During the Great Recession, many news stories focused on a rising number of discouraged workers. The implication of many of these stories is that the unemployment situation was worse than indicated by the unemployment rate because of the existence of these discouraged workers. a. What are some of the reasons typically given for not including discouraged workers in the unemployment rate calculation? b. Show mathematically that if discouraged workers are treated as unemployed that the unemployment rate would increase. c. Show mathematically that the unemployment rate as defined by the Bureau of Labor Statistics would be lower if data on the underground economy was more available.
> A number of empirical studies suggest that labor demand is very elastic while labor supply is very inelastic. Assume too that payroll taxes are about 15 percent and legislated to be paid half by the employee and half by the employer. a. What would happen
> Suppose the Cobb-Douglas production function given in equation 4-1 applies to a developing country. Instead of thinking of immigration from a developing to a developed country, suppose a developed country invests large amounts of capital (foreign direct
> Consider the policy application of environmental disasters and the labor market that was presented in the text. a. How do labor demand and labor supply typically shift following a natural disaster? b. The data on changes in employment and wages in Table
> A monopsonist’s demand for labor can be written as VMPE = 40 - 0.004ED. Labor is supplied to the firm according to w = 5 + 0.01ES. Thus, the firm’s marginal cost of hiring workers when it hires off of this supply schedule is MCE = 5 + 0.02ES. a. How much
> In the cobweb model of labor market equilibrium (Figure 4-17), the adjustments in employment can be small with adjustment being fast, or the adjustments in employment can be large with adjustment being slow. The result that comes about depends on the ela
> Figure 4-6 shows that a payroll tax will be completely shifted to workers when the labor supply curve is perfectly inelastic. In this case, for example, a new $2 payroll tax will lower the wage by $2, will not affect employment, and will not result in an
> Figure 4-9 discusses the changes to a labor market equilibrium when the government mandates an employee benefit for which the cost exceeds the worker’s valuation (panel a) and for which the cost equals the worker’s val
> In a particular industry, labor supply is ES = 10 + w and labor demand is ED = 40 -4w, where E is the level of employment and w is the hourly wage. a. What are the equilibrium wage and employment if the labor market is competitive? What is the unemployme
> A firm’s technology requires it to combine 5 person-hours of labor with 3 machine hours to produce 1 unit of output. The firm has 15 machines in place and the wage rate rises from $10 per hour to $20 per hour. What is the firm’s short-run elasticity of l
> What type of instrumental variable is needed to estimate the labor supply elasticity? Can you think of any historical instances that would allow for this?
> What happens to employment in a competitive firm that experiences a technology shock such that at every level of employment its output is 200 units per hour greater than before?
> Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 6 and r = 4. These prices then shift to w = 4 and r = 2. a. In which direction will the
> Union A wants to represent workers in a firm that would hire 20,000 workers if the wage rate is $12 and would hire 10,000 workers if the wage rate is $15. Union B wants to represent workers in a firm that would hire 30,000 workers if the wage rate is $20
> Figure 3-18 in the text shows the ratio of the federal minimum wage to the average hourly manufacturing wage. Figure 3-18: a. Describe how this ratio has changed from the 1950s to the 1990s. What might have caused this apparent shift in fundamental eco
> Consider a production model with two inputs—domestic labor (EDom) and foreign labor (EFor). The market is originally in equilibrium in that Then a wage shock occurs to cause a substantial amount of outsourcing. Specifically, as a resu
> Draw on a single graph the time to transition to a new labor equilibrium when a firm faces variable adjustment costs for the following two firms. a. A trucking firm currently employs 100 drivers. If the economy enters an expansionary period, the firm wou
> Which one of Marshall’s rules suggests why labor demand should be relatively inelastic for public school teachers and nurses? Explain.
