# Practice Problem Set 5 (ANSWERS)

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2 2. Suppose that the supply and marginal revenue product of labour curves faced by a monopsonist are as follows: Units of Labour (N) Supply MRP N MC Supply with Min Wage MC with Min Wage a) Filled in above. b) The monopsonist will hire additional units of labour as long as the MRP N is greater than the MC. This is true up and including the 4 th worker (where the monopsonist is just indifferent between hiring and not hiring the worker). The wage is given from the supply curve. In this case the wage will be \$5.70. c) Filled in above. d) The firm s hiring decision rule has not changed. However, with the minimum wage the MC of the 5 th worker is below the marginal revenue product of the 5 th worker. The firm will hire this worker. For the 6 th worker the MC jumps up to \$7.80 which is well above the MRP. The wage paid is equal to the minimum wage of \$6. Therefore, the number of workers hired increases to Currently, the payroll tax for Employment Insurance and the CPP/QPP in Canada are structured (approximately) as follows: Tax Tax payment t W h : if W h E payment t E : if W h E where t is the tax rate, W is the wage, h is hours worked and E is the level of earnings above which the worker is no longer taxed. The rationale is that since there is a ceiling on the level of wages that are covered by employment insurance or old age insurance benefits (called maximum insurable earnings), there should be a ceiling on the earnings to which the tax contributions are applied. This means that after the employee has earned E dollars, then the tax rate on further hours is zero.

3 a) Assume that output depends on labour input as the simple sum of the number of hours worked by employees (i.e. an hour worked by an existing or new employee is equally productive). Derive the marginal cost of hiring an additional hour of labour services, depending on the number of hours worked by the employee (incorporating the payroll tax). The marginal cost of hiring one more hour of labour is W (1 + t) if Wh < E-bar, which is the earnings ceiling, and W if Wh > E-bar. b) In a diagram with # hours on the vertical axis and # employees (bodies) on the horizontal axis show how the structure of these taxes may affect the firm s choice between employees and hours. This cost structure gives the firm the incentive to increase the number of hours worked by an individual once he/she has reached the threshold of E-bar. After this point, we expect to see longer hours, because if more workers are hired, the payroll taxes must be paid until the new hires have worked sufficient hours to earn E-bar. If the workers have not reached that threshold, the firm is indifferent between lengthening the workweek and adding new workers. c) Economists argue that eliminating the cap on payroll taxes will have a positive effect on employment. Discuss the merits of this argument referring to your answer in part b. Collecting payroll taxes on all earnings would remove the incentive to work the existing labour force longer hours at the expense of hiring new workers. The tax would then be neutral as far as the decision of hiring more workers versus working the existing labour force longer hours is concerned. Most labour economist would argue in favour of this proposal, as it should raise the level of employment. 4. a) In perfectly competitive markets the long-run labour demand curve is less elastic than the short-run labour demand curve. Disagree. The long run labour demand curve is more elastic than the short-run labour demand curve because the firm has more flexibility in the long-run to respond to wage changes. In the short-run: capital is fixed so there can be no substitution effect, There is however a scale effect. In the long-run: there will be both a substitution effect as well as a scale effect because capital is not fixed. We can illustrate the difference by looking at the response of a firm to a wage change from w 0 to w 1 : Short-run: the firm will reduce the scale of operation by reducing the number of employees from N 1 to N 2 SR (note that capital is fixed at k 1 ). Long-run: the firm will reduce the scale and substitute away from labour towards capital employment falls further from N 1 to N 2 LR.

4 w (k=k 2 ) w 1 (k=k 1 ) w 0 D 2 SR D 1 SR D LR N 2 LR N 2 SR N 1 a) Because inputs tend to be specialized, Production Possibility Frontiers are concave with respect to the origin. Agree: Beer 100 A B 15 Wine The PPF is shaped as drawn above because it is assumed that the inputs used in the production of beer are specialized for beer production. For example, we might think that the workers who produce beer have special skills associated with beer production that are not used in the production of wine. Also, we might think that the land used to produce hops and wheat used in beer production will have special characteristics that are distinct from the ideal land used to produce grapes. Recall that the slope of the PPF gives the opportunity cost of wine in terms of units of beer (i.e. how much beer we have to give up in order to produce one more unit of wine). With specialized inputs we would expect the opportunity cost of wine to go up as the country produces more wine (e.g. as we move from A to B). This is because a movement from A to B may require the country to begin using workers or land (inputs) to produce wine that are really more suited for the production of beer. It will require more brewmasters and land suited for hops and wheat to produce more wine. In other words, the number of units of beer we have to give up will start to increase (the slope will become steeper). c) The labour demand curve in an industry that is characterized by monopoly is less elastic than that of an industry characterized by competition. Agree. The key difference between a perfectly competitive firm and one that has monopoly power in the output market is the output demand curves faced by the two firms. For the competitive firm, the output demand curve is perfectly elastic at the industry price of the output

5 (i.e. horizontal at the price). For the monopolist, on the other hand, the output demand curve is simply the downward sloping industry demand curve. This has important implications for the input market as well. This implies that the industry labour demand curve for a perfectly competitive firm which is just equal to the sum of the individual firm s labour demand curves equals: MP N x P. Where price represents the perfectly competitive firm s marginal revenue of output. For the monopolist, however, the marginal revenue of output decreases with the level of output. Thus, the industry demand curve in a monopoly equals MP N x MR. Therefore, as the firm tries to expand output (which implies an increase in labour) only the marginal product of labour falls in the case of a perfectly competitive firm whereas both the marginal product of labour and marginal revenue fall for the monopolist. Thus, the slope of the labour demand curve for the monopolist is steeper than the competitors. The industry demand curve under monopoly is, therefore, less elastic.

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