Question

Question 4. (20 marks) a. A firm buys inputs K and L at $70 a unit and $30 a unit respectively and faces the production function $Q = 40K^{0.5}L^{0.5}$. What is the cheapest way it can produce 500 units of output? b. Use the Hessian to prove that this is a minimum.

          Question 4. (20 marks)
a. A firm buys inputs K and L at $70 a unit and $30 a unit respectively and faces the
production function $Q = 40K^{0.5}L^{0.5}$. What is the cheapest way it can produce 500 units
of output?
b. Use the Hessian to prove that this is a minimum.

Question 4. (20 marks)
a. A firm buys inputs K and L at 70 a unit and30 a unit respectively and faces the
production function Q = 40K^0.5L^0.5. What is the cheapest way it can produce 500 units
of output?
b. Use the Hessian to prove that this is a minimum.

Added by Dennis P.

Principles of Economics

Gregory Mankiw 8th Edition

Instant Answer

Solved by Expert Suman Saurav Thakur

03/08/2022

Step 1

The cost function can be expressed as C = 70K + 30L, where K is the quantity of input K and L is the quantity of input L. We want to produce 500 units of output, so we have Q = 500. Substituting the production function Q = 40K^0.5L^0.5, we get 500 = Show more…

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a. A firm buys inputs K and L at $70 a unit and $30 a unit respectively and faces the production function Q=40K^0.5L^0.5. What is the cheapest way it can produce 500 units of output? b. Use the Hessian to prove that this is a minimum.