How to Derive Aggregate Labor Demand Curve
A labor market uses the concepts of supply and demand in a different way than a market for goods or services. In a labor market, different households supply labor, and firms demand it. Labor supply and demand curves can be graphed in an X-Y graph, with the X-axis representing the number of laborers and the Y-axis representing the real hourly wage, which is a measure of the amount of goods a laborer can purchase with his hourly earnings. An aggregate labor supply, or NS, curve provides graphic information on how many people in the labor force are willing to work at a job for at each of a range of real hourly wages. The NS curve has an upward slope because typically, the higher a job’s hourly wage, the more people want to work at that job. An aggregate labor demand, or ND, curve shows how many workers a firm wants to hire at each of a range of real hourly ranges. The ND curve slopes downward because as the hourly wage for a job increases, the fewer the workers the firm will be able to hire if it wants its work force to earn the firm more money than they cost the firm to employ. If you want to graph an ND curve for a labor market, then you can derive the requisite information from the principle that the marginal product of labor is equivalent to the real wage in equilibrium. The real wage in equilibrium is the point on the X-Y axis graph at which the ND curve intersects the NS curve.
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Instructions
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Familiarize yourself with the following terms and acronyms: marginal product of labor, or MPN; aggregate employment, or "N"; real wage in equilibrium, or "W"; aggregate supply of labor, or NS; and aggregate demand of labor, or ND.
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Consider, for example, that MPN = 200 - 0.5N, and NS = 300 + 8W.
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Understand that MPN = W. This is the key equation from which you will be able to derive the ND curve.
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Set up the following equation: W = 200 - 0.5N. Solve for N to find that N = 400 - 2W. Remember that equation W = 200 - .5N is valid because MPN = W and MPN = 200 - 0.5N.
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Understand that N = ND in this scenario. As such, set up the equation ND = 400 - 2W.
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Find the exact values for N and W for the labor equilibrium by setting up an equation in which ND = NS. The equation will read as follows: 400 - 2W = 300 + 8W. Solve for W to find that W = 10.
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Input a value of 10 for W in the equation N = 400 - 2W. Solve for N to find that N = 380.
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Conclude that the labor market equilibrium occurs in the market when the wage is 10 and labor is 380. Graph the coordinates (380, 10) on your X-Y chart to see where ND and SD intercept.
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Graph additional points on the ND curve. Note that when you enter a value of 300 for N in the equation N = 400 – 2W, W has a value of 50. Plot the point (300, 50) on your X-Y axis graph. Enter a value of 390 for N in the equation N = 400 – 2W, which will yield a value of 5 for labor. Plot the point (390, 5) on your X-Y axis graph. Draw a straight line between the points (300, 5) and (390, 5) to see a graphical rendering of the ND curve.
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Tips & Warnings
Use traditional graphing paper with 20 squares per inch to create a more accurate graph and prevent careless errors.
When simplifying or solving the algebraic equations to derive the ND, make sure to double-check your work and use the order of operations and proper distribution methods for combing polynomials. It only takes one computation error to skew your entire graph and resulting analysis.
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