15. Cost curves.pdf - Long-run Cost Curves Short-run cost curves Scope and Learning Economies Economics Lecture 15 Firm theory Costs Curves Anna

15. Cost curves.pdf - Long-run Cost Curves Short-run cost...

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Long-run Cost Curves Short-run cost curves Scope and Learning Economies Economics - Lecture 15 Firm theory Costs Curves Anna D’Ambrosio Polytechnic of Turin Chapter 8, Besanko & Braeutigam, Microeconomics , 4th Edition 1 / 36
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Long-run Cost Curves Short-run cost curves Scope and Learning Economies Costs Curves 1 Long-run Cost Curves 2 Short-run cost curves 3 Scope and Learning Economies 2 / 36
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Long-run Cost Curves Short-run cost curves Scope and Learning Economies Long-run total cost curves Comparative statics allow studying how the optimal input combination changes by changes in the input prices. We can also study how the minimized total costs TC change when changing the target output q . Suppose a firm wants to increase output from 1 to 2 million units per year: TC will go up (necessarily!) 3 / 36
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Long-run Cost Curves Short-run cost curves Scope and Learning Economies Long-run total cost curves The long-run total cost curve shows how minimized cost varies with output Because the cost-minimizing input combination moves us to higher isocost lines, the long-run total cost curve must be increasing in q In the long run, by q = 0, TC = 0 4 / 36
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Long-run Cost Curves Short-run cost curves Scope and Learning Economies Finding the Total Cost curve from a Production function An application Consider again the production function q = 50 ( LK ) 1 / 2 . How does minimized total cost depend on the output q and the input prices w and r for this production function? What is the graph of the long-run total cost curve when w = 25 and r = 100? 5 / 36
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Long-run Cost Curves Short-run cost curves Scope and Learning Economies Total costs and changes in the price of one single input How does a change in the input price affect total costs? Suppose the price of K increases, holding output and the price of labour constant. As we know, the isocost will roll around the isoquant changing the cost-minimising input combination from A to B. The new input combination will correspond to higher total costs, holding output fixed. 6 / 36
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Long-run Cost Curves Short-run cost curves Scope and Learning Economies Total costs and changes in the price of one single input For any positive amounts of inputs employed in production, an increase in the price of K will result in a new TC curve that lies above the original one at every q > 0 (Not the case if the optimum is a corner solution) 7 / 36
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Long-run Cost Curves Short-run cost curves Scope and Learning Economies Total costs and a proportionate increase in all input prices A given percentage increase in both input prices leaves the cost-minimizing input combination unchanged, while the total cost curve shifts up by exactly the same percentage In the optimal choice diagram, the cost-minimising combination will occur at the same point A: - w r = - aw ar , so tangency is unaffected 8 / 36
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Long-run Cost Curves Short-run cost curves Scope and Learning Economies Total costs and a proportionate increase in all input prices While the proportions of inputs employed will remain the same, if w 2 = aw 1 and r 2 = ar 1 , TC 2 = w 2 L + r 2 K = a ( w 1 L + r 1 K ) = aTC 1 The TC curve will rotate upwards 9 / 36
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