301lec10

301lec10 - Microeconomics 301 Department of Economics UBC...

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Unformatted text preview: Microeconomics 301 Department of Economics UBC Winter 2008 Production Theory and Firm’s Optimal Decisions Topics: Profit maximization Costs of Production Total costs, variable costs, marginal costs, fixed costs Long-Run and Short-Run Cost Curves Production Decision, shut down. 1 The Firm’s Profit-Maximization Prob- lem Firm s profits = Revenue- Total Costs • The firm uses inputs i 1 ,...,i m and also incurs the fixed cost FC to start up produc- tion (building, land for production factory, road, licenses, etc.) • The price of output is p o and prices of inputs are p 1 ,...,p m . The firm has no effect on prices: it is small compared to the market. Firm s Revenue = p o q Firm s Total Costs = j = n X j =1 p j i j + FC 2 Then the firm’s profit-maximization prob- lem is: Choose inputs to: max i 1 ,...,i n p o q- j = n X j =1 p j i j- FC = p F ( i 1 ,...,i j ,...,i n )- j = n X j =1 p j i j- FC (1) ∑ j = n j =1 p j i j = V C is the firm’s variable cost FC is fixed cost. There is a distinction between sunk and non-sunk fixed cost. 3 Costs Very important concepts. All informa- tion about production function is contained in the cost function. Important issues: • Account for all inputs. Opportunity cost of an input: its value in the second- best use. • Allocate inputs to variable and fixed costs correctly. Some costs vary with output. These are variable costs. Other costs remain the same no mat- ter the amount of output. These are fixed costs. 4 We will typically deal with two inputs: capital K and labor L . Sometimes, we will add technology A . Then, we have F ( K,L ) or F ( K,L,A ). • Two input case: F ( K,L ). marginal revenue product of capital: p ∂F ( K,L ) ∂K marginal revenue product of labor: p ∂F ( K,L ) ∂L MRTS =- dK dL = F L ( K,L ) F K ( K,L ) 5 Solving the Firm’s Profit-Maximization Problem max i 1 ,...,i n π = p o q- j = n X j =1 p j i j- FC p o F ( i 1 ,...,i j ,...,i n )- j = n X j =1 p j i j- FC First-order conditions are: p ∂F ( i 1 ,...,i j ,...,i n ) ∂i j = p j The first-order condition can be stated in words as: at the optimum, marginal revenue product of each input must be equal to marginal cost of this input ....
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This note was uploaded on 01/28/2011 for the course ECON 301 taught by Professor Chapple during the Spring '08 term at UBC.

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301lec10 - Microeconomics 301 Department of Economics UBC...

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