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Chapter 2

ECO204Y5 Chapter 2: Test 2 Notes

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Department
Economics
Course
ECO204Y5
Professor
Kathleen Wong
Semester
Fall

Description
CHAPTER 5: Uncertainty and Consumer Behaviour • In a world of uncertainty, individual behavior may sometimes seem unpredictable, even irrational, and perhaps contrary to the basic assumptions of consumer theory 5.1 Describing Risk • EXAMPLE: o considering investing in a company that explores for offshore oil o if the exploration effort is successful, the company’s stock will increase from $30 to $40 per share; if not, the price will fall to $20 per share o thus there are two possible future outcomes: a $40-per-share price and a $20-per-share price Probability • probability: likelihood that a given outcome will occur o Example: ▪ Probability that the oil exploration is successful might be ¼ ▪ Probability that it is unsuccessful is ¾ ▪ NOTE: probabilities for all possible outcomes must add up to 1 Expected Value • Expected value: probability-weighted average an event • Payoff: value associated with a possible outcome • Expected value measures the central tendencythe payoff or value that we would expect on average • Example: o Two possible outcomes: success yields a payoff of $40 per share and failure a payoff of $20 per share o Denoting “probability of” by Pr, express the expected value as 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑉𝑎𝑙𝑢𝑒 = Pr 𝑠𝑢𝑐𝑐𝑒𝑠𝑠 ($40/𝑠ℎ𝑎𝑟𝑒) + Pr(𝑓𝑎𝑖𝑙𝑢𝑟𝑒)($20/𝑠ℎ𝑎𝑟𝑒) = ( )($40/𝑠ℎ𝑎𝑟𝑒) + ( )($20/𝑠ℎ𝑎𝑟𝑒) = $25/𝑠ℎ𝑎𝑟𝑒 4 4 • If there are two possible outcome having payoffs 𝑋 1nd 𝑋 ,2and if the probabilities of each outcome are given by 𝑃𝑟 1nd 𝑃𝑟 ,2then the expected value is 𝐸 𝑋 = 𝑃𝑟 𝑋1 1𝑃𝑟 𝑋 2 2 • When there are n possible outcomes, the expected value becomes 𝐸 𝑋 = 𝑃𝑟 𝑋 + 𝑃𝑟 𝑋 + ⋯+ 𝑃𝑟 𝑋 1 1 2 2 𝑛 𝑛 Variability • Variability: extent to which possible outcomes of an uncertain event differ • Example: o choosing between two part-time summer sales jobs that have the same expected income ($1500) o the first job is based entirely on commission–the income earned depends on how much you sell: there are two equally likely payoffs for this job: $2000 for a successful sales effort and $1000 for one that is less successful o the second job is salaried: it is very likely (.99 probability) that you will earn $1510, but there is a .01 probability that the company will go out of business, in which case you would earn only $510 in severance pay o Note that these two jobs have the same expected income: ▪ For Job 1, expected income is .5($2000) + .5($1000) = $1500; ▪ For Job 2, expected income is .99($1510) + .01($510) = $1500 o However, the variability of the possible payoffs is different o Deviations: difference between expected payoff and actual payoff o by themselves, deviations do not provide a measure of variability because they are sometimes positive and sometimes negative, and the average of the probability-weighted deviations is always 0 ▪ for Job 1, the average deviation is .5($500) + .5(−$500) = 0; ▪ for Job 2, the average deviation is .99($10) + .01(−$990) = 0 o standard deviation: square root of the weighted average of the squares of the deviations of the payoffs associated with each outcome from their expected values o another measure of variability, variance, is the square of the standard deviation o average of the squared deviations: ▪ Job 1, .5($250000) + 0.5($250000) = $250000 ▪ Job 2, .99($100) + .01($980100) = $9900 o The second job is less risky than the first; the standard deviation of the incomes is much lower o in general, when there are two outcomes with payoffs 𝑋 and 1 , 2 occurring with probability 𝑃𝑟1and 𝑃𝑟 2 and E(X) is the expected value of the outcomes, the standard deviation is given by , where 𝜎 = 𝑃𝑟 [1𝑋 −1𝐸(𝑋)) ] + 𝑃𝑟 [(2 − 𝐸2𝑋)) ] 2 Decision Making • Example: o choosing between the two sales jobs described in our original example o which job would you take? ▪ If you dislike risk, you will take the second job: It offers the same expected income as the first but with less risk o But suppose we add $100 to each of the payoffs in the first job, so that the expected payoff increases from $1500 to $1600 o The two jobs can now be described as follows:
