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

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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
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The Firm’s Profit-Maximization Prob- lem Firm 0 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 0 s Revenue = p o q Firm 0 s Total Costs = j = n X j =1 p j i j + FC 2
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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 0 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
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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
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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 0 ∂F ( K, L ) ∂K marginal revenue product of labor: p 0 ∂F ( K, L ) ∂L MRTS = - dK dL = F L ( K, L ) F K ( K, L ) 5
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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 0 ∂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 . 6
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Steps in the solutions of the firm’s maximization problem: (i) Solve the system of the n first-order conditions (by substitution) to derive the optimal inputs (ii) Put the optimal inputs back into the production function to compute the opti- mal output.
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