A Firm Has the Following Long- Run Production Function Y

Essay

A firm has the following long- run production function y = z₁^1/2z₂^1/2
where z₁ and z₂ are the two inputs used in production and y is the output. Let w₁ and w₂ be the input prices.
i)What is the returns to scale of this production function?
ii)Assume both inputs are variable and the input prices are w₁ = 4 and w₂ = 9. The firm minimizes cost. Derive the conditional input demand functions.
iii)Derive an equation for the output expansion path.
iv)Find the firm's long- run total cost function.