DOCSLIB.ORG

Review: 1. What Is a Production Function? 700 Eu • 2

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Review: 1. What Is a Production Function? 700 Eu • 2 Review Objective: Derive firm’s Supply curve Price Supply Review: 1. What is a production function? 700 Eu • 2. What is the marginal product of some input? 3. What is the MRTS? 400 Eu • 4. What are decreasing returns to scale? 0 600 1500 Quantity Review How much does it cost the firm to produce q units? The firm’s cost function specifies the cost to produce q units Total costs are determined by the production function and the costs of inputs But there are many different combinations of inputs that can produce q units. The firm’s problem is to choose the combination of inputs that minimizes costs. The Cost Function Example 1. A firm requires a single input to produce output, with production function f(L)=√L. If the wage is w=$10, how much does it cost to produce 3 units? How much does it cost to produce Q units? Example 2: A firm needs 2 workers and 1 machine to produce a single unit. The wage is w = 5 and rent is r = 10. What is the cost of producing 10 units? What is the cost function? Example 3: A firm can produce 1 unit of output with either 2 workers or with 1 machine. If the wage is w=5 and rent is r = 5. What is the cost of producing 10 units? Derive the cost function TC(Q)? The Cost Function When the firm hires L workers and K units of capital the total cost is: w = wage rate L = Quantity of Labor r = price per unit of capital services K = Quantity of Capital The total costs are: TC wL rK The Cost Function If are many different combinations of inputs that can produce Q units. The firm’s problem is to choose the best combination of inputs (that minimizes costs). The firm’s problem is to choose L and K that solve, First Order Conditions: w MPL w MPL MPK OR MRTSL,K OR r MPK r w r The Cost Function Definition: The iso-cost line is the set of combinations of labor and capital that yield the same total cost for the firm. Example: The wage is w = $10 per hour and the rent is r = $20 per hour. The iso-cost line for TC = $1,000 is all the combination L and K such that: 10L + 20K=1,000 or K = 50-0.5L The Cost Function The iso-cost lines is K=(TC/r)+(w/r)L K TC2/r TC2 TC1/r TC0/r TC1 TC0 L TC0/w TC1/w TC2/w The Cost Function The Firm’s problem: K min wL rK The isocost line TC2/r s.t.F(K, L) Q TC1/r The isoquant for Q. TC0/r The firm must choose a point on the isoquant. Q L TC0/w TC1/w TC2/w Deriving The Cost Function Key explanation: How to derive the cost function The Cost Function Example: Suppose a firm needs 10 workers and 1 machine to produce a single unit. What is the production function? The wage is w = 5 and rent is r = 100. What is the cost of producing 50 units? What is the cost function? Solution: The production function F(L,K)= Min[0.1L,K]. To produce 50 units we need 50 machines and 500 workers, and the total cost will be 500*5+50*100=7,500 The Cost Function Example: Suppose F(K,L)=L + 2K, the wage is w = 1 and rent is r = 1. What is the cost of producing 1000 units? Derive the cost function TC(Q)? Do the same if the cost of capital increases to r=4 Solution: If MPL/w > MPK /r the productivity of a dollar spent on labor is larger than the productivity of a dollar spent on capital. If MPL/w < MPK /r the productivity of a dollar spent on labor is smaller than the productivity of a dollar spent on capital. Deriving The Cost Function Example: Suppose F(K,L)= 50L1/2K1/2, the wage is w = $5 and rent is r = $20. What is the cost of producing 1,000 units? Derive the cost function TC(Q)? To get the cost of 1,000 units we need to ficure out how many workers and machines to use: 1. Optimality condition: MPL/MPK = w/r or K/L = 5/20 2. Use the production constriant: 50L1/2K1/2=1,000 K = 10; L = 40; And the total cost is 5*40+20*10=400 The Cost Function MP MP At point E L K w r The firm can increase labor and decrease capital, and produce for less. MP MP At point F L K w r The firm can decrease labor and increase capital, and produce for less. The Cost Function Example: As Quantity increases from 1 million to 2 million the cost minimizing input combination moves from point A to point B The Cost Function What happens when the price of input changes? Suppose price of capital r = 1 and quantity of output Q0 is constant. When price of labor w = 1 the isocost line is C1, optimal point A. But, when price of labor rises w = 2 isocost line is C2, optimal point B Key point: When the price of an input rises, we use less of that input and more of the other - An increase in the wage decreases the optimal quantity of labor and increases the quantity of capital. - An increase in rent decreases the optimal quantity of capital and increases the quantitty labor The Cost Function Question: How does the total cost curve shift if the price of all inputs rises by the same amount? The price of inputs increases proportionately by 10%. 