HW-4-soln

HW-4-soln - Economics 101: problem set 4 solutions 1. Total...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Economics 101: problem set 4 solutions 1. Total capital is K = 4 and total labor is L = 25. Production functions are x = K 1 2 x L 1 2 x y = K 1 2 y L 1 2 y Find and sketch the production possibility frontier. Solution: in this setup, if K x is the level of capital allocated to the production of good x , K- K x = K y = 4- K x will be the level of capital allocated to the production of good y . Similarly, if L x is the level of labor allocated to the production of good x , L- L x = L y = 25- L x will be the level of labor allocated to the production of good y . Recall that along the production possibility frontier, RTS x = RTS y . We may then compute RTS x =- MPL x MPK x =- x L x x K x = 1 2 K 1 2 x L- 1 2 x 1 2 K- 1 2 x L 1 2 x = K x L x Since the calculations for RTS y will be identical, we know as well that RTS y = K y L y . Then the production possibility frontier is defined by K x L x = K y L y . Equating the rates of technological substitution we obtain RTS x = RTS y K x L x = K y L y K x L x = 4- K x 25- L x K x (25- L x ) = L x (4- K x ) L x = 25 4 K x Then we have x = 5 2 K x = 2 5 L x This is the same as K x = 2 5 x L x = 5 2 x Then for y , we find y = 4- 2 5 x 1 2 25- 5 2 x 1 2 = 10 1- 1 10 x 1 2 1- 1 10 x 1 2 = 10- x March 1, 2011 1 Economics 101: problem set 4 solutions With this, we have a neat closed form of our production possibility frontier, y = 10- x . Graphically, this is seen in Figure 1 2 4 6 8 10 2 4 6 8 10 Production possibility frontier x y Figure 1: production possibility frontier for question 1 2. Total capital is K = 4 and total labor is L = 25. Production functions are x = K 2 3 x L 1 3 x y = K 1 3 y L 2 3 y Find and sketch the production possibility frontier....
View Full Document

This note was uploaded on 10/23/2011 for the course ECON 101 taught by Professor Buddin during the Winter '08 term at UCLA.

Page1 / 16

HW-4-soln - Economics 101: problem set 4 solutions 1. Total...

This preview shows document pages 1 - 3. Sign up to view the full document.

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