> How does the amount of unemployment created by an increase in the minimum wage depend on the elasticity of labor demand? Do you think an increase in the minimum wage will have a greater unemployment effect in the fast-food industry or in the lawn-care/la
> Several states set their own minimum hourly wage above the federal minimum wage. To offset higher minimum wages, many of these states offer firms tax incentives that lower the cost of borrowing and/or lower the firm’s tax liability on profits. In general
> Suppose the hourly wage is $10 and the price of each unit of capital is $25. The price of output is constant at $50 per unit. The production function is f(E,K) = E½K ½, so that the marginal product of labor is MPE = (½)(K/E) ½ . If the current capital
> Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits one machine to do the work of three workers. The firm wants to produce 100 units of output. Suppose
> Consider two workers with identical preferences, Phil and Bill. Both workers have the same life cycle wage path in that they face the same wage at every age, and they know what their future wages will be. Leisure and consumption are both normal goods. a.
> In 1999, 4,860 TANF recipients were asked how many hours they worked in the previous week. In 2000, 4,392 of these recipients were again subject to the same TANF rules and were again asked their hours of work during the previous week. The remaining 468 i
> Explain why a lump-sum government transfer can entice some workers to stop working (and entices no one to start working) while the earned income tax credit can entice some people who otherwise would not work to start working (and entices no one to stop w
> Shelly’s preferences for consumption and leisure can be expressed as U(C, L) = (C - 100) × (L - 40) This utility function implies that Shelly’s marginal utility of leisure is C - 200 and her marginal utility of consumption is L - 40. There are 110 (non-s
> Currently a firm pays 10% of each employee’s salary into a retirement account, regardless of whether the employee also contributes to the account. The firm is considering changing this system to a 10% match, meaning that the firm will match, up to 10% of
> Cindy gains utility from consumption C and leisure L. The most leisure she can consume in any given week is 110 hours. Her utility function is U (C, L) = C × L. This functional form implies that Cindy’s marginal rate of substitution is C/L. Cindy receive
> Tom earns $15 per hour for up to 40 hours of work each week. He is paid $30 per hour for every hour in excess of 40. Tom faces a 20 percent tax rate and pays $4 per hour in child care expenses for each hour he works. Tom receives $80 in child support pay
> What is the effect of an increase in the price of market goods on a worker’s reservation wage, probability of entering the labor force, and hours of work?
> The absolute value of the slope of the consumption-leisure budget line is the aftertax wage, w. Suppose some workers earn w for up to 40 hours of work each week and then earn 2w for any hours worked thereafter (called overtime). Other workers may earn w
> Consider a person who can work up to 80 hours each week at a pretax wage of $20 per hour but faces a constant 20 percent payroll tax. Under these conditions, the worker maximizes her utility by choosing to work 50 hours each week. The government proposes
> Over the last 100 years, real household income and standards of living have increased substantially in the United States. At the same time, the total fertility rate, the average number of children born to a woman during her lifetime, has fallen in the Un
> Presently, there is a minimum and maximum social security benefit paid to retirees. Between these two bounds, a retiree’s benefit level depends on how much she contributed to the system over her work life. Suppose Social Security was changed so that ever
> A worker plans to retire at the age of 65, at which time he will start collecting his retirement benefits. Then there is a sudden change in the forecast of inflation when the worker is 63 years old. In particular, inflation is now predicted to be higher
> Under current law, most Social Security recipients do not pay federal or state income taxes on their Social Security benefits. Suppose the government proposes to tax these benefits at the same rate as other types of income. What is the impact of the prop
> How many hours will a person allocate to leisure activities if her indifference curves between consumption and goods are concave to the origin?