1. Cost minimization input stays same (Why?). 2. TC curve shifts up by the same 10 percent Fixed and Variable Inputs Some inputs are fixed and some vary Total Variable Costs – the costs of variable inputs Total Fixed Costs – the cost of fixed inputs; does not vary with output •Fixed costs but not sunk: become zero if no production takes place Q=0 • Fixed and sunk: positive even if Q=0 Fixed and Variable Inputs Example: Q 50 LK capital fixed at K Q2 L* (Q) 2500 K Q2 TC(Q) w* L* (Q) rK w* rK 2500 K Long Run Cost Curve Definition For given input prices: The average cost function is the long run total cost function divided by output, Q. ATC(Q) = TC(Q)/Q The marginal cost function is the rate of change of total cost as output varies MC(Q) = TC(Q)/Q Long Run Total Cost Key points: When marginal cost is lower than average cost, average cost is decreasing in quantity. When marginal cost is greater than average cost, average cost is increasing in quantity. When marginal cost equals average cost, average cost is minimized. Economies Of Scale Definitions We say that a cost function exhibits economies of scale, if the average cost decreases as output rises, all else equal. We say that a cost function exhibits diseconomies of scale, if the average cost increases as output rises, all else equal. The smallest quantity at which the long run average cost curve attains its minimum point is called the minimum efficient scale. Economies Of Scale Economies of scale, diseconomies of scale, minimum efficient scale. AC ($/yr) AC(Q) Q (units/yr) 0 Q* = MES Economies Of Scale Why are there economies of Scale? 1. Increase returns to scale- Fixed costs - More production permits more specialized inputs. 2. Decreasing return to scale- Organizational structure and managerial costs - Adding software engineers increases communication costs: If there are n engineers, there are ½n*(n – 1) pairs, so that communication costs rise at the square of the project size - “The Peter Principle”: Workers move up until they become incompetent - System slack: it is easier to hide inefficiencies in a large organization than in a small one Economies Of Scale 24 Economies of scale and Returns to scale - When the production function exhibits decreasing returns to scale, the long run average cost function exhibits diseconomies of scale. - When the production function exhibits increasing returns to scale, the long run average cost function exhibits economies of scale. - When the production function exhibits constant returns to scale, the long run average cost function is flat: it neither increases nor decreases with output..
Load more

Recommended publications
  • Perfect Competition--A Model of Markets
    Econ Dept, UMR Presents PerfectPerfect CompetitionCompetition----AA ModelModel ofof MarketsMarkets StarringStarring uTheThe PerfectlyPerfectly CompetitiveCompetitive FirmFirm uProfitProfit MaximizingMaximizing DecisionsDecisions \InIn thethe ShortShort RunRun \InIn thethe LongLong RunRun FeaturingFeaturing uAn Overview of Market Structures uThe Assumptions of the Perfectly Competitive Model uThe Marginal Cost = Marginal Revenue Rule uMarginal Cost and Short Run Supply uSocial Surplus PartPart III:III: ProfitProfit MaximizationMaximization inin thethe LongLong RunRun u First, we review profits and losses in the short run u Second, we look at the implications of the freedom of entry and exit assumption u Third, we look at the long run supply curve OutputOutput DecisionsDecisions Question:Question: HowHow cancan wewe useuse whatwhat wewe knowknow aboutabout productionproduction technology,technology, costs,costs, andand competitivecompetitive marketsmarkets toto makemake outputoutput decisionsdecisions inin thethe longlong run?run? Reminders...Reminders... u Firms operate in perfectly competitive output and input markets u In perfectly competitive industries, prices are determined in the market and firms are price takers u The demand curve for the firm’s product is perceived to be perfectly elastic u And, critical for the long run, there is freedom of entry and exit u However, technology is assumed to be fixed The firm maximizes profits, or minimizes losses by producing where MR = MC, or by shutting down Market Firm P P MC S $5 $5 P=MR D
    [Show full text]
  • Managerial Economics Unit 6: Oligopoly
