Factor Demands x As the last two questions might lead you to believe, the marginal value of labor is what guides hiring decisions for a competitive price taking firm. The marginal product of labor MPL tells us how many more physical units of output we can expect by hiring one more unit of labor. If we multiply this by the price of a unit of output P (measured in dollars per unit of output) we arrive at the marginal value product of labor MVPL = P . MPL(K, L) On competitive markets, pricetaking profit maximizing firms will want to hire a new worker workers so long as the marginal value product of labor (how much new value or revenues the hired worker generates for the firm) exceeds the cost of hiring that worker which will be equal to the wage. If you look again at the geogebra app above above and you click on the 'Hire' checkbox you'll see the right panel look something like this: 3 Cli.lp_ 4\"! :1)' AIPL(L7 1") 25 15 O5 Since this is a competitive pricetaking firm it takes both the price at which it sells output (here P = 1dollar/unit, A = 1, and K = 16) as well as the wage and rental rate at which it hires its labor and capital as given. As drawn, the firm is facing a competive wage of w : $1.00 per hour of labor. The firm can hire as many workers as it wants at that wage so we think of the firm as if it were facing a perfecly elastic or horizontal supply of labor at that wage. It should now be clear that the downward sloping marginal value product of labor curve is the competitive firm's demand for labor. To see this think of the firm that has so far hired L : 2 workers and is contemplating the hiring a third worker. It's easy to verify that if the firm were to hire that third worker their marginal value product would be $1.15 per hour. That's the amount by which they would increase firm revenues. Hiring that worker costs only $1 per hour so hiring a third worker increases firm profits by $0.15 per hour, so it's worth hiring that worker. The firm will keep increasing the number of workers hired we will allow the firm to hire fractional number of hours of work. As you can see from the diagram when the firm hires 4 hours of labor the marginal value product of the last worker hired is exactly $1 which is what it costs to hire the last fractional unit. The firm will not hire more workers, because the next hour hired will have a marginal value product below the $1 it costs to hire it. Similarly the firm won't hire any less than 4 workers because, as we just saw, profits could be increased from there.. In summary we find the labor hired by the competitive firm at the point where its marginal value product of labor line (it's demand for labor curve intersects the horizontal labor supply line. Graph 23 On the bottom half of the page draw a graph of marginal value product of laborjust like the diagram above. Label the curve LD for labor demand. Clearly label the axes. The horizontal should be labeled hours of work and the vertical can be measured in $/hour G] SFM104 Review Suppose A21, P21, and K216. Suppose that the labor wage falls from w=$1 per hour to w=$0.50 dollars per hour. How many workers will the firm now hire? Use the geogebra app (or work through the math) to find it. A 1 B 4 \\/ 16 Correct answer D 64 Graph 2.b On top of the same graph that you just drew, draw the entire new labor demand X curve (marginal value product of labor curve) that would result if we increased capital at this firm from K = 10 to K = 25. Assume A : 1, P : l, and w : 1 as before. Label the new curve L'D SFN105 Review When K=10 and w=1 the firm wanted to hire L=4 hours of work. How many hours of work does the firm want to hire when K rises to K=25. Enter a number only to indicate the number of hours the firm would want to hire (with decimals) 6.25 Correct answer O Check My Answer Graph 2.c Draw in indicator lines to show the number of hours the firm now hires