Formula sheet exam1 draft 1 summer 2016 PDF

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Formula sheet exam 1...

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ECN 303

FORMULA SHEET EXAM I

Marginal Product of Labor:

𝑀𝑃𝐿 =

∆𝐿

Average Product of Labor:

𝐴𝑃𝐿 =

𝐿

∆𝑄

𝐴𝑃𝐾 =

𝜕𝑄

=

𝜕𝐿

𝑄

Marginal Product of Capital: 𝑀𝑃𝐾 = Average Product of Capital:

DRAFT

∆𝑄

𝜕𝑄

=

∆𝐾

𝜕𝐾

𝑄

𝐾

Power Function Rule: Given 𝑦 = 𝑎𝑥 𝑏 , where a and b are constants, the first derivative of y is 𝑑𝑦 = 𝑏𝑎𝑥 𝑏−1 𝑑𝑥 Rules of Exponents: i.) 𝑥 𝑎 𝑥 𝑏 = 𝑥 𝑎+𝑏 %∆𝑋 =

Percent Change in X:

ii.) (𝑥 𝑎 )𝑏 = 𝑥 𝑎𝑏 iii.) 𝑥 𝑎 𝑦 𝑎 = (𝑥𝑦)𝑎 𝑋1 −𝑋0

1

𝑥𝑎

× 100

𝑋0

𝑀𝑅𝑇𝑆 =

Marginal Rate of Technical Substitution: Linear Production Function:

iv.) 𝑥 −𝑎 =

𝑀𝑃𝐿

𝑀𝑃𝐾

𝑄 = 𝛼𝑋1 + 𝛽𝑋2 , where X1 and X2 are inputs and 𝛼 and 𝛽 are constants 𝑄 = 𝐴𝐿𝛼 𝐾𝛽 , where A, 𝛼 , and 𝛽 are constants.

Cobb-Douglas Production Function:

Cobb-Douglas Marginal Products: 𝑀𝑃𝐿 = 𝛼𝐴𝑃𝐿 , 𝑀𝑃𝐾 = 𝛽𝐴𝑃𝐾 𝛼

𝐾

Cobb-Douglas MRTS: 𝑀𝑅𝑇𝑆 = ( ) × ( 𝐿 ) 𝛽 Returns to Scale Elasticity: 𝑅𝑇𝑆𝜖 = Isocost Equation:

𝑇𝐶

%∆𝑄

%∆𝑖𝑛 𝑎𝑙𝑙 𝑖𝑛𝑝𝑢𝑡𝑠

𝑤

𝐾 = 𝑟 0 − ( 𝑟 ) 𝐿 , where 𝑇𝐶0 is a fixed value of total cost and w and r are the unit prices of labor and capital respectively

Input Substitution Effects: Long Run Average Cost: Long Run Marginal Cost:

∆𝐿 = 𝐿1 − 𝐿0 𝐴𝐶 = 𝑀𝐶 =

∆𝐾 = 𝐾1 − 𝐾0

𝐿𝑅𝑇𝐶 𝑄

∆𝐿𝑅𝑇𝐶 ∆𝑄

=

𝑑𝐿𝑅𝑇𝐶 𝑑𝑄...