    Managerial Economics Unit 6: Oligopoly Rudolf Winter-Ebmer Johannes Kepler University Linz Summer Term 2019 Managerial Economics: Unit 6 - Oligopoly1 / 45 OBJECTIVES Explain how managers of firms that operate in an oligopoly market can use strategic decision-making to maintain relatively high profits Understand how the reactions of market rivals influence the effectiveness of decisions in an oligopoly market Managerial Economics: Unit 6 - Oligopoly2 / 45 Oligopoly A market with a small number of firms (usually big) Oligopolists \know" each other Characterized by interdependence and the need for managers to explicitly consider the reactions of rivals Protected by barriers to entry that result from government, economies of scale, or control of strategically important resources Managerial Economics: Unit 6 - Oligopoly3 / 45 Strategic interaction Actions of one firm will trigger re-actions of others Oligopolist must take these possible re-actions into account before deciding on an action Therefore, no single, unified model of oligopoly exists I Cartel I Price leadership I Bertrand competition I Cournot competition Managerial Economics: Unit 6 - Oligopoly4 / 45 COOPERATIVE BEHAVIOR: Cartel Cartel: A collusive arrangement made openly and formally I Cartels, and collusion in general, are illegal in the US and EU. I Cartels maximize profit by restricting the output of member firms to a level that the marginal cost of production of every firm in the cartel is equal to the market's marginal revenue and then charging the market-clearing price. F Behave like a monopoly I The need to allocate output among member firms results in an incentive for the firms to cheat by overproducing and thereby increase profit.
    [Show full text]
  • Perfect Competition
    Perfect Competition 1 Outline • Competition – Short run – Implications for firms – Implication for supply curves • Perfect competition – Long run – Implications for firms – Implication for supply curves • Broader implications – Implications for tax policy. – Implication for R&D 2 Competition vs Perfect Competition • Competition – Each firm takes price as given. • As we saw => Price equals marginal cost • PftPerfect competition – Each firm takes price as given. – PfitProfits are zero – As we will see • P=MC=Min(Average Cost) • Production efficiency is maximized • Supply is flat 3 Competitive industries • One way to think about this is market share • Any industry where the largest firm produces less than 1% of output is going to be competitive • Agriculture? – For sure • Services? – Restaurants? • What about local consumers and local suppliers • manufacturing – Most often not so. 4 Competition • Here only assume that each firm takes price as given. – It want to maximize profits • Two decisions. • ()(1) if it produces how much • П(q) =pq‐C(q) => p‐C’(q)=0 • (2) should it produce at all • П(q*)>0 produce, if П(q*)<0 shut down 5 Competitive equilibrium • Given n, firms each with cost C(q) and D(p) it is a pair (p*,q*) such that • 1. D(p *) =n q* • 2. MC(q*) =p * • 3. П(p *,q*)>0 1. Says demand equals suppl y, 2. firm maximize profits, 3. profits are non negative. If we fix the number of firms. This may not exist. 6 Step 1 Max П p Marginal Cost Average Costs Profits Short Run Average Cost Or Average Variable Cost Costs q 7 Step 1 Max П, p Marginal
    [Show full text]
  • Quantifying the External Costs of Vehicle Use: Evidence from America’S Top Selling Light-Duty Models
    QUANTIFYING THE EXTERNAL COSTS OF VEHICLE USE: EVIDENCE FROM AMERICA’S TOP SELLING LIGHT-DUTY MODELS Jason D. Lemp Graduate Student Researcher The University of Texas at Austin 6.9 E. Cockrell Jr. Hall, Austin, TX 78712-1076 [email protected] Kara M. Kockelman Associate Professor and William J. Murray Jr. Fellow Department of Civil, Architectural and Environmental Engineering The University of Texas at Austin 6.9 E. Cockrell Jr. Hall, Austin, TX 78712-1076 [email protected] The following paper is a pre-print and the final publication can be found in Transportation Research 13D (8):491-504, 2008. Presented at the 87th Annual Meeting of the Transportation Research Board, January 2008 ABSTRACT Vehicle externality costs include emissions of greenhouse and other gases (affecting global warming and human health), crash costs (imposed on crash partners), roadway congestion, and space consumption, among others. These five sources of external costs by vehicle make and model were estimated for the top-selling passenger cars and light-duty trucks in the U.S. Among these external costs, those associated with crashes and congestion are estimated to be the most practically significant. When crash costs are included, the worst offenders (in terms of highest external costs) were found to be pickups. If crash costs are removed from the comparisons, the worst offenders tend to be four pickups and a very large SUV: the Ford F-350 and F-250, Chevrolet Silverado 3500, Dodge Ram 3500, and Hummer H2, respectively. Regardless of how the costs are estimated, they are considerable in magnitude, and nearly on par with vehicle purchase prices.
