# Monopoly and Monopsony Labor Market Behavior

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1 Monopoly and Monopsony abor Market Behavior 1 Introduction For the purposes of this handout, let s assume that firms operate in just two markets: the market for their product where they are a seller) and the labor market where they are a buyer) 1. If the firm faces a competitive output market, regardless of what quantity they produce they get the constant market price P for each unit sold. If they face a competitive labor market, regardless of how many people they hire they have to pay each worker the constant market wage w. Sometimes firms have market power - the ability to manipulate the price of the market good based on the quantity they use or produce. In the extreme case, firms may be the only seller or buyer in a market. If the firm is the only seller, it is called a monopolist, and can change P depending on how much it produces. If it is the only buyer, it is a monopsonist, and can change w depending on how much labor it employs. 2 Review of the General abor Supply Model et there be only one input in production - labor. Profit maximizing firms choose labor by setting the marginal cost of labor equal to the marginal benefit or marginal revenue product) of labor. In a competitive model, both P and w are taken as given - the only thing that isn t determined by market forces is the marginal product of labor. The first order conditions FOC) for profit maximization are 2 MRP = MC MP MR = MC 1) 1 In reality, firms may operate in many markets, selling multiple goods and using multiple inputs in production. They may face competitive markets in some and have market power in others. 2 The FOC is a result of a generic maximization problem such as max P Q)) Q) C) where the maximization is done over. Prepared by Nick Sanders, UC Davis Graduate Department of Economics 2006

2 where MP = doutput dabor = d MR = drevenue doutput = dr MC = dcosts dabor = dc d When firms take output price and wage as given, 1) simplifies to MP P = w 2) Now let s consider how things change when P or w is allowed to change with Q and, respectively. 3 The Monopolist abor Decision Since a monopolist is the only producer in a market, they see the entire demand curve when making their production decision. As such, the more they produce, the lower the price in the market. We represent this with an inverse demand curve where price is presented as a function of quantity supplied, or P P Q), where dp < 0. Returning to equation 1), MC is still w, because the firm takes the price of its inputs as given. MR, however, is no longer simply P, but is now MR monopolist dp Q) Q) = = P Q) + dp Q = P 1 + dp ) Q P = P ) 3) 2

3 where is the elasticity of demand percentage change in quantity demanded divided by percentage change in price) which is assumed to be negative 3. So for a monopolist MR monopolist = P 1 some nonzero number) < P which reflects that each additional unit sold in the market lowers the price of all other units sold, and at a given wage monopolists will hire less labor than perfectly competitive firms. As monopolists employ less labor, they have lower production and thus generate a higher market price than competitive firms. 3.1 Monopolist example et the firm face the inverse demand function P Q) = 50 2Q and a cost function C) = 50. The marginal productivity of labor is constant at 5, i.e. Q) = 5. Find the optimal level of employment for the firm, the optimal quantity produced, and the price in the market Solution Since the marginal productivity of labor is constant at 5, the only variation in the marginal revenue product of labor will be marginal revenue. To find marginal revenue, we first need to construct the revenue function, which is price times quantity, or 50 2Q) Q. The marginal revenue function is then d 50 2Q) Q) = d 50Q 2Q2 ) = 50 4Q 4) Equation 4) times the marginal product of labor gives the marginal revenue product of labor. Since we know the marginal product of labor d equals 5 as Q) = 5), MRP = Note that in the case of perfect competition, firms face a perfectly elastic demand curve, which implies that =. This means that for perfect competition 1 = 1 = 0 and 3) is back to 2). 3

4 The marginal cost of labor is the derivative of the cost function with respect to, or d50) d = 50, which is the same as saying the wage in the labor market is 50. Setting marginal cost equal to marginal revenue product then gives = = = Total production is Q2) = 5 2 = 10, and price is given by P 10) = ) = The Monopsonist abor Decision Since a monopsonist is the only buyer in a market, they see the entire supply curve when making their purchasing decisions. If they are a monopsonist in the labor market, the more people they hire, the higher the wage. Assuming they are a non-discriminating monopsonist, hiring one additional worker means they have to pay all workers employed the now higher wage. The marginal cost of labor is now a function of the quantity hired, or MC MC ). Again going back to equation 1), now MR = P because the firm takes the price of its good as given, but assuming labor is the only factor of production) MC monopsonist = dcosts d d[w) ] = d = w) + dw d = w 1 + dw ) d w 5) where dw d > 0 due to an upward sloping labor supply curve4 ) and w 4 Under perfect competition, the firm s labor hiring decision cannot affect the wage, so dw d simplifies to w ) w, and we re back to the usual competitive result of MC = w. 4 dw > 0, so d w > 0 and = 0. That means 5)

5 w 1 + dw d w) > w. Since each worker costs more for a monopsonist to hire than it would for a perfectly competitive firm, for a given price monopsonists hire less labor than firms in perfect competition. 4.1 Monopsonist Example et a non-discriminating firm face a perfectly elastic demand curve with a price of \$5 note that saying their demand curve is perfectly elastic is equivalent to saying they face a fixed price that doesn t change with production). Their marginal productivity of labor is constant at 10 Q) = 10), and labor is the only factor of production. They face a labor supply curve equal to s = 8w 32. Find the optimal amount of labor hired and the wage in the market Solution The marginal revenue product of the monopsonist is constant here, since M R = P = 5 and MP = 10. But their marginal cost of labor is changing since with each person they hire, they need to pay all workers a higher wage. To find MC, we first need to construct the cost curve, and then take the derivative of that with respect to labor. The cost curve is the amount of labor hired times the wage, or w. The wage is given by the labor supply function, which we can mess with to get w. = 8w 32 8w = + 32 w = ) 5

6 which means the cost function C) and the marginal cost function MC are C) = 8 + 4) MC ) = dc)) d = ) We can now set marginal revenue product of labor equal to marginal cost of labor 7) and solve for. MRP = MC MP MR = MC 10 5 = = = 184 Plugging that in to 6) gives w = = 27. We can also get quantity produced, since Q) = 10 Q184) = We don t need to calculate price, since that is taken as fixed an is independent of labor hired/quantity produced. A-1 Appendix - Proofs Assuming Decreasing MP No need to worry about learning and memorizing the stuff in this section... this is just for those people that like to have mathematical intuition with their results. Again, I repeat, do not spend your time trying to memorize this. That being said, for those of you that are still reading, I ll continue. If we assume decreasing marginal productivity of labor, we can prove mathematically that monopolists and monopsonists hire less labor than competitive firms under the same wages and prices, respectively). 6

7 A-1.1 Monopolist Given some wage w, let s compare the first order conditions for competitive firm labor demand and the monopolist labor demand. For both, at the optimal equation 1) holds. But for the ) monopolist, the left hand side of 1) is MP P while for the perfectly competitive firm it is MP P. This implies MP monopolist MP monopolist P ) ) = MP competitive = MP competitive P Since ) < 1, it must be that MP monopolist > MP competitive, which implies that for the optimal, monopolist < competitive remember marginal product of labor is decreasing in ). A-1.2 Monopsonist Given some price P, using the FOC for the monopsonist and the fact that MRP competitive MRP monopsonist MP monopsonist 1 + dw d w MP monopsonist = w 1 + dw ) d w monopsonist MP 1 + dw d w P ) = MP competitive P by 2) = MP competitive 1 + dw ) d w P ) = w = w Since ) 1 + dw d w > 1, it must be that at the optimal amount of labor, MP monopsonist > MP competitive. 7

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