380 L14-Profits

# 380 L14-Profits - Profits Profit π is defined by(1 Pq vk...

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Unformatted text preview: Profits Profit, π , is defined by (1) ( , ) Pq vk wl Pf k l vk wl π =-- =-- where P is price of output and all other notation should be clearly in mind from cost minimization. The first term to the right of = is total revenue while the other terms accumulate costs. Again (1) is an accounting identity and isn’t the focus of economists which is , (2) ( , , ) max k l P v w Pq vk wl π π = =-- . That is, (2) is a theory of behavior. Firms strive to maximize profits by choosing the right amount of capital and labor to hire. Presumably there is an even harder and more serious problem behind (2) which is deciding which product to produce (the one where profit is highest for specialized firms). It is easily discussed but we will focus on (2) for now. Besides leaving dynamic issues aside, a related issue is that (2) says nothing about uncertainty. Firms know prices, and the production function (technology). Profit Maximizing Input Choice Directly for a Competitive Firm (P is taken as fixed) The first order conditions associated with (2) are: (3) f P v k k π ∂ ∂ =- = ∂ ∂ (4) f P w l l π ∂ ∂ =- = ∂ ∂ . The first term is the marginal contribution to revenue of the input and represents a marginal benefit to the firm. It is variously called marginal revenue product or as I prefer the value of the marginal product. The second is the marginal factor cost or price of the input. Second order conditions are satisfied if production is concave in inputs for a unique maximum. This requires diminishing marginal product: 0; k l MP MP k l ∂ ∂ < < ∂ ∂ . By solving (3) and (4), we obtain factor demands * * ( , , ), and ( , , ) k P v w l P v w . These are the profit maximizing choice of inputs. Supply is determined as * * * ( , ) q f k l = . Graph. Example 1: I’ll illustrate this with a single input and a production function q l = . First order conditions are: 2 .5 * (4 ') .5 , , , 2 P P l w or l w- = = and supply is * 2 ( /2 ) 2 P q P w w = = . So how much labor demand will there be if P=10 and w=1. How would the problem above be amended to include a fixed input, where , 9 q k l k = = ?...
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380 L14-Profits - Profits Profit π is defined by(1 Pq vk...

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