Long-Run Average Cost. Econ 410: Micro Theory. Long-Run Average Cost. Long-Run Average Cost. Economies of Scale & Scope Minimizing Cost Mathematically

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1 Slide 1 Slide 3 Econ 410: Micro Theory & Scope Minimizing Cost Mathematically Friday, November 9 th, 2007 Cost But, at some point, average costs for a firm will tend to increase. Why? Factory space and machinery may make it more difficult for workers to do their jobs efficiently The Office Space Effect At some point, the availability of inputs may become limited. The Walmart Effect can t last forever. LRAC Output Slide 2 Slide 4 Why is the long-run average cost curve U-shaped? As output increases, a firm s average cost of production is likely to decline to a point. Why? Worker Specialization Adam Smith, anyone? A larger scale can provide flexibility Quantity discounts for inputs Walmart, anyone? Capital $3000 $2000 A When input proportions change, the firm s expansion path is no longer a straight line The concept of returns to scale no longer applies B C Labor The idea of economies of scale reflects the fact that input proportions can change as the firm changes its level of production.

2 Slide 5 Slide 7 Cost Increase in output is greater than the increase in inputs Diseconomies of Scale Increase in output is less than the increase in inputs U-shaped LRAC shows economies of scale for relatively low output levels and diseconomies of scale for higher levels LRAC Output When E C is equal to 1, MC = AC Costs increase proportionately with output Neither economies nor diseconomies of scale When E C < 1, MC < AC Economies of scale AC is declining When E C > 1, MC > AC Diseconomies of scale Both MC and AC are rising Slide 6 Slide 8 Increasing Returns to Scale Output more than doubles when the quantities of all inputs are doubled Doubling of output requires less than a doubling of cost Economies of scale are measured in terms of cost-output elasticity, E C. E C is the percentage change in the cost of production resulting from a 1% increase in output E C C MC C Q Q AC At the current level of output, long-run marginal cost is $50 and long-run average cost is $75. This implies that: a) There are neither economies nor diseconomies of scale. b) There are economies of scale. c) There are diseconomies of scale. d) The cost-output elasticity is greater than 1.

3 Slide 9 Slide 11 & Optimal Plant Size Consider the book s illustration of the relationship between short run and long run cost curves: Many firms will produce more than one product when those products are closely linked Examples: McDonald s - Hamburgers & French Fries Microsoft Word & Excel What are some advantages to joint production? Sharing of capital, labor, marketing, and management resources Slide 10 Slide 12 If a firm is deciding how big its facility should be, what is the optimal quantity for that the plant should be able to produce? When a firm makes the decision to produce multiple products, they must also choose how much of each product to produce The various quantity choices can be illustrated using product transformation curves Curves showing the various combinations of outputs that can be produced with a given set of inputs Remember Axes are changing!

4 Slide 13 Slide 15 Number of Fries Each curve shows the combinations of the 2 goods that can be produced with a given combination of L & K. O 1 O 2 O 1 illustrates a lower level of output than O 2. O 2 requires more capital and labor than O 1. Why are these curves negatively sloped? Why are these curves concave? Number of Big Macs The degree of economies of scope (SC) can be measured by the percentage of cost saved by producing products jointly: SC Interpretation: With economies of scope, the joint cost is less than the sum of the individual costs If SC > 0 Economies of scope If SC < 0 Diseconomies of scope C(q1 ) C(q2 ) C(q1, q2 ) C(q, q ) The greater the value of SC, the greater the economies of scope 1 2 Slide 14 Slide 16 There is no direct relationship between economies of scope and economies of scale A firm s production could easily have one without the other Example Dunder-Mifflin could easily sell both pink and blue paper, but may still have management inefficiencies as it gets large Mathematical Interpretation Just as we can illustrate the consumer s problem by maximizing utility mathematically, we can show the firm s problem in a similar way Minimizing cost subject to production constraints If a firm knows that it needs to produce a specific quantity, how can it do so for the least cost possible? Lagrange multipliers can show us the answer!

5 Slide 17 Slide 19 Mathematical Interpretation Recall that a competitive firm takes the prices of labor as capital (r & w) as given r and w are treated as exogenous What does the firm s problem look like? Minimize C = wl+ rk subject to F(K,L) = Q 0 What are the steps to solving this? 1. Set up the Lagrange function 2. Differentiate with respect to K, L, and λ 3. Solve for K and L Your task: Work in pairs to find the solution to this problem Make sure you can both understand how to do the problem when you re finished Use the Lagrange multiplier tools that you already know. If you have questions, ask! The pair that chooses to present their answers to the class will win a prize! Slide 18 Slide 20 Suppose your firm has the following production function: Q = L.5 K.5 You know that w = $5 and r = $10 What combination of labor and output will you select if you want to produce 1000 units of output at the lowest cost possible? What is the total cost of producing this output? For next time Read pages of your textbook Make sure you can do the Lagrange problem we ve discussed in class!