Wednesday, October 31 Lecture: Labor Markets
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1 Amherst College Department of Economics Economics 111 Section 3 Fall 2012 Wednesday, October 31 ecture: abor Markets abor Markets: Demand and Supply Every market includes to essential elements: demand and supply. To illustrate the labor market e place the age on the vertical axis and the quantity of labor on the horizontal axis. The age is measured in dollars per hour and the quantity in hours. In equilibrium, the quantity of labor demanded equals the quantity of labor supplied. We shall begin ith the market demand curve for labor and then discuss the market supply curve. Wage ($/hour) * S D Market Demand Curve for abor Question: Who demands labor? Ansers: Firms demand labor. The market demand curve for labor provides the ansers to the folloing series of hypothetical questions: Ho many hours of labor ould firms hire (the quantity demanded), if the age ere, given that everything else remains the same. Note that the demand curve is donard sloping. This just means that as the age increases firms respond by hiring less labor. This makes sense, doesn t it? Question: Where does the market demand curve for labor come from? Claim: the market demand curve for labor is the horizontal sum of each firm s individual demand curve for labor. To justify this, suppose that there are only to firms in the beer industry: Firm A and Firm B. Wage ($/hour) If = If = If =20 If =10 The diagram to the right illustrates the demand curve for the to beer firms, Firm A and Firm B. D A is Firm A s demand curve; D B is Firm B s Firm A s demand curve ansers a long series of D A hypothetical questions: If the age ere, ho many hours of labor ould Firm A hire? Similarly, Firm B s demand curve ansers a long series of hypothetical questions also: If the age ere, ho many hours of labor ould Firm B hire? Firm A * abor (hours) D abor (hours) Firm B D B
2 2 If the age ere $10 per hour, Firm A s demand curve tells us ho many hours of labor Firm A ould hire and Firm B s demand curve tells us ho many hours of labor Firm B ould hire. Consequently, to determine ho many hours of labor all firms ould hire if the age ere $10 per hour, e simply sum the number of hours hired by Firm A and Firm B together. We have just found one point on the market demand curve. Firm A Firm B Market Demand Curve 20 If =10 D A D B To find another point on the market demand curve, suppose that the age ere $20 per hour. If the age ere $20 per hour, Firm A s demand curve tells us ho many hours of labor Firm A ould hire and Firm B s demand curve tells us ho many hours of labor Firm B ould hire. Consequently, to determine ho many hours of labor all firms ould hire if the age ere $20 per hour, e simply sum the number of hours hired by Firm A and Firm B together. We have just found a second point on the market demand curve. Firm A Firm B Market Demand Curve If =20 10 D A D B No, it is clear that once e have each firm s individual demand curve, e can construct the market demand curve by summing each individual firm s demand curve horizontally. Firm A Firm B Market Demand Curve D A D B D
3 3 Where does an individual firm s demand curve for labor come from? We no kno here the market demand curve for labor comes from: the market demand curve is the horizontal summation of each individual firm s demand curve. So, the next question e ant to address is: here does an individual firm s demand curve come from? Recall that a firm s individual demand curve provides the ansers to the folloing series of questions: Ho many hours of labor ould firms hire (the quantity demanded), if the age ere, given that everything else remains the same. Ho does an individual firm decide on ho on much labor to hire? Question: hat is a firm interested in? Anser: profit. What does profit equal? Profit = Total Revenue Total Cost = TR TC The firm ill hire the number of hours of labor that makes its profits as large as possible; that is, the firm ill hire the profit maximizing number of hours. Question: What information ould e need to determine hether or not a firm as maximizing its profits? Claim: We need to kno the firm s marginal revenue product of labor and marginal expense of labor: Marginal Revenue Product of abor ( ) = Change in the firm s total revenue resulting from hiring one more or one less hour of labor. Marginal Expense of abor (ME ) = Change in the firm s total cost resulting from hiring one more or one less hour of labor. More specifically, a firm is maximizing its profits only if marginal revenue product of labor equals marginal expense of labor. To convince you of this, first e shall sho that henever marginal revenue product of labor exceeds marginal expense of labor, the firm can increase its profits by hiring more hours of labor; to do so, suppose that = $50 and ME =$ If one more hour of If one more hour of labor ere hired labor ere hired TR ould rise by $50 TC ould rise by $ What ould happen to profit if one more hour of labor ere hired? Profit = TR TC $50 $ Since total revenue rises by $50 and total cost rises by only $, profits ould increase by $20. In general, henever the marginal revenue of labor is greater than marginal expense of labor, profit can be increased by hiring more labor: > ME Hiring more labor increases profit
4 4 Next, e ant to sho that henever that marginal revenue of labor is less than marginal expense of labor a firm can increase its profit by hiring feer hours of labor; to do this, suppose that = $20 and ME =$ If one feer hour of If one feer hour of abor ere hired labor ere hired TR ould fall by $20 TC ould fall by $ What ould happen to profit if one less hour of labor ere hired? Profit = TR TC $20 $ Since total revenue falls by $20 and total cost falls by $, profits ould increase by $10. In general, henever the marginal revenue of labor is less than marginal expense of labor, profit can be increased by hiring less labor: < ME Hiring less labor increases profit So, if marginal revenue product of labor exceeds the marginal expense of labor, a firm can increase its profit by hiring more labor; on the other hand, if marginal revenue of labor is less than the marginal expense of labor, a firm can increase its profit by hiring less labor. Therefore, henever profits are being maximized, marginal revenue product of labor must equal marginal expense of labor: > ME = ME < ME More labor Profit ess labor increases profit maximized increases profit What should e do next? We should focus on the marginal expense and the marginal revenue product of labor. Marginal Expense of abor Recall the definition of the marginal revenue product of labor: Marginal Expense of abor (ME ) = Change in the firm s total cost resulting from hiring one more or one less hour of labor. When a firm hires a orker for one more hour its total cost ill rise by an amount equal to the age. Therefore, the marginal expense of labor equals the age: ME = What does the marginal expense of labor curve look like? The marginal expense of labor curve is just a horizontal line equals to the age: If = If = ME = ME = If =20 If =10 ME =20 ME = 10