> Consider a small island economy in which almost all jobs are in the tourism industry. A law is passed mandating that all workers in the tourism industry be paid the same national hourly wage, even though workers differ in their skills and effort. In fact
> During the debate over a federal spending bill, Senator A proposed changing the schedule for paying out unemployment benefits to be one where benefits were doubled but offered for half the current duration (so that UI benefits would expire after 13 weeks
> Suppose the government proposes to increase the level of UI benefits for unemployed workers. A particular industry is now paying efficiency wages to its workers in order to discourage them from shirking. What is the effect of the proposed legislation on
> Compare two unemployed workers: one is 25 years old while the other is 55 years old. Both workers have similar skills and face the same wage offer distribution. Suppose that both workers also incur similar search costs. Which worker will have a higher as
> a. How does the exclusion of nonworking welfare recipients affect the calculation of the unemployment rate? Use Tables 525 and 569 of the 2008 U.S. Statistical Abstract to estimate what the 2005 unemployment rate would have been if welfare recipients had
> Suppose the marginal revenue from search is MR = 50 - 1.5w where w is the wage offer at hand. The marginal cost of search is MC = 5 + w a. Why is the marginal revenue from search a negative function of the wage offer at hand? b. Can you give an economic
> The previous question concerned the unemployment rate and the distribution of weeks of unemployment immediately prior to the Great Recession. Now consider Table 627 of the 2011 U.S. Statistical Abstract, and repeat parts (a) and (b) from Problem 12-2. Ge
> Consider Table 610 of the 2008 U.S. Statistical Abstract. a. How many workers aged 20 or older were unemployed in the United States during 2006? How many of these were unemployed less than 5 weeks, 5 to 14 weeks, 15 to 26 weeks, and 27 or more weeks? b.
> Consider the standard job search model as described in the text. a. Why are the asking wage and expected unemployment duration positively related? b. Can the standard job search model explain why unemployment duration is longer, on average, for secondary
> Unemployment insurance automatically stimulates the economy during an economic contraction, which is good from the workers’ point of view. From the firm’s point of view, however, the UI system can be overbearing on business during prolonged contractions.
> Suppose the current UI system pays $500 per week for up to 15 weeks. The government considers changing to a UI system that requires someone to be unemployed for five weeks before receiving any benefits. After five weeks, the person receives a lump-sum pa
> a. Use Table 571 of the 2008 U.S. Statistical Abstract to describe how unemployment rates have changed for males, females, whites, blacks, and Hispanics since 1970. b. Use Table 609 of the 2008 U.S. Statistical Abstract to describe how educational status
> Consider Figure 12-19 in the text. What happened to the unemployment rate in France, Germany, and Italy from 1970 to 2000? What do you think explains this pattern?
> Suppose 25,000 persons become unemployed. You are given the following data about the length of unemployment spells in the economy: Duration of Spell (in months)......…..Exit Rate 1……………………………………………….0.60 2………………………………….……….…..0.20 3………………………………….……………0.
> Consider a firm that offers the following employee benefit. When a worker turns 60 years old, she is given a one-time opportunity to quit her job, and in return the firm will pay her a bonus of 1.5 times her annual salary and pay her health insurance pre
> a. The analysis of Figure 11-5 does not mention the price of output. What is implicitly being assumed about the product market in the analysis? b. Instead of thinking of output as depending on the wage level, the analysis in Figure 11-5 can be altered to
> Consider three firms identical in all aspects (including the probability with which they discover a shirker), except that monitoring costs vary across the firms. Monitoring workers is very expensive at Firm A, less expensive at Firm B, and cheapest at Fi
> Consider three firms identical in all aspects except their monitoring efficiency, which cannot be changed. Even though the cost of monitoring is the same across the three firms, shirkers at Firm A are identified almost for certain; shirkers at Firm B hav
> Suppose a firm’s technology requires it to hire 100 workers regardless of the wage level or market demand conditions. The firm, however, has found that worker productivity is greatly affected by its wage. The historical relationship between the wage leve
> All workers start working for a particular firm when they are 20 years old. The value of each worker’s marginal product is $18 per hour. In order to prevent shirking on the job, a delayed-compensation scheme is imposed. In particular, the wage level at e
> A firm hires two workers to assemble bicycles. The firm values each assembly at $12. Charlie’s marginal cost of allocating effort to the production process is MC = 4N, where N is the number of bicycles assembled per hour. Donna’s marginal cost is MC = 6N
> Taxicab companies in the United States typically own a large number of cabs and licenses; taxicab drivers then pay a daily fee to the owner to lease a cab for the day. In return, the drivers keep all of their fares (so that, in essence, they receive a 10
> Some compensation schemes include a signing bonus while others include the potential to receive annual year-end bonuses. a. From the firm’s perspective, what are the benefits of offering a signing bonus? What are the benefits of offering a year-end bonus
> Economists and psychologists have long wondered how worker effort relates to wages. Specifically, the question is whether worker effort responds to increased wages alone or whether effort also responds to relative wages. a. Design a classroom experiment
> Many public school teachers pay a fixed percentage of their salary into a retirement system. Upon retirement, suppose teachers receive a retirement benefit that depends on their years of service and the salaries they earned during their last two years on
> a. Personal injury lawyers typically do not charge a client unless they obtain a monetary award on their client’s behalf. Why? b. What would happen to the number of lawsuits if lawyers had to charge an hourly rate win or lose and could not charge a fixed
> a. How does the offering of stock options to CEOs attempt to align CEO incentives with shareholder incentives? b. Enron was a company that was ruined in part because of the stock options offered to upper management. Explain. c. In addition to accounting
> a. Why would a firm ever choose to offer profit-sharing to its employees in place of paying piece rates? b. Describe the free-riding problem in a profit-sharing compensation scheme. How might the workers of a firm “solve” the free-riding problem?
