Reference no: EM131019517

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 - cN^²

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

b. APn = Q/N = a/N + bN/N - CN^² / N

= a/N + b - CN

3. Cubic Short-run

Q = a + bN + cN^² - dN^³

a. MPn = dQ/dN = b + 2cⁿ - 3dN^²

b. APn = Q/N = a/N + bN/N + CN^²/N - dN^³/N

= a/N + b + CN - dN^²