Question

Given the following production function with three types of inputs: Q=0.95 0.6 0.3R02 where Q = quantity produced, L = units of labor, K = units of capital and Runits of land. Determine the following when L = 15, K = 11, and R = 7 (1) The production elasticity of labor is (round to the first digit after the decimal) (2) There will be a percentage increase in demand if the capital used in production percentage increases by 5% (round to the first digit after the decimal, do not put percent sign" in the answer.) (3) There will be a percentage increase in demand if the land used in production percentage increases by 10% (round to the first digit after the decimal, do not put "percent sign" in the answer) (4) Considering all of these three types of inputs together, this company exhibits returns to scale. (Fill one of the following words into the blank "increasing" "constant" or "decreasing Do not include quotation marks in your answer)

Answer 1

The production function is Q = 0.95*L^(0.6)*K^(0.3)*R^(0.2)

With this production function, the production elasticity of labor = the power coefficient of L = 0.6

The production elasticity of capital = the power coefficient of K = 0.3

The production elasticity of land = the power coefficient of R = 0.2

(1)

The production elasticity of labor is 0.6

(2)

% increase in the capital = 5%

Hence, the % increase in the demand = production elasticity of capital * % increase in the capital = 0.3*5%

=1.5%

Hence, the correct answer is 1.5

(3)

% increase in the land = 10%

Hence, the %increase in the demand = production elasticity of land * % increase in the land

=0.2*10%

=2%

Hence, the correct answer is 2

(4)

Let L' = xL

K' = xK

R' = xR

Q' = 0.95*L'^(0.6)*K'^(0.3)*R'^(0.2)

=0.95*(xL)^(0.6)*(xK)^(0.3)*(xR)^(0.2)

=x^(0.6 + 0.3 + 0.2)*0.95*L^(0.6)*K^(0.3)*R^(0.2)

=x^(1.1)*0.95*L^(0.6)*K^(0.3)*R^(0.2)

>xQ

Thus, the company exhibit increasing returns to scale.