> Suppose there are 100 workers in an economy with two firms. All workers are worth $35 per hour to firm A but differ in their productivity at firm B. Worker 1 has a value of marginal product of $1 per hour at firm B, worker 2 has a value of marginal produ
> Several states recently passed laws restricting bargaining rights for public employees. Most notably the changes tended to restrict the union’s right to negotiate over fringe benefits such as health care and retirement benefits. a. What problems were the
> At the competitive wage of $20 per hour, firms A and B both hire 5,000 workers (each working 2,000 hours per year). The elasticity of demand is -2.5 and -0.75 at firms A and B respectively. Workers at both firms then unionize and negotiate a 12 percent w
> Suppose the union’s resistance curve is summarized by the following data. The union’s initial wage demand is $10 per hour. If a strike occurs, the wage demands change as follows: Length of Strike:……………………Hourly Wage Demanded 1 month……………………………………………….$9
> Consider the same setup as in the previous problem, but now the union is allowed to specify any wage, w, and the firm is then allowed to hire as many workers as it wants (up to 225) at the daily wage of w. What wage will the union set in order to maximiz
> Consider a firm that faces a constant per unit price of $1,200 for its output. The firm hires workers, E, from a union at a daily wage of w, to produce output, q, where q = 2 E ½ Given the production function, the marginal product of labor is 1/ E 1/2 .
> A bank has $5 million in capital that it can invest at a 5 percent annual interest rate. A group of 50 workers comes to the bank wishing to borrow the $5 million. Each worker in the group has an outside job available to him or her paying $50,000 per year
> Figure 10-3 demonstrates some of the trade-offs involved when deciding to join a union. a. Provide a graph that shows how the presence of union dues affects the decision to join a union. (Assume all workers pay a flat rate for dues.) Show on your graph h
> Suppose the union in problem 10-1 has a different utility function. In particular, its utility function is given by U = (w - w*) × E where w * is the competitive wage. The marginal utility of a wage increase is still E, but the marginal utility of employ
> Soon after the football season ended in 2011, the National Football League Players Association (NFLPA), which is the union for the players in the National Football League (NFL), and the team owners (the NFL) experienced a labor impasse in the form of a l
> Major League Baseball players are not eligible for arbitration or free-agency until they have been in the league for several years. During these “restricted” years, a player can only negotiate with his current team. Consider a small-market team that happ
> Use a graph to demonstrate the likely bargaining outcomes of three industries, all with identical union resistance curves. a. Firm A has been losing money recently as wages and fringe benefits have risen from 63 to 89 percent of all costs in just the las
> Consider Table 632 in the 2008 U.S. Statistical Abstract. a. Calculate the union wage effect. Calculate the union effect on total benefits. Calculate the union effect on total compensation. b. Note that for nonunion workers, retirement and savings increa
> In Figure 10-7 , the contract curve is PZ. a. Does point P represent the firm or the workers having all of the bargaining power? Does point Z represent the firm or the workers having all of the bargaining power? Explain. b. Suppose the union has the powe
> Suppose the economy consists of a union and a nonunion sector. The labor demand curve in each sector is given by L = 1,000,000 - 20 w. The total (economy wide) supply of labor is 1,000,000, and it does not depend upon the wage. All workers are equally sk
> Suppose the firm’s labor demand curve is given by w = 20 - 0.01E where w is the hourly wage and E is the level of employment. Suppose also that the union’s utility function is given by U = w × E It is easy to show that the marginal utility of the wage fo
> Use DerivaGem to check that equation (19.4) is satisfied for the option considered in Section 19.1. (Note: DerivaGem produces a value of theta ‘‘per calendar day.’’ The theta in equation (19.4) is ‘‘per year.’’)
