ECN 303 FORMULA SHEET
Marginal Product of Labor:
๐๐๐ฟ=โ๐
โ๐ฟ =๐๐
๐๐ฟ
Average Product of Labor:
๐ด๐๐ฟ=๐
๐ฟ
Marginal Product of Capital:
๐๐๐พ=โ๐
โ๐พ =๐๐
๐๐พ
Average Product of Capital:
๐ด๐๐พ=๐
๐พ
Power Function Rule of Calculus : Given ๐ฆ = ๐๐ฅ๐, where a and b are constants, the first
derivative of y is ๐๐ฆ
๐๐ฅ =๐๐๐ฅ๐โ1
Addition Rule of Calculus: Given ๐ฆ = ๐(๐ฅ)+ ๐(๐ฅ),
๐๐ฆ
๐๐ฅ =๐๐
๐๐ฅ +๐๐
๐๐ฅ
Multiplication Rule of Calculus: Given ๐ฆ = ๐(๐ฅ)๐(๐ฅ),
๐๐ฆ
๐๐ฅ = ๐ ๐๐
๐๐ฅ + ๐ ๐๐
๐๐ฅ
Rules of Exponents: i.) ๐ฅ๐๐ฅ๐= ๐ฅ๐+๐ ii.) (๐ฅ๐)๐= ๐ฅ๐๐ iii.) ๐ฅ๐๐ฆ๐= (๐ฅ๐ฆ)๐ iv.) ๐ฅโ๐ =1
๐ฅ๐
Percent Change in X: %โ๐ = ๐1โ๐0
๐0ร100
Marginal Rate of Technical Substitution: ๐๐
๐๐ = ๐๐๐ฟ
๐๐๐พ
Linear Production Function: ๐ = ๐ผ๐1+ ๐ฝ๐2, where X1 and X2 are inputs and ๐ผ and ๐ฝ are
constants
Cobb-Douglas Production Function: ๐ = ๐ด๐ฟ๐ผ๐พ๐ฝ, where A, ๐ผ, and ๐ฝ are constants.
