Topic 1 - Summary of Key Production, Cost, and Profit Maximization Concepts

Production Function

input-output relationship [Q=f(K, L)]

Marginal Physical Product (MP)

partial derivative of Q with respect to K or L

Average Product (AP)

Quantity over K or L

Law of Diminishing Marginal Productivity

the additional quantity produced by using an additional unit of the input increases until it reaches a peak then decreases

Isoquant

locus of points, each point representing a

combination of inputs which yields the

same level of output

Marginal Rate of Technical Substitution

negative of the slope of the isoquant

Marginal Rate of Technical Substitution Formula

Marginal Product of L over Marginal Product of K

Isocost

locus of points, each point representing a

combination of inputs that a firm can

purchase at the same time given its budget

Total Cost Function

C = wL + rK

Tangency Condition

slope of the isocost = slope of the isoquant

slope of isocost

-w/r

Profit Maximizing Condition

MR=MC

Is cost minimization equivalent to Profit Maximization?

Both cost min and prof max require L*, K*, and C*. Profit max requires Q*. This means that by maximizing profit, costs are automatically being minimized, but the opposite may not be true.