 ▪ Job 1: Expected Income = $1600 Standard Deviation = $500 ▪ Job 2: Expected Income = $1500 Standard Deviation = $99.50 o job 1 offers a higher expected income but is much riskier than job 2 o which job is preferred depends on the individual o people’s attitudes toward risk affect many of the decisions they make 5.2 Preferences Toward Risk • expected utility: sum of the utilities associated with all possible outcomes, weighted by the probability that each outcome will occur • Example: o consumer has an income of $15,000 and is considering a new but risky sales job that will either double her income to $30,000 or cause it to fall to $10,000 o each possibility has a probability of .5 Current Job: 𝐸 𝑢 = 𝑢 $15000 = 13.5 New Job: 𝐸 𝑢 = ( )𝑢 $10000 + ( )𝑢 $30000 = 0.5 10 + 0.5 18 = 14 ( ) 2 2 o New job is preferred to original job because the expected utility of 14 is greater than the original utility of 13.5 o The old job involved no riskit guaranteed an income of $15000 and a utility level of 13.5 o The new job is risky but offers both a higher expected income ($20000) and, more importantly, a higher expected utility o If she wishes to increase her expected utility, she will take the risky job Different Preferences Toward Risk • risk averse: condition of preferring a certain income to a risky income with the same expected value o has diminishing marginal utility of income • Example: o A woman who is risk averse can have either a certain income of $20,000, or a job yielding an income of $30,000 with probability .5 and an income of $10,000 with probability .5 (so that the expected income is also $20,000) o the expected utility of the uncertain income is 14 o compare the expected utility associated with the risky job to the utility generated if $20,000 were earned without risk o this latter utility level, 16, is clearly greater than the expected utility of 14 associated with the risky job; 𝑈 > 𝐸(𝑈) • For a risk-averse person, losses are more important (in terms of the change in utility) than gains • risk neutral: condition of being indifferent between a certain income and an uncertain income with the same expected value o the marginal utility of income is constant for a risk-neutral person • Example: o the utility associated with a job generating an income of either $10,000 or $30,000 with equal probability is 12, as is the utility of receiving a certain income of $20,000; 𝑈 = 𝐸(𝑈) • risk loving: condition of preferring a risky income to a certain income with the same expected value • Example: o the expected utility of an uncertain income, which will be either $10,000 with probability .5 or $30,000 with probability .5, is higher than the utility associated with a certain income of $20,000; 𝐸(𝑈) > 𝑈 𝐸 𝑢 = ( )𝑢 $10000 + ( )𝑢 $30000 = 0.5 3 + 0.5 18 = 10.5 > 𝑢 $20000 = 8 ) 2 2 RISK PREMIUM • risk premium: maximum amount of money that a risk-averse person will pay to avoid taking a risk RISK AVERSION AND INCOME • Other things being equal, risk-averse people prefer a smaller variability of outcomes • Example: o when there are two outcomesan income of $10,000 and an income of $30,000the risk premium is $4000 o consider a second risky job, there is a .5 probability of receiving an income of $40000, with a utility level of 20, and a .5 probability of getting an income of 0, with a utility level of 0 o expected income is again $20000, but expected utility is only 10: 𝐸𝑥𝑝𝑒𝑐𝑡𝑒𝑑 𝑈𝑡𝑖𝑙𝑖𝑡𝑦 = .5𝑢 $0 + .5𝑢 $40000 = 0 + .5 20 = 10 o compared to a hypothetical job that pays $20,000 with certainty, the person holding this risky job gets 6 fewer units of expected utility: 10 rather than 16 units o at the same time, however, this person could also get 10 units of utility from a job that pays $10,000 with certainty o thus the risk premium in this case is $10,000, because this person would be willing to give up $10,000 of her $20,000 expected income to avoid bearing the risk of an uncertain income • the greater the variability of income, the more the person would be willing to pay to avoid the risky situation RISK AVERSION AND INDIFFERENCE CURVES • indifference curves are upward sloping: because risk is undesirable, the greater the amount of risk, the greater the expected income needed to make the individual equally well off 5.4 The Demand for Risky Assets Assets • asset: something that provides a flow of money or services to its owner • monetary flow that one receives from asset ownership can take the form of an explicit payment, such as the rental income from an apartment building or the dividend on shares of common stock • sometimes the monetary flow from ownership of an asset is implicit: it takes the form of an increase or decrease in the price or value of the asset • an increase in the value of an asset is a capital gain; a decrease is