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Unformatted text preview: ch 10: COSTS 1 Cost function Derivation of the cost function mathematically and graphically Some more concepts associated with costs Total fixed cost and total variable cost Average fixed cost and average variable cost Marginal cost Short run vs long run costs ch 10: COSTS 2 What does the cost of production depends on? Level of output The factor prices (prices of inputs) The type of production technology Efficiency of production Naturally a cost function is one that somehow relates all of the above. Definition: It is a function C(q, w K , w L ) that relates the minimum costs C to a given output amount q. Note minimum costs C to a given output, implying an efficient relation between C and q. ch 10: COSTS 3 Mathematically We obtain the cost function by solving the cost minimization problem: such that In words: choose the inputs so as to minimize the costs to produce an output q at given prices of labor and capital. Again, use Lagrange multipliers to solve Let K*(q) and L*(q) be the solutions to the cost minimization problem for output level q The cost function is C(q)= w K K* (q) + w L L* (q) This is the socalled longrun cost function ch 10: COSTS 4 ) , ( m i n , L K f q L w K w L K L K Graphically solving the cost minimization problem....
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 Spring '11
 Beryl Li
 Macroeconomics

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