Suppose the Production Function for Widgets Is Given by Y

question 57

Essay

Suppose the production function for widgets is given by Y = KL - 0.8K² - 0.2L² where Y represents the annual quantity of widgets produced, K represents annual capital input, and L represents annual labour input.
i)Supposing K = 10, graph the total and average product of labour curves. At what level of labour input does this average product reach a maximum? How many widgets are produced at that point?
ii)Again assuming that K = 10 graph the marginal product of labour (MPL)curve. At what level of labour input does MPL = 0?
iii)Suppose that the capital inputs were increased to K = 20. How would your answers to parts a and b change?

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Definitions:

Preferred Stock

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

Net Income

The total profit or loss of a business after all expenses, including taxes and operating costs, have been deducted from total revenue.

Common Stock

A type of equity security that represents ownership in a corporation, giving the shareholder voting rights and a share in the company’s profits through dividends.

Dividends

Payments made by a corporation to its shareholder members, typically derived from the company's profits.