a capital loss Risky and Riskless Assets • risky asset: asset that provides an uncertain flow of money or services to its owner • riskless (or risk-free) asset: asset that provides a flow of money or services that is known with certainty o Example: ▪ Short-term government bondscalled Treasury billsare riskless, or almost riskless ▪ They mature is a few months, there is very little risk from an unexpected increase in the rate of inflation ▪ Passbook savings accounts ▪ Short-term certificates of deposit Asset Returns • Return: total monetary flow of an asset as a fraction of its price o Examples: ▪ a bond worth $1000 today that pays out $100 this year (and every year) has a return of 10 percent ▪ an apartment building was worth $10 million last year, increased in value to $11 million this year, and also provided rental income (after expenses) of $0.5 million, it would have yielded a return of 15 percent over the past year ▪ a share of General Motors stock was worth $80 at the beginning of the year, fell to $72 by the end of the year, and paid a dividend of $4, it will have yielded a return of -5 percent (the dividend yield of 5 percent less the capital loss of 10 percent) • When people invest their savings in stocks, bonds, land, or other assets, they usually hope to earn a return that exceeds the rate of inflation • thus, by delaying consumption, they can buy more in the future than they can by spending all their income now • often express the return on an asset in reali.e., inflation-adjustedterms. • Real return: simple (or nominal) return on an asset, less the rate of inflation o Example: ▪ with an annual inflation rate of 5 percent, our bond, apartment building, and share of GM stock have yielded real returns of 5 percent, 10 percent, and −10 percent, respectively EXPECTED VERSUS ACTUAL RETURNS • Because most assets are risky, an investor cannot know in advance what returns they will yield over the coming year • expected return: return that an asset should earn on average • actual return: return that an asset earns The Trade-Off Between Risk and Return • Example: o a woman wants to invest her savings in two assetsTreasury bills, which are almost risk free, and a representative group of stocks o she must decide how much to invest in each asset; she might invest only in Treasury bills, only in stocks, or in some combination of the two o denote the risk-free return on the Treasury bill by 𝑅 , where the 𝑓 expected and actual returns are the same o expected return from investing in the stock market be 𝑅 and the actual 𝑚 return be 𝑟 𝑚 o the actual return is risky o the risky asset will have a higher expected return than the risk-free asset (𝑅 > 𝑅 ) otherwise the risk-averse investors will only buy Treasury bills 𝑚 𝑓 and no stocks would be sold THE INVESTMENT PORTFOLIO • to determine how much money, the investor should put in each asset, let’s set 𝑏 equal to the fraction of her savings places in the stock market and (1- 𝑏) the fraction used to purchase Treasury bills • the expected return on her total portfolio, 𝑅 , is a weighted average of the 𝑝 expected return on the two assets: 𝑅 𝑝 𝑏𝑅 +𝑚(1 − 𝑏)𝑅 𝑓 • Example: o Treasury bills pay 4 percent 𝑓𝑅 = .04), the stock market’s expected return is 12 percent 𝑚𝑅 = .12), and 𝑏 = 1/2 1 1 o 𝑅 𝑝 2(0.12 + (1 − 2 0.04 = 0.08 • one measure of riskiness of the portfolio is the standard deviation of its return, 𝜎𝑚 • standard deviation of the portfolio𝑝 𝜎 (with one risky and one risk-free asset) is the fraction of the portfolio invested in the risky asset times the standard deviation of that asset: 𝜎𝑝= 𝑏𝜎 𝑚 The Investor’s Choice Problem • the expected return on the portfolio can be written as 𝑅 = 𝑅 + 𝑏(𝑅 − 𝑅 ) 𝑝 𝑓 𝑚 𝑓 (𝑅𝑚− 𝑅 𝑓 𝑅𝑝= 𝑅 𝑓 𝜎 𝜎𝑝 𝑚 RISK AND THE BUDGET LINE • this equation is the budget line because it describes the trade-off between risk (𝜎𝑝) and the expected return (𝑝 ) • equation for a straight line: becaus𝑚 𝑅 𝑓 𝑅 and𝑚𝜎 are constants, the slope (𝑅𝑚−𝑅𝑓) 𝜎𝑚 is a constant, as is the interce𝑓t, 𝑅 • the equation says that the expected return on the portfoli𝑝 𝑅 increases as the standard deviation of that return𝑝𝜎 increases • call the slope of this budget line, the price of risk: extra risk that an investor must incur to enjoy higher expected return • Example: o if our investor wants no risk, she can invest all her funds in Treasury bills (𝑏 = 0) and earn an expected return 𝑓 o to receive a higher expected return, she must incur some risk o she could invest all her funds in stocks (𝑏 = 1), earning an expected return 𝑅 but incurring a standard deviation 𝜎 𝑚 𝑚 o or she might invest some fraction of her funds in each type of asset, earning an expected return somewhere between 𝑅 and 𝑅 and facing a 𝑚 𝑓 standard deviation less than 𝜎 but greater than zero 𝑚 RISK AND INDIFFERENCE CURVES SUMMARY 1. Consumers and managers frequently make decisions in which there is uncertainty about the future. This uncertainty is characterized by the term risk, which applies when each of the possible outcomes and its probability of occurrence is known. 
