# 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 ½

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 - cN²

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

b. APn = Q/N = a/N + bN/N - CN² / N

= a/N + b - CN

3. Cubic Short-run

Q = a + bN + cN² - dN³

a. MPn = dQ/dN = b + 2cⁿ - 3dN²

b. APn = Q/N = a/N + bN/N + CN²/N - dN³/N

= a/N + b + CN - dN²

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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.

Marginal Products and Average Products

The number of repairs produced by a computer repair shop depends on the number of workers as follows:

#of Workers #of Repairs

0 0

1 8

2 20

3 35

4 45

5 52

6 57

7 60

Assume that all inputs other than labor are fixed in the short run.

a)Add 2 additional columns to the table, and enter the marginal product and average product for each number of workers

b)Over what range of labor input are there increasing returns to labor? Diminishing returns to labor? Negative returns to labor?

c) Over what range of labor input is marginal product greater than average product? What is happening to average product as employment increases over this range?

d)Over what range of labor input is marginal product smaller than average product? What is happening to average product as employment increases over this range?

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