unsafe hazardous dirty working conditions 11 Suppose that a employers must pay higher wages to attract workers from wider geographic areas and hence higher wages are associated with longer commuting distances less of the amenity closeness of j ob to home and b female have greater tastes for having jobs close to their homes than do males Use the hedonic wage model to show graphically why a malefemale wage differential might emerge independent of skill differences or gender discrimination Consider two employeesa man and a woman Both have the same skill set but different preferences for wage and nonwage amenities Assume the nonwage amenity is proximity of job to home The man has indifference curves over wages and nonwage amenities that are atter than the woman s indicating that the woman puts more priority on having a job that is close to home In contrast the man is willing to travel far for work as long as the wage is high enough Potential employers realize that individuals desire both wage and nonwage amenities and both are costly to provide As a consequence an employerfirm that is making a given level of profit P can only increase wages if they reduce the nonwage amenity and viceversa Suppose there are two types of employers Employer 1 has a hard time finding a factory that is close to where workers live while Employer 2 has insider information ie friends with real estate agent and finds a factory that is close to where workers live That means Employer 1 has a steeper isoprof1t curve than Employer 2 When these rms and workers match with each other the female worker who has the steeper indifference curve will reach a higher level of utility at the point of tangency with Employer 2the firm that has the factory close to the city The male worker will obtain a higher level of utility at the point of tangency with Employer lthe firm that can offer high wages but is located outside the city As a consequence the man matches with Employer 1 and gets a high wage but works far from home The woman matches with Employer 2 and gets a lower wage but works closer to home This wage differential is illustrated in the diagram below Employer 1 Wage Employer 2 Close to home Homework 2 Solutions Chapter 3 3 In 2006 the United States had a population of 299 million of which 70 million were either under 16 years of age or institutionalized Approximately 151 million people were either employed or unemployed but actively seeking work What was the participation rate in 2006 If everything stayed the same by 2011 but there were 5 million more unemployed individuals actively seeking work what is the labor force participation rate in 201 1 The labor force participation rate is calculated as noninstitutional population 16 years or older in the labor forcenoninstitutional population over 16 100 Using the numbers given we can calculate 151 29970 100 655 If there were 5 million more unemployed individuals but everything else stayed the same by 2011 this means that the labor force participation rate would now be 156 29970 100 681 9 Use a workleisure diagram to demonstrate that a if AfricanAmericans have labor market opportunities that are inferior to those of whites and b nonlabor income is available in the form of say disability bene ts AfricanAmericans will have lower participation rates even though the workleisure preferences indifference curves of AfricanAmericans and whites are identical Consider a scenario where the workleisure preferences of an AfricanAmerican and white person are identical Ifthe AfricanAmerican faces inferior work opportunities compared to the white person we can illustrate this as the AfricanAmerican receiving lower wages for the same amount of work as the white person Lower wages imply a atter budget constraint Furthermore if there are nonlabor income benefits available to the AfricanAmerican person this increases his income at 24 hours of leisure 0 hours of work by the amount of the benefit This is illustrated in the figure below Using the same indifference curve for both individuals we see that while the white person participates in the labor market the AfricanAmerican person is better off not participating Note that the budget lines have been drawn so that both the AfricanAmerican and white person have some nonlabor income say savings but that the AfricanAmerican is additionally eligible for some extra nonlabor income via disability benefits Income African wiafram American 24 Leisure 11 The addedworker effect can be explained in terms of the income effect while the discouragedworker effect is based on the substitution effect Do you agree Yes The addedworker effect is based on a reduction in the partner s nonwage income We know lower nonwage income increases the probability of working so the income effect encourages indiViduals to enter into the market The discouragedworker effect can be explained by a reduction in the wage rate that people get offered during economic downturns This lowers the opportunity cost of leisure price of leisure and so people are more likely to consume leisure The discouraged worker effect results in people staying out of the labor force Additional Problem 1 Use a workleisure diagram to explain how rising real wages for females would increase labor force participation Assume that before the wage rate increase the female was not in the labor force and received some nonwage income from her husband s wage earnings Illustrate both the income and substitution effects in the diagram The diagram below illustrates the workleisure decision of the woman The initial budget constraint is Wiold and is kinked at 24 hours of leisure because she receives nonlabor income Her optimal workleisure decision is at Ul where she consumes 24 hours of leisure and works 0 hours When the wage rate increases the budget constraint gets steeper Winew and she reaches optimal point U2 with more income and less leisure than at Ul She participates in the labor market The income and substitution effects are illustrated in the move from Ul to U2 income effect and U2 to U2 substitution effect The income effect is nonexistent because the individual did not work any hours initially so she can t work any less than that even if there is an increase in income Hence from Ul to U2 employment hours don t change income effect represented through parallel shift of initial budget line up to the new indifference curve The substitution effect is illustrated by an increase in work hours and decrease of leisure from U2 to U2 At the higher wage rate the price of leisure has increased so the woman substitutes away from the less expensive good and works more She is able to maintain this increase in market work by purchasing more good intensive commodities rather than timeintensive ones Income Leisure
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