 2. Consumers and investors are concerned about the expected value and the variability of uncertain out-comes. The expected value is a measure of the central tendency of the values of risky outcomes. Variability is frequently measured by the standard deviation of outcomes, which is the square root of the probability- weighted average of the squares of the deviation from the expected value of each possible outcome. 
 3. Facing uncertain choices, consumers maximize their expected utility–an average of the utility associated with each outcome–with the associated probabilities serving as weights. 
 4. A person who would prefer a certain return of a given amount to a risky investment with the same expected return is risk averse. The maximum amount of money that a risk-averse person would pay to avoid taking a risk is called the risk premium. A person who is indifferent between a risky investment and the certain receipt of the expected return on that investment is risk neutral. A risk- loving consumer would prefer a risky investment with a given expected return to the certain receipt of that expected return. 5. Consumer theory can be applied to decisions to invest in risky assets. The budget line reflects the price of risk, and consumers’ indifference curves reflect their attitudes toward risk. CHAPTER 6: Production • theory of the firm: explanation of how a firm makes cost-minimizing production decisions and how its cost varies with its output The Production Decisions of a Firm 1. Production technology: • Describe how inputs (such as labor, capital, and raw materials) can be transformed into outputs (such as cars and televisions) • Just as a consumer can reach a level of satisfaction from buying different combinations of goods, the firm can produce a particular level of output by using different combinations of inputs 2. Cost Constraints: • Firms must take into account the prices of labor, capital, and other inputs • Just as a consumer is constrained by a limited budget, the firm will be concerned about its cost of production 3. Input Choices: • Given its production technology and the prices of labor, capital, and other inputs, the firm must choose how much of each input to use in producing its output • just as a consumer takes account of the prices of different goods when deciding how much of each good to buy, the firm must take into account the prices of different inputs when deciding how much of each input to use 6.1 Firms and Their Production Decisions • concept of a firmrun by managers separate from the firm’s owners, and who hire and manage a large number of workers The Technology of Production • firms take inputs and turn them into outputs (or products) • factors of production: inputs into the production process (e.g., labor, capital, and materials) • can divide inputs into the broad categories of labor, materials, and capital, each of which might include more narrow subdivisions • Labor inputs include skilled workers (carpenters, engineers) and unskilled workers (agricultural workers), as well as the entrepreneurial efforts of the firm’s managers • Materials include steel, plastics, electricity, water, and any other goods that the firm buys and transforms into final products • Capital includes land, buildings, machinery and other equipment, as well as inventories The Production Function • Production function: function showing the highest output that a firm can produce for every specified combination of inputs • keep our analysis simple by focusing on only two, labor L and capital K 𝑞 = 𝐹(𝐾,𝐿) • inputs and outputs are flows • Because the production function allows inputs to be combined in varying proportions, output can be produced in many ways • As the technology becomes more advanced and the production function changes, a firm can obtain more output for a given set of inputs • Production functions describe what is technically feasible when the firm operates efficientlythat is, when the firm uses each combination of inputs as effectively as possible • The presumption