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A Competitive Firm Uses a Single Input X to Produce

question 51

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A competitive firm uses a single input x to produce its output y.The firm's production function is given by y =x3/2 for quantities of x between 0 and 4.For quantities of a greater than 4, the firm's output is y = 4 + x.If the price of the output y is $1 and the price of the input x is $3, how much x should the firm use to maximize its profit?

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Definitions:

Auction

A public sale in which goods or services are sold to the highest bidder.

Total Surplus

The combined total of consumer and producer surplus, indicating the overall net gain to society from producing and consuming goods and services.

Producer Surplus

The difference between what producers are willing to sell a product for and the price they actually receive.

Equilibrium Price

The selling price where the quantity of goods on offer is equal to the quantity consumers want to buy.

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