Answer to Question #307798 in Microeconomics for lydia

Question

Given the Cobb - Douglas production q1 = 50l0.3K0.5,q2 = 50L0.4K0.6,and q3 =50l0.5K0.6..Calculate the level of output when L = 10 and K = 15 for each production function.. Calculate the level of output when both inputs double L = 20 and K =30...What types of returns to scale does each production function exhibit

Answer 1

$Q_1=50L^{0.3}K^{0.5}$

$Q_2=50L^{0.4}K^{0.6}$

$Q_3=50L^{0.5}K^{0.6}$

Level of output When;

L=10 and K=15

$Q_1=50\times 10^{0.3}\times 15^{0.5}$

$=386.38$

$Q_1=50\times 10^{0.4}\times 15^{0.6}$

$=637.71$

$Q_1=50\times 10^{0.5}\times 15^{0.6}$

$=802.83$

The level of output when both inputs double L = 20 and K =30

$Q_1=50\times 20^{0.3}\times 30^{0.5}$

$=672.73$

$Q_2=50\times 20^{0.4}\times 30^{0.6}$

$=1,275.42$

$Q_3=50\times 20^{0.5}\times 30^{0.6}$

$=1,720.91$

 Returns to scale do each production function exhibit;

Q₁- 0.8 is <1 Hence the production function exhibits decreasing return to scale.

Q₂ - 1=1 Hence the production function exhibits decreasing return to scale.

Q₃- 1.1 is >1 Hence the production function exhibits increasing return to scale.