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