Answer to Question #220799 in Microeconomics for Geeorge Ben

Question

Question 1: A producer has a production function Q= 5K^0.7 L^0.5 and buys K at $12 a unit and L at $9 a unit. What input combination will minimize the cost of producing 190 units of output, and hence determine the Total Cost?

Question 2: A firm has a budget of $350 to spend on the three inputs X, Y, and Z whose prices per unit are $4, $2 and $5 respectively. What combination of X, Y and Z should it employ to maximize output if it faces the production function Q= 24X^0.3Y^0.2Z^0.3

Also calculate the maximum output of the firm.

Answer 1

+ L = 30

K*L = 45

L = 30

-

5K

K*(30

—

5K) = 45

5K^2

—

30K + 45 = 0

K^2

—

6K + 9 = 0

(K

—

3)^2 = 0

K = 3 units

L = 15 unit