# computing marginal product and average product of labor

Given algebraic equations, need to graph the marginal product and average product for linear short-run, quadratic short-run, and cubic short-run production functions. Plug in numbers to graph. See attachment.Thank you.

Production Functions (Algebraic)

Graph the marginal product (MP) and average product (AP) for each of the following equations by plugging in numbers. (Graph the highlighted equations).

1. Linear Short-run. N = labor

a. MP n = the change in output / the change in labor

= dQ / dN = b

b. AP n = Q / N = a/N + bN/N

= a/N + b

Example: Supppose b = 10 10 + 5/1 = 15

a= 5 10 + 5/2 = 12 Â½

N = 1 10 + 5/3 = 11 2/3

Make Y-axis Q (output) and X-axis N (labor) and graph.

2. Quadratic Short-run

Q = a + bN - cNÂ²

a. MPn = dQ/dN = b - 2cN

b. APn = Q/N = a/N + bN/N - CNÂ² / N

= a/N + b - CN

3. Cubic Short-run

Q = a + bN + cNÂ² - dNÂ³

a. MPn = dQ/dN = b + 2cⁿ - 3dNÂ²

b. APn = Q/N = a/N + bN/N + CNÂ²/N - dNÂ³/N

= a/N + b + CN - dNÂ²

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#### Solution Preview

See attached excel and word document for explanation. Essentially you are starting with a production function of various forms. Linear, Quadratic, or a ...

#### Solution Summary

Given three different production functions (linear, quadratic, cubic) I derive the marginal product of labor and the average product of labor. the results are then graphed and discussed.