A Firm Has the Following Long- Run Production Function Y

question 5

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.

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Definitions:

Floatation Costs

Expenses incurred by a company when it issues new securities, including underwriting fees, legal fees, and registration fees.

Required Rate of Return

The required rate of return is the minimum annual percentage earned by an investment that will entice individuals or companies to put money into a particular security or project.

Preferred Stock

A class of ownership in a corporation that has a higher claim on its assets and earnings than common stock, usually with fixed dividends.

After-Tax Cost of Debt

The interest expense on debt adjusted for taxes, showing the actual cost of debt financing after considering the tax shield.