5 5 Marginal Revenue Product of abor Claim: a firm s marginal revenue product of labor equals its marginal product of labor times the price of the firm s product. = MP MR To justify this claim, e begin by revieing the definitions: Marginal Revenue Product of abor ( ) = Change in the firm s total revenue resulting from hiring one more or one less hour of labor. Marginal Product of abor (MP ) = Change in the firm s production resulting from hiring one more or one less hour of labor. Marginal Revenue (MR) = Change in the firm s total revenue resulting from one more or less unit of output Focus on a beer firm. Assume that the firm s marginal physical product of labor is 6 cans for beer and marginal revenue equals $2 per can. MP = 6 MR = $2 To calculate marginal revenue product, suppose that the beer firm hires a orker for one more hour: If one more hour of labor ere hired Since MP = 6 Beer production increases by 6 cans Since MR = $2 Each additional can increases total revenue by $2 for a total of 6 2 = $12 When the firm hires 1 more hour of labor its total revenues rise by 6 $2 = $12; therefore, the marginal revenue product of labor equals $12: = 6 2 = $12 We can generalize this relationship: = MP MR Shape of the Marginal Revenue Product of abor Curve Claim: The marginal revenue product of labor curve is a donard sloping curve; that is, as the firm hires more labor, the marginal revenue product of labor decreases. To understand hy note that e just shoed that the marginal revenue product of labor equals the marginal product of labor times the price: = MP MR MP Marginal Physical Product of abor (MP ) Recall Mr. Atkins apple orchard. As Mr. Atkins hired more labor, the marginal product of labor decreased: As the firm hires more labor MP decreases MP
6 6 Marginal Revenue (MR) Perfect Competition MR = Price Perfectly competitive firm takes the price as given, as a constant Imperfect Competiton P MR < Price Price Marginal Revenue < Price MR D Q Putting both parts together: As a firm hires more labor: = MP MR Decreases Remains the same or decreases As the firm hires more labor, it produces more output MR decreases Hence, as a firm hires more labor, decreases. The curve is donard sloping. The firm s individual demand curve is its marginal revenue product of labor curve Recall that the firm s individual demand curve ansers the folloing series of hypothetical questions: If the age ere, ho hours of labor ould the firm hire? Recall that to maximize profits, the marginal revenue product of labor must equal the marginal expense of labor. = ME Furthermore, If = The marginal revenue product of labor curve is donard sloping: If = curve is donard sloping If =20 The marginal expense of labor equals the age: ME = If =10 No, let us put these to relationships together. The firm s individual demand curve is its marginal revenue product of labor curve. ME =1000 ME =750 ME =500 ME = 10
7 7 Market Supply Curve for abor: Backard Bending Backard bending supply curve for labor. abor versus eisure abor Provides income eisure Provides pleasure More labor leads to less leisure and vice versa. As the age rises you can earn more income Working becomes Income more attractive rises Work more Enjoy the income earned abor eisure eisure abor Substitute Income Effect abor for eisure Substitute Effect Summary: The substitution effect and the income effect tend to counteract each other: As the age rises Substitute Effect More abor Income Effect ess abor Wage S Income Effect Dominates The shape of the supply curve depends on hich effect dominates. When the age is lo, the substitution effect dominates; hen the age is high, the income effect dominates: As the age rises o Wage Income o Place a high value on additional income More abor Upard Sloping High Wage Income High Place a high value on leisure Enjoy the income you are earning ess abor Donard Sloping Substitution Effect Dominates abor
8 8 Tying Up a oose End: To Profit Maximizing Rules Ho Are They Related? We shall argue that the to profit maximizing rules are equivalent; they are to different sides of the same coin. The first rule vies profit maximization from the perspective of production and the second from the perspective of labor: Ho much output Ho much labor should the firm produce? should the firm hire? MR = MC = ME Change in TR Change in TC Change in TR change in TC resulting from a resulting from a hen 1 more or hen 1 more or 1 unit change in 1 unit change in 1 less hour of 1 less hour of the quantity of the quantity of labor is hired labor is hired output produced output produced We shall explain this by continuing to use our example. To make the discussion less abstract, assume the marginal product of labor as 6 cans of beer, the price of beer as $2 per can, and the age is $12 per hour: MP = 6 MR = 2 = 12 We can no calculate the marginal revenue product of labor and the marginal expense of labor: = MP MR ME = = 6 2 = 12 = 12 The firm is folloing the second profit maximizing rule. Consequently, to sho that the rules are equivalent, e need to sho that the first profit maximizing rule ill be met automatically. It is not difficult to do so. What does marginal cost equal? To anser this question, consider hat happens to total cost and production hen the firm hires 1 more hour of labor: 1 more hour of labor is hired MP = 6 ME = 12 Firm produces Total cost 6 more cans increases by $12 é ã If firm produces Total cost 1 more can increase by $2 é ã MC = 2 MR = MC. The first profit maximizing rule is satisfied.
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