> Suppose the risk-free rates are as in Problem 4.30. What is the value of an FRA where the holder pays LIBOR and receives 7% (semiannually compounded) for a six-month period beginning in 18 months? The current forward rate for this period is 6% (semiannua
> A trader has a put option contract to sell 100 shares of a stock for a strike price of $60. What is the effect on the terms of the contract of (a) A $2 dividend being declared (b) A $2 dividend being paid (c) A 5-for-2 stock split (d) A 5% stock dividend
> Explain why collateral requirements will increase in the OTC market as a result of new regulations introduced since the 2008 credit crisis.
> A bank offers a corporate client a choice between borrowing cash at 11% per annum and borrowing gold at 2% per annum. (If gold is borrowed, interest must be repaid in gold. Thus, 100 ounces borrowed today would require 102 ounces to be repaid in 1 year.)
> A stock price is $29. A trader buys one call option contract on the stock with a strike price of $30 and sells a call option contract on the stock with a strike price of $32.50. The market prices of the options are $2.75 and $1.50, respectively. The opti
> Call options on a stock are available with strike prices of $15, $1712 , and $20, and expiration dates in 3 months. Their prices are $4, $2, and $12 , respectively. Explain how the options can be used to create a butterfly spread. Construct a table showi
> A trader sells a put option with a strike price of $40 for $5. What is the trader’s maximum gain and maximum loss? How does your answer change if it is a call option?
> What does a stop order to sell at $2 mean? When might it be used? What does a limit order to sell at $2 mean? When might it be used?
> Explain two ways in which a bear spread can be created.
> Use a three-step tree to value an American futures put option when the futures price is 50, the life of the option is 9 months, the strike price is 50, the risk-free rate is 3%, and the volatility is 25%.
> An index provides a dividend yield of 1% and has a volatility of 20%. The risk-free interest rate is 4%. How long does a principal-protected note, created as in Example 12.1, have to last for it to be profitable for the bank issuing it? Use DerivaGem. E
> A foreign currency is currently worth $0.64. A 1-year butterfly spread is set up using European call options with strike prices of $0.60, $0.65, and $0.70. The risk-free interest rates in the United States and the foreign country are 5% and 4% respective
> What is the result if the strike price of the put is higher than the strike price of the call in a strangle?
> A 6-month American call option on a stock is expected to pay dividends of $1 per share at the end of the second month and the fifth month. The current stock price is $30, the exercise price is $34, the risk-free interest rate is 10% per annum, and the vo
> Company X wishes to borrow U.S. dollars at a fixed rate of interest. Company Y wishes to borrow Japanese yen at a fixed rate of interest. The amounts required by the two companies are roughly the same at the current exchange rate. The companies have been
> A stock price is currently $100. Over each of the next two 6-month periods it is expected to go up by 10% or down by 10%. The risk-free interest rate is 8% per annum with continuous compounding. What is the value of a 1-year European call option with a s
> What trading strategy creates a reverse calendar spread?
> On July 1, 2017, a company enters into a forward contract to buy 10 million Japanese yen on January 1, 2018. On September 1, 2017, it enters into a forward contract to sell 10 million Japanese yen on January 1, 2018. Describe the payoff from this strateg
> Suppose that in Table 3.5 the company decides to use a hedge ratio of 1.5. How does the decision affect the way the hedge is implemented and the result? Table 3.5 Data for the example on rolling oil hedge forward. Date Apr. 2017 Sept. 2017 Feb. 2018