    [Show full text]
  • Total Cost and Profit
    4/22/2016 Total Cost and Profit Gina Rablau Gina Rablau - Total Cost and Profit A Mini Project for Module 1 Project Description This project demonstrates the following concepts in integral calculus: Indefinite integrals. Project Description Use integration to find total cost functions from information involving marginal cost (that is, the rate of change of cost) for a commodity. Use integration to derive profit functions from the marginal revenue functions. Optimize profit, given information regarding marginal cost and marginal revenue functions. The marginal cost for a commodity is MC = C′(x), where C(x) is the total cost function. Thus if we have the marginal cost function, we can integrate to find the total cost. That is, C(x) = Ȅ ͇̽ ͬ͘ . The marginal revenue for a commodity is MR = R′(x), where R(x) is the total revenue function. If, for example, the marginal cost is MC = 1.01(x + 190) 0.01 and MR = ( /1 2x +1)+ 2 , where x is the number of thousands of units and both revenue and cost are in thousands of dollars. Suppose further that fixed costs are $100,236 and that production is limited to at most 180 thousand units. C(x) = ∫ MC dx = ∫1.01(x + 190) 0.01 dx = (x + 190 ) 01.1 + K 1 Gina Rablau Now, we know that the total revenue is 0 if no items are produced, but the total cost may not be 0 if nothing is produced. The fixed costs accrue whether goods are produced or not. Thus the value for the constant of integration depends on the fixed costs FC of production.
    [Show full text]
  • Profit Maximization and Cost Minimization ● Average and Marginal Costs
    Theory of the Firm Moshe Ben-Akiva 1.201 / 11.545 / ESD.210 Transportation Systems Analysis: Demand & Economics Fall 2008 Outline ● Basic Concepts ● Production functions ● Profit maximization and cost minimization ● Average and marginal costs 2 Basic Concepts ● Describe behavior of a firm ● Objective: maximize profit max π = R(a ) − C(a ) s.t . a ≥ 0 – R, C, a – revenue, cost, and activities, respectively ● Decisions: amount & price of inputs to buy amount & price of outputs to produce ● Constraints: technology constraints market constraints 3 Production Function ● Technology: method for turning inputs (including raw materials, labor, capital, such as vehicles, drivers, terminals) into outputs (such as trips) ● Production function: description of the technology of the firm. Maximum output produced from given inputs. q = q(X ) – q – vector of outputs – X – vector of inputs (capital, labor, raw material) 4 Using a Production Function ● The production function predicts what resources are needed to provide different levels of output ● Given prices of the inputs, we can find the most efficient (i.e. minimum cost) way to produce a given level of output 5 Isoquant ● For two-input production: Capital (K) q=q(K,L) K’ q3 q2 q1 Labor (L) L’ 6 Production Function: Examples ● Cobb-Douglas : ● Input-Output: = α a b = q x1 x2 q min( ax1 ,bx2 ) x2 x2 Isoquants q2 q2 q1 q1 x1 x1 7 Rate of Technical Substitution (RTS) ● Substitution rates for inputs – Replace a unit of input 1 with RTS units of input 2 keeping the same level of production x2 ∂x ∂q ∂x RTS
    [Show full text]
  • Marginal Social Cost Pricing on a Transportation Network
    December 2007 RFF DP 07-52 Marginal Social Cost Pricing on a Transportation Network A Comparison of Second-Best Policies Elena Safirova, Sébastien Houde, and Winston Harrington 1616 P St. NW Washington, DC 20036 202-328-5000 www.rff.org DISCUSSION PAPER Marginal Social Cost Pricing on a Transportation Network: A Comparison of Second-Best Policies Elena Safirova, Sébastien Houde, and Winston Harrington Abstract In this paper we evaluate and compare long-run economic effects of six road-pricing schemes aimed at internalizing social costs of transportation. In order to conduct this analysis, we employ a spatially disaggregated general equilibrium model of a regional economy that incorporates decisions of residents, firms, and developers, integrated with a spatially-disaggregated strategic transportation planning model that features mode, time period, and route choice. The model is calibrated to the greater Washington, DC metropolitan area. We compare two social cost functions: one restricted to congestion alone and another that accounts for other external effects of transportation. We find that when the ultimate policy goal is a reduction in the complete set of motor vehicle externalities, cordon-like policies and variable-toll policies lose some attractiveness compared to policies based primarily on mileage. We also find that full social cost pricing requires very high toll levels and therefore is bound to be controversial. Key Words: traffic congestion, social cost pricing, land use, welfare analysis, road pricing, general equilibrium, simulation, Washington DC JEL Classification Numbers: Q53, Q54, R13, R41, R48 © 2007 Resources for the Future. All rights reserved. No portion of this paper may be reproduced without permission of the authors.