that production is always technically efficient need not always hold, but it is reasonable to expect that profit-seeking firms will not waste resources The Short Run versus the Long Run • Short run: period of time in which quantities of one or more production factors cannot be changed • Fixed input: production factor that cannot be varied • Long run: amount of time needed to make all production inputs variable • In the short run, firms vary the intensity with which they utilize a given plant and machinery; in the long run, they vary the size of the plant • All fixed inputs in the short run represent the outcomes of previous long-run decisions based on estimates of what a firm could profitably produce and sell • assume that capital is the fixed input, and labor is variable 6.2 Production with One Variable Input (Labor) Average and Marginal Products • average product (𝐴𝑃 )𝐿 output per unit of a particular input • The average product of labor measures the productivity of the firm’s workforce in terms of how much output each worker produces on average 𝑂𝑢𝑡𝑝𝑢𝑡 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑙𝑎𝑏𝑜𝑟 (𝐴𝑃 ) 𝐿 = 𝑞/𝐿 𝐿𝑎𝑏𝑜𝑟 𝑖𝑛𝑝𝑢𝑡 • Marginal product (𝑀𝑃 )𝐿 additional output produced as an input is increased by one unit Δ𝑞 • The marginal product of labor can be written as Δ𝐿in other words, the change in output q resulting from a 1-unit increase in labor input ∆𝐿 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑜𝑢𝑡𝑝𝑢𝑡 Δ𝑞 𝑀𝑎𝑟𝑔𝑖𝑛𝑎𝑙 𝑝𝑟𝑜𝑑𝑢𝑐𝑡 𝑜𝑓 𝑙𝑎𝑏𝑜𝑟 (𝑀𝑃 ):𝐿= 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑙𝑎𝑏𝑜𝑟 𝑖𝑛𝑝𝑢𝑡 = Δ𝐿 The Slopes of the Product Curve • the marginal product is positive as long as output is increasing, but becomes negative when output is decreasing • when the marginal product is greater than the average product, the average product is increasing • when the marginal product is less than the average product, the average product is decreasing The Average Product of Labor Curve • The average product of labor is the total product divided by the quantity of labor input • the average product of labor is given by the slope of the line drawn from the origin to the corresponding point on the total product curve The Marginal Product of Labor Curve • the marginal product of labor is the change in the total product resulting from an increase of one unit of labor • the marginal product of labor at a point is given by the slope of the total product at that point THE RELATIONSHIP BETWEEN THE AVERAGE AND MARGINAL PRODUCTS The Law of Diminishing Marginal Returns • law of diminishing marginal returns: principle that as the use of an input increases with other inputs fixed, the resulting additions to output will eventually decrease • The law of diminishing marginal returns usually applies to the short run when at least one input is fixed • However, it can also apply to the long run • Even though inputs are variable in the long run, a manager may still want to analyze production choices for which one or more inputs are unchanged • Do not confuse the law of diminishing marginal returns with possible changes in the quality of labor as labor inputs are increased (as would likely occur, for example, if the most highly qualified laborers are hired first and the least qualified last) • do not confuse diminishing marginal returns with negative returns Labor Productivity • labor productivity: average product of labor for an entire industry or for the economy as a whole • Because the average product measures output per unit of labor input, it is relatively easy to measure (total labor input and total output are the only pieces of information you need) • Labor productivity can provide useful comparisons across industries and for one industry over a long period • But labor productivity is especially important because it determines the real standard of living that a country can achieve for its citizens PRODUCTIVITY AND THE STANDARD OF LIVING • Technological change: development of new technologies allowing factors of production to be used more effectively 6.3 Production with Two Variable Inputs • in the analysis of the short-run production function in which one input, labour, is variable, and the other, capital, is fixed • in the long-run both labour and capital are variable • the firm can produce its output in a variety of ways by combining different amounts of labor and capital Isoquants • Example: o Examining the production technology of a firm that uses two inputs and can vary both of them o The inputs are labour and capital and that they are used to produce