Chapter 8. Review: Derive the Long-run Total Cost Curve. A Diagram. Cost Cuves

Transcription

1 hapter 8 ost uves Review: Derive the Long-run Total ost urve To illustrate minimization of the cost of producing a given output for the long run: Plot the isoquant for the given output. Find the isocost line that is closest to the origin, but just touches the isoquant. The cost associated with that isocost line is the minimum cost of producing the given output So we are now able to associate a level of total cost for this output. Repeat for each different level of output. A Diagram K = 20 = 10 = 30 = = 170 = L 1

2 Long-Run Total ost urve Long-run Average and Marginal ost urves Define Average ost and Marginal ost These are functions of : ( ) T A ( ) = ΔT M ( ) = for small Δ Δ Relating T, A, M urves A: The slope of a ray from the origin to a point on the total cost curve gives average cost at that output. M: In the graph of the total cost curve, the slope of the curve at a point (i.e., the slope of a very small interval around the point) is M at that output. 2

3 Long-Run Total ost urve uestion In the previous slide, the slope of the green line measures: A: Average cost of production when 30 units are A: Average cost of production when 15 units are A: Marginal cost of production when 15 units are A: Marginal cost of production when 30 units are uestion In the previous slide, the slope of the green measures: A: Average cost of production when 5 units are A: Average cost of production when 10 units are A: Marginal cost of production when 5 units are A: Marginal cost of production when 10 units are 3

4 Long-Run Total ost urve uestion In the previous slide, the slope of the purple line measures: A: Average cost of production when 30 units are A: Average cost of production when 15 units are A: Marginal cost of production when 15 units are A: Marginal cost of production when 30 units are uestion In the previous slide, the slope of the purple line measures: A: Average cost of production when 30 units are A: Average cost of production when 15 units are A: Marginal cost of production when 15 units are A: Marginal cost of production when 30 units are 4

5 Long-Run Total ost urve uestion In the previous slide, it appears that as output increases, the marginal cost of production: A: Is constant. B: Rises, then falls. : Falls, then rises. D: It is impossible to answer based on the diagram. uestion In the previous slide, it appears that as output increases, the marginal cost of production: A: Is constant. B: Rises, then falls. : Falls, then rises. D: It is impossible to answer based on the diagram. 5

6 Long-Run Total ost urve uestion In the previous slide, it appears that as output increases, the average cost of production: A: Is constant. B: Rises, then falls. : Falls, then rises. D: It is impossible to answer based on the diagram. uestion In the previous slide, it appears that as output increases, the average cost of production: A: Is constant. B: Rises, then falls. : Falls, then rises. D: It is impossible to answer based on the diagram. 6

7 Plotting A and M Functions Because the units are the same, it is possible to plot A and M curves in a single diagram. A and M are both measured in units of $/output-unit. T cannot be plotted with A and M because the units differ (the units for T are $). Both A and T are functions of output. A and M The relationship between A and M curves: When M < A, A is falling. When M > A, A is rising. When M = A, A is at its minimum (neither rising nor falling) A and M: Diagram $/unit M A 7

8 Long-Run Total ost urve B A uestion At which point is marginal cost equal to average cost? A: A B: B : uestion At which point is marginal cost equal to average cost? A: A B: B : 8

9 Review: Derivation of the Short-Run Total ost Function In the short-run, at least one input quantity is fixed Suppose that K is fixed. At each output, ask how much L is needed to produce that output with the fixed level of K. alculate the cost of that (L,K) combination. Short-run Average and Marginal ost urves Short-run average cost and short-run marginal cost are defined in relation to ST in the same way that long-run average and marginal costs were related to the long-run total cost curve. Short-run ost Minimization: Diagram K With capital fixed, find the amount of labor needed to produce a given output, then find the isocost through that point. K 1 = 20 = 10 = 30 L 9

10 Short-Run Total ost urve LRT and SRT Share a Point What about that point? In the preceding diagram, in the short run, we happen to have K fixed at exactly the level that would be chosen in the long run if we were planning to produce 20 units of output. At all other output rates, SRT is above LRT. Short- and Long-Run osts For (almost) any output, it is less costly to produce that output in the long-run scenario Why? Because you can choose the best capital stock for producing that output rather than using a capital stock that you are stuck with. However, for one output level, the capital stock that you are stuck with in the short-run happens to be at the same level you would choose in the long-run. For this output level, short-run total cost and long-run cost take on the same value. 10

11 Short- and Long-Run Total osts The long-run total cost curve is the lower envelope of the family of short-run total cost curves. Short-Run Total ost urve Short-Run Total ost urve 11

12 Short-Run Total ost urve Short- and Long-Run Average osts The long-run average cost curve is the lower envelope of the family of short-run average cost curves. Short- and Long-Run Average osts 12

13 Short-run and Long-run Marginal osts Explaining the Preceding Diagram Plot a diagram showing long-run average cost and the family of short-run average cost curves. Draw short-run marginal cost curves also. At the output rates where short-run A curves share a point with the long-run A, short-run M also contributes a point to longrun marginal cost. Shifting ost urves When input prices change, cost curves shift (higher input prices generally raise costs of production). 13

14 Fixed and Variable osts in the Short-run In the short run, it is possible to break down total costs into fixed and variable costs: ST = TF + TV Dividing each term above by : ST TF TV = + SA = AF + AV Economies of Scale onsider the long-run average total cost curve: Where A is downward sloping, we have economies of scale (the elasticity of total cost with respect to output is less than one). Where A is upward sloping, we have diseconomies of scale (the elasticity of total cost with respect to output is greater than one). Where A is flat, we have neither economies nor diseconomies of scale (the elasticity of total cost with respect to output is equal to one). Elasticity of total cost with respect to output Show that the elasticity of total cost with respect to output is the ratio of marginal cost to average cost: ΔT T Δ ΔT ΔT Δ M = = = Δ T T A 14

15 Economies of Scope Economies of Scope exist when: (, ) < ( ) + ( ) T T T More on osts Learning by Doing may result in lowering of cost curves over time Note: We have been looking at a static cost curve relevant for a particular period, not at how costs might change over time. Empirically Estimated ost Functions: Skip section 8.5 (pp ). Notation Summary (Define These!) T A M ST TV TF SA AV AF SM 15

16 The End 16