A firm has the following long- run production function y = z₁^1/2z₂^1/2
where z₁and z₂are the two inputs used in production and y is the output. Let w₁and w₂be 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.

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The Answer of A firm has the following long- run production function y = z₁^1/2z₂^1/2 where z₁and z₂are the two inputs used in production and y is the output. Let w₁and w₂be 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.

A Firm Has the Following Long- Run Production Function Y