    [Show full text]
  • Externalities and Public Goods Introduction 17
    17 Externalities and Public Goods Introduction 17 Chapter Outline 17.1 Externalities 17.2 Correcting Externalities 17.3 The Coase Theorem: Free Markets Addressing Externalities on Their Own 17.4 Public Goods 17.5 Conclusion Introduction 17 Pollution is a major fact of life around the world. • The United States has areas (notably urban) struggling with air quality; the health costs are estimated at more than $100 billion per year. • Much pollution is due to coal-fired power plants operating both domestically and abroad. Other forms of pollution are also common. • The noise of your neighbor’s party • The person smoking next to you • The mess in someone’s lawn Introduction 17 These outcomes are evidence of a market failure. • Markets are efficient when all transactions that positively benefit society take place. • An efficient market takes all costs and benefits, both private and social, into account. • Similarly, the smoker in the park is concerned only with his enjoyment, not the costs imposed on other people in the park. • An efficient market takes these additional costs into account. Asymmetric information is a source of market failure that we considered in the last chapter. Here, we discuss two further sources. 1. Externalities 2. Public goods Externalities 17.1 Externalities: A cost or benefit that affects a party not directly involved in a transaction. • Negative externality: A cost imposed on a party not directly involved in a transaction ‒ Example: Air pollution from coal-fired power plants • Positive externality: A benefit conferred on a party not directly involved in a transaction ‒ Example: A beekeeper’s bees not only produce honey but can help neighboring farmers by pollinating crops.
    [Show full text]
  • Economic Evaluation Glossary of Terms
    Economic Evaluation Glossary of Terms A Attributable fraction: indirect health expenditures associated with a given diagnosis through other diseases or conditions (Prevented fraction: indicates the proportion of an outcome averted by the presence of an exposure that decreases the likelihood of the outcome; indicates the number or proportion of an outcome prevented by the “exposure”) Average cost: total resource cost, including all support and overhead costs, divided by the total units of output B Benefit-cost analysis (BCA): (or cost-benefit analysis) a type of economic analysis in which all costs and benefits are converted into monetary (dollar) values and results are expressed as either the net present value or the dollars of benefits per dollars expended Benefit-cost ratio: a mathematical comparison of the benefits divided by the costs of a project or intervention. When the benefit-cost ratio is greater than 1, benefits exceed costs C Comorbidity: presence of one or more serious conditions in addition to the primary disease or disorder Cost analysis: the process of estimating the cost of prevention activities; also called cost identification, programmatic cost analysis, cost outcome analysis, cost minimization analysis, or cost consequence analysis Cost effectiveness analysis (CEA): an economic analysis in which all costs are related to a single, common effect. Results are usually stated as additional cost expended per additional health outcome achieved. Results can be categorized as average cost-effectiveness, marginal cost-effectiveness,
    [Show full text]
  • THE COSTS of PRODUCTION WHAT ARE COSTS? Costs As Opportunity Costs Economic Profit Versus Accounting Profit
    THE COSTS OF PRODUCTION The Market Forces of Supply and Demand •Supply and demand are the two words that economists use most often. •Supply and demand are the forces that make market economies work. •Modern microeconomics is about supply, demand, and market equilibrium. WHAT ARE COSTS? •According to the Law of Supply:y •Firms are willing to produce and sell a greater quantity of a good when the price of the good is high. •This results in a supply curve that slopes upward. •The Firm’s Objective•The economic goal of the firm is to maximize profits. Total Revenue, Total Cost, and Profit •Total Revenue•The amount a firm receives for the sale of its output. •Total Cost•The market value of the inputs a firm uses in production. •Profit is the firm’s total revenue minus its total cost. •Profit = Total revenue - Total cost Costs as Opportunity Costs •A firm’s cost of production includes all the opportunity costs of making its output of goods and services. •Explicit and Implicit Costs •A firm’s cost of production include explicit costs and implicit costs. •Explicit costs are input costs that require a direct outlay of money by the firm. •Implicit costs are input costs that do not require an outlay of money by the firm. Economic Profit versus Accounting Profit •Economists measure a firm’s economic profit as total revenue minus total cost, including both explicit and implicit costs. •Accountants measure the accounting profit as the firm’s total revenue minus only the firm’s explicit costs. •When total revenue exceeds both explicit and implicit costs, the firm earns economic profit.