food • Isoquant: curve showing all possible combinations of inputs that yield the same output ISOQUANT MAPS • isoquant map: graph combining a number of isoquants, used to describe a production function • is another way of describing a production function, just as an indifference map is a way of describing a utility function • Each isoquant corresponds to a different level of output, and the level of output increases as we move up and to the right in the figure Input Flexibility • Isoquants show the flexibility that firms have when making production decisions: they can usually obtain a particular output by substituting one input for another • Example: o Fast-food restaurants have recently faced shortages of young, low-wage employees o Companies have responded by automatingadding self-service salad bars and introducing more sophisticated cooking equipment o They have also recruited older people to fill positions • by taking into account this flexibility in the production process, can choose input combinations that minimize cost and maximize profit Diminishing Marginal Returns • Even though both labor and capital are variable in the long run, it is useful for a firm that is choosing the optimal mix of inputs to ask what happens to output as each input is increased, with the other input held fixed • The outcome reflects diminishing marginal returns to both labour and capital • Example: o Draw a horizontal line at a particular level of capitalsay 3 o when labor is increased from 1 unit to 2 (from A to B), output increases by 20 (from 55 to 75) o when labor is increased by an additional unit (from B to C), output increases by only 15 (from 75 to 90) o thus there are diminishing marginal returns to labor both in the long and short run o because adding one factor while holding the other factor constant eventually leads to lower and lower incremental output, the isoquant must become steeper as more capital is added in place of labor and flatter when labor is added in place of capital o There are also diminishing marginal returns to capital o with labor fixed, the 𝑀𝑃𝐾decreases as capital is increased o when capital is increased from 1 to 2 and labor is held constant at 3, the marginal product of capital is initially 20 (75 – 55) but falls to 15 (90 – 75) when capital is increased from 2 to 3 Substitution Among Inputs • with two inputs that can be varied, a manager will want to consider substituting one input for another • marginal rate of technical substitution (MRTS): amount by which the quantity of one input can be reduced when one extra unit of another input is used, so that output remains constant • when the negative sign is removed, we call the slope the marginal rate of technical substitution (MRTS) • marginal rate of technical substitution of labor for capital is the amount by which the input of capital can be reduced when one extra unit of labor is used, so that output remains constant • this is analogous to the marginal rate of substitution (MRS) in consumer theory • like the MRS, the MRTS is always measured as a positive quantity: −𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑀𝑅𝑇𝑆 = 𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑙𝑎𝑏𝑜𝑢𝑟 𝑖𝑛𝑝𝑢𝑡 −Δ𝐾 𝑀𝑅𝑇𝑆 = Δ𝐿 (𝑓𝑜𝑟 𝑎 𝑓𝑖𝑥𝑒𝑑 𝑙𝑒𝑣𝑒𝑙 𝑜𝑓 𝑞) • ∆𝐾 and ∆𝐿 are small changes in capital and labour along an isoquant o the MRTS is equal to 2 when labor increases from 1 unit to 2 and output is fixed at 75 o the MRTS falls to 1 when labor is increased from 2 units to 3, and then declines to 2/3 and to 1/3 o as more and more labor replaces capital, labor becomes less productive and capital becomes relatively more productive o therefore, we need less capital to keep output constant, and the isoquant becomes flatter DIMINISHING MRTS • the MRTS falls as we move down along an isoquant • the mathematical implication is that isoquants, like indifference curves, are convex, or bowed inward • The diminishing MRTS tells us that the productivity of any one input is limited • As more and more labor is added to the production process in place of capital, the productivity of labor falls • Similarly, when more capital is added in place of labor, the productivity of capital falls • Production needs a balanced mix of both inputs • the MRTS is closely related to the marginal products of labor (𝐿𝑃 ) and capital (𝑀𝑃 ) 𝐾 𝑎𝑑𝑑𝑖𝑡𝑖𝑜𝑛𝑎𝑙 𝑜𝑢𝑡𝑝𝑢𝑡 𝑓𝑟𝑜𝑚 𝑖𝑛𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑢𝑠𝑒 𝑜𝑓 𝑙𝑎𝑏𝑜𝑢𝑟 = 𝑀𝑃 𝐿 Δ𝐿 𝑀𝑃 𝐾 𝑟𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 𝑖𝑛 𝑜𝑢𝑡𝑝𝑢𝑡 𝑓𝑟𝑜𝑚 𝑑𝑒𝑐𝑟𝑒𝑎𝑠𝑒𝑑 𝑢𝑠𝑒 𝑜𝑓 𝑐𝑎𝑝𝑖𝑡𝑎𝑙 = Δ𝐾 • since we