Question

A firm has the production function y=4z₁+10z₂. Input prices are w₁=5 and w₂=6

a) What is the cost minimizing input bundle?
b) What is the minimum cost to produce 500 units of output?

Answer 1

To find the cost minimizing input bundle, we need to determine the optimal combination of inputs that minimizes the cost of production.

Step-by-step explanation:

To find the cost minimizing input bundle, we need to determine the optimal combination of inputs that minimizes the cost of production. In this case, the firm's production function is y=4z₁+10z₂, where y represents the quantity of output, z₁ represents the quantity of input 1, and z₂ represents the quantity of input 2.

To minimize the cost of production, we need to find the values of z₁ and z₂ that satisfy the production function while minimizing the cost function. Since the input prices are w₁=5 and w₂=6, the cost function is C = 5z₁ + 6z₂.

Therefore, we need to solve the production function y=4z₁+10z₂ subject to the cost constraint C = 5z₁ + 6z₂. This can be done by using an optimization technique such as the Lagrange multiplier method or substitution method.