Lecture_17_Cost_Curves

Lecture_17_Cost_Curves - Lecture 17: Cost Curves c...

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Unformatted text preview: Lecture 17: Cost Curves c & 2008 Je/rey A. Miron Outline 1. Introduction 2. Average Costs in the Short Run 3. Marginal Costs 4. Example 5. Long-Run Costs 6. Discrete Levels of Plan Size 7. Long-Run Marginal Costs 8. Example 9. Short-Run versus Long-Run Costs, One More Time 1 Introduction We have examined the cost-minimizing behavior of a &rm, focusing on the algebra of cost functions and factor demand functions. Now we turn to a graphical presentation, which will supplement the algebra we have done already. 1 2 Average Costs in the Short Run So far we have written the cost function in general terms: c ( w 1 ; w 2 ; y ) From here on, we usually take input prices as given, so it is convenient to simply write costs as a function of y : c ( y ) The input prices are still there, but in the background. We want to focus on under- standing the shape of the cost function, i.e., how costs change as the level of output changes. We start with the short-run, taking one factor as &xed. To avoid confusion, it is useful to include this &xed factor as an explicit argument in the cost function. Thus, whenever you want to emphasize that you are using the short run cost function, write things like c s ( y; k ) or MC ( y; k ) . To characterize the shape of cost functions, we &rst note that some costs are independent of the level of output, i.e., they are &xed, while other costs change with the amount of output produced, i.e., they are variable. Total costs can therefore be written as c ( y; k ) = c v ( y; k ) + F and the graph looks like this: 2 Graph: A Cost Function y = x 2 = 6 + 3 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 y c( ) c(y,k) Two key things to note. First, in the short-run, costs can be strictly positive at a zero level of output. Second, the cost curve can rise linearly, less than linearly, or more than linearly. For most purposes, it is useful to work with something other than the total cost curve. The reason is that we want to focus on magnitudes that are comparable to price, which is measured on a per unit basis. The relevant concepts turn out to be average costs and marginal costs. The reason to focus on this is not totally obvious yet. Intuitively, however, it makes sense that the average cost of any good should bear some relation, in equilibrium, to its price. Thus, this aspect of the cost function is a useful way to summarize it. Something similar holds for marginal cost. So, we next consider the average cost function, the average variable cost function, and the average &xed cost function. Speci&cally, we consider AC ( y; k ) = c ( y; k ) y = c v ( y; k ) y + F y = AV C ( y; k ) + AFC ( y; k ) 3 What do these functions look like? The average &xed cost function starts at in&nity when y = 0 and goes to zero as y goes to in&nity: 4 Graph: Average Fixed Costs y = 3 =x 1 2 3 4 5 6 7 8 9 1 2 3 4 5 6 7 8 9 y c( ) AFC The average variable cost function is likely to have the following shape: 5 Graph: Average Variable Costs y = ( x & 5) 2 = 2 + 2 1 2 3 4 5 6 7 8...
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Lecture_17_Cost_Curves - Lecture 17: Cost Curves c...

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