    [Show full text]
  • Principles of Microeconomics
    PRINCIPLES OF MICROECONOMICS A. Competition The basic motivation to produce in a market economy is the expectation of income, which will generate profits. • The returns to the efforts of a business - the difference between its total revenues and its total costs - are profits. Thus, questions of revenues and costs are key in an analysis of the profit motive. • Other motivations include nonprofit incentives such as social status, the need to feel important, the desire for recognition, and the retaining of one's job. Economists' calculations of profits are different from those used by businesses in their accounting systems. Economic profit = total revenue - total economic cost • Total economic cost includes the value of all inputs used in production. • Normal profit is an economic cost since it occurs when economic profit is zero. It represents the opportunity cost of labor and capital contributed to the production process by the producer. • Accounting profits are computed only on the basis of explicit costs, including labor and capital. Since they do not take "normal profits" into consideration, they overstate true profits. Economic profits reward entrepreneurship. They are a payment to discovering new and better methods of production, taking above-average risks, and producing something that society desires. The ability of each firm to generate profits is limited by the structure of the industry in which the firm is engaged. The firms in a competitive market are price takers. • None has any market power - the ability to control the market price of the product it sells. • A firm's individual supply curve is a very small - and inconsequential - part of market supply.
    [Show full text]
  • Cost Functions Definitions of Costs Economic Cost
    Cost Functions [See Chap 10] . 1 Definitions of Costs • Economic costs include both implicit and explicit costs. • Explicit costs include wages paid to employees and the costs of raw materials. • Implicit costs include the opportunity cost of the entrepreneur and the capital used for production. 2 Economic Cost • The economic cost of any input is its opportunity cost: – the remuneration the input would receive in its best alternative employment 3 1 Model • Firm produces single output, q • Firm has N inputs {z 1,…z N}. • Production function q = f(z 1,…z N) – Monotone and quasi-concave. • Prices of inputs {r 1,…r N}. • Price of output p. 4 Firm’s Payoffs • Total costs for the firm are given by total costs = C = r1z1 + r2z2 • Total revenue for the firm is given by total revenue = pq = pf (z1,z2) • Economic profits ( π) are equal to π = total revenue - total cost π = pq - r1z1 - r2z2 π = pf (z1,z2) - r1z1 - r2z2 5 Firm’s Problem • We suppose the firm maximizes profits. • One-step solution – Choose (q,z 1,z 2) to maximize π • Two-step solution – Minimize costs for given output level. – Choose output to maximize revenue minus costs. • We first analyze two-step method – Where do cost functions come from? 6 2 COST MINIMIZATION PROBLEM . 7 Cost-Minimization Problem (CMP) • The cost minimization problem is min 1zr 1 + r2 z2 s.t. f (z1, z2 ) ≥ q and z1, z2 ≥ 0 • Denote the optimal demands by zi*(r 1,r 2,q) • Denote cost function by C(r 1,r 2,q) = r 1z1*(r 1,r 2,q) + r 2z2*(r 1,r 2,q) • Problem very similar to EMP.
    [Show full text]