DOC PREVIEW
UNC-Chapel Hill ECON 410 - Economies of Scale & Scope Minimizing Cost Mathematically

This preview shows page 1-2 out of 5 pages.

Save
View full document
View full document
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience
View full document
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience
Premium Document
Do you want full access? Go Premium and unlock all 5 pages.
Access to all documents
Download any document
Ad free experience

Unformatted text preview:

Slide 1Econ 410: Micro TheoryEconomies of Scale & ScopeMinimizing Cost MathematicallyFriday, November 9th, 2007Slide 2Long-Run Average Cost 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?Slide 3Long-Run Average 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.OutputCostLRACSlide 4Long-Run Average Cost When input proportions change, the firm’s expansion path is no longer a straight line The concept of returns to scale no longer applies The idea of economies of scalereflects the fact that input proportions can change as the firm changes its level of production.Capital25507510015050Labor100150300200A$2000200B$3000300CSlide 5Economies of Scale Economies of Scale 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 levelsOutputCostLRACSlide 6Economies of Scale Increasing Returns to Scale Output more than doubles when the quantities of all inputs are doubled Economies of Scale Doubling of output requires less than a doubling of cost Economies of scale are measured in terms of cost-output elasticity, EC.  ECis the percentage change in the cost of production resulting from a 1% increase in outputACMCQQCCECSlide 7Economies of Scale When ECis equal to 1, MC = AC Costs increase proportionately with output Neither economies nor diseconomies of scale When EC< 1, MC < AC Economies of scale AC is declining When EC> 1, MC > AC Diseconomies of scale Both MC and AC are risingSlide 8Sample Exam Question 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.Slide 9Economies of Scale Economies of Scale & Optimal Plant Size Consider the book’s illustration of the relationship between short run and long run cost curves:Slide 10Economies of Scale 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?Slide 11Economies of Scope 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 resourcesSlide 12Economies of Scope 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!Slide 13Economies of ScopeNumber of Big MacsNumberof FriesO1illustrates a lower level of output than O2. O2requires more capital and labor than O1.Each curve shows the combinations of the 2 goods that can be produced with a given combination of L & K.O2O1Why are these curves concave?Why are these curves negatively sloped?Slide 14Economies of Scope 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 largeSlide 15Economies of Scope 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 The greater the value of SC, the greater the economies of scope The degree of economies of scope (SC) can be measured by the percentage of cost saved by producing products jointly:)qC(q)qC(q)C(q)C(qSC ,,212121Slide 16Mathematical 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!Slide 17Mathematical 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+ rKsubject to F(K,L) = Q0 What are the steps to solving this?1. Set up the Lagrange function2.Differentiate with respect to K, L, and λ3. Solve for K and LSlide 18Sample Exam Question Suppose your firm has the following production function:Q = L.5K.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?Slide 19Sample Exam Question 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 20For next time… Read pages 256-260 of your textbook Make sure you can do the Lagrange problem we’ve discussed in


View Full Document

UNC-Chapel Hill ECON 410 - Economies of Scale & Scope Minimizing Cost Mathematically

Download Economies of Scale & Scope Minimizing Cost Mathematically
Our administrator received your request to download this document. We will send you the file to your email shortly.
Loading Unlocking...
Login

Join to view Economies of Scale & Scope Minimizing Cost Mathematically and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Economies of Scale & Scope Minimizing Cost Mathematically 2 2 and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?