Answer to Question #143603 in Microeconomics for Ananya

Question

For the production function given by q=e^0.3tK^0.75L^0.25 where the technical coefficient is denoted by e^0.3t. Both K and L grow at the rate at 1% per annum each, compute the annual growth rate of output

Answer 1

q=$e^{0.3t}*K^{0.75}*L^{0.25}$

technical coefficient = e^0.3t

growth in K

$K\times * \frac{101}{100}$ = 1.01K

$L\times * \frac{1.01}{100}$ = 1.01L

$qc=e^{0.3t}\times(1.01K^{0.75}\times1.01L^{0.25}$

q_c=$e^{0.3t}*1.007491K^{0.75}*1.007491L^{0.25}$

$qc=e^{0.3t}\times 1.015037K^{0.75}L^{0.25}$

annual change = $[\frac{(qc – q)}q]\times100$

annual change = $e^{0.3t}\times1.015037K^{0.75}L^{0.25} - e^{0.3t}\times K^{0.75}L^{0.25}/ e^{0.3t}K^{0.75}L^{0.25}$

annual change = $\frac{e^{0.3t}\times K^{0.75}L^{0.25}(1.015037-1)}{e^{0.3t} \times K^{0.75}L^{0.25}(1)}$

annual change = $0.015037\times100 = 1.50\%$