Question 7 You produce shoes (Q) with labor (L) and capital (K). The production process is as so: Q = 400L - 20L2 +...

Question

Question

business economics

Add a comment Improve this question Transcribed image text

Answer 1

Answer #1

Answer

A firm hires both inputs at equal marginal product per dollar

$\frac{MPL}{wage}=\frac{MPK}{r}$

$MPL=\frac{\partial Q}{\partial L}=\frac{\partial \left ( 400L-20L^2+600K-10K^2 \right )}{\partial L}=400-40L\\ MPL=\frac{\partial Q}{\partial K}=\frac{\partial \left ( 400L-20L^2+600K-10K^2 \right )}{\partial K}=600-20K\\ \frac{400-40L}{20}=20-2L=\frac{600-20K}{30}=20-\frac{2}{3}K\\ 20-2L=20-\frac{2}{3}K\\ L=\frac{1}{3}K\\ from\ cost\\ wL+rK=TC\\ 20L+30K=550\\ 20*\frac{1}{3}K+30K=550\\ \frac{110}{3}K=550\\ K=15$

the frim should hire 15 units of capital.

Add a comment

Answer 2

Question 7 You produce shoes (Q) with labor (L) and capital (K). The production process is as so: Q = 400L - 20L2 +...

Homework Answers

Add Answer to:
Question 7 You produce shoes (Q) with labor (L) and capital (K). The production process is as so: Q = 400L - 20L2 +...

Post as a guest

Earn Coins