class handout

class handout - MRTS = L K We need to substitute for K...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Class Handout (October 2) 100B, Prof. Jacobsen 1. Suppose that q = f ( L , K ) = L 2 + K 2 ( ) 1 2 , and q = 20, and K = 16 (in the short run). a. Find the amount of labor, L , employed by the firm. L = 12 b. Calculate the marginal product of labor. Does the production function satisfy diminishing marginal returns to labor? MP L = L L 2 + K 2 ( ) 1/2 The function does not satisfy diminishing marginal returns to labor: ! MP L ! L = K 2 L 2 + K 2 ( ) 3/2 > 0 c. Derive the marginal rate of technical substitution (MRTS) in the long run ( K is no longer fixed at 16). MRTS = ! L K
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
d. Does the production function have a diminishing |MRTS|? Take absolute value first:
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MRTS = L K We need to substitute for K (because it is a function of L along an isoquant). From the definition of an isoquant: q = L 2 + K 2 ( ) 1/2 q 2 = L 2 + K 2 K = q 2 ! L 2 ( ) 1/2 Substituting: MRTS = L q 2 ! L 2 ( ) 1/2 ! MRTS ! L = q 2 q 2 " L 2 ( ) 3/2 > This function does not have a diminishing |MRTS|. The isoquants are concave: e. Does the production function satisfy increasing returns to scale, constant returns to scale, or decreasing returns to scale? The function is constant returns to scale....
View Full Document

This note was uploaded on 08/09/2009 for the course ECON 100B taught by Professor Rauch during the Winter '07 term at UCSD.

Page1 / 2

class handout - MRTS = L K We need to substitute for K...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online