are keeping output constant by moving along an isoquant, the total change in output must be zero (𝑀𝑃 𝐿(Δ𝐿) + 𝑀𝑃 (𝐾K) = 0 𝑀𝑃 𝐿 Δ𝐾 = −( ) = 𝑀𝑅𝑇𝑆 𝑀𝑃 𝐾 Δ𝐿 • the marginal rate of technical substitution between two inputs is equal to the ratio of the marginal products of the inputs Production FunctionsTwo Special Cases • Two extreme cases of production functions show the possible range of input substitution in the production process: perfect substitutes and fixed-proportions production function • Perfect Substitutes: o the MRTS is constant at all points on an isoquant • Fixed-Proportions Production Function: o Sometimes called a Leontief production function o It is impossible to make any substitution among inputs o Each level of output requires a specific combination of labour and capital: additional output cannot be obtained unless more capital and labour are added in specific proportions o As a result, the isoquants are L-shaped, just as indifference curves are L- shaped when two goods are perfect complements o Example: ▪ the reconstruction of concrete sidewalks using jackhammers ▪ It takes one person to use a jackhammerneither two people and one jackhammer nor one person and two jackhammers will increase production o points A, B, and C represent technically efficient combinations of inputs o to produce output 𝑞 , a quantity of labor 𝐿 and capital 𝐾 can be used, 1 1 1 as at A o If capital stays fixed at 1 , adding more labor does not change output o Nor does adding capital with labor fixed at 𝐿 1 o on the vertical and the horizontal segments of the L-shaped isoquants, either the marginal product of capital or the marginal product of labor is zero o Higher output results only when both labor and capital are added, as in the move from input combination A to input combination B o The fixed-proportions production function describes situations in which methods of production are limited 6.4 Returns to Scale • in the long run, with all inputs variable, the firm must consider the best way to increase output • one way to do so is to change the scale of the operation by increasing all of the inputs to production in proportion • Example: o If it takes one farmer working with one harvesting machine on one acre of land to produce 100 bushels of wheat, what will happen to output if we put two farmers to work with two machines on two acres of land? o Output will almost certainly increase, but will it double, more than double, or less than double? o Returns to scale: the rate at which output increases as inputs are increased proportionately INCREASING RETURNS TO SCALE • Increasing returns to scale: situation in which output more than doubles when all inputs are doubled • This might arise because the larger scale of operation allows managers and workers to specialize in their tasks and to make use of more sophisticated, large-scale factories and equipment • Example: the automobile assembly line is a famous example of increasing returns • If there are increasing returns, then it is economically advantageous to have one large firm producing (at relatively low cost) rather than to have many small firms (at relatively high cost) because this large firm can control the price that it sets, it may need to be regulated • Example: increasing returns in the provision of electricity is one reason why we have large, regulated power companies CONSTANT RETURNS TO SCALE • Constant returns to scale: situation in which output doubles when all inputs are doubled • the size of the firm’s operation does not affect the productivity of its factors: because one plant using a particular production process can easily be replicated, two plants produce twice as much output • Example: a large travel agency might provide the same service per client and use the same ratio of capital (office space) and labor (travel agents) as a small agency that services fewer clients DECREASING RETURNS TO SCALE • Decreasing returns to scale: situation in which output less than doubles when all inputs are doubled • applies to some firms with large-scale operations • Eventually, difficulties in organizing and running a large-scale operation may lead to decreased productivity of both labor and capital • Communication between workers and managers can become difficult to monitor as the workplace becomes more impersonal • Thus, the decreasing-returns case is likely to be associated with the problems of coordinating tasks and maintaining a useful line of communication between management and workers Describing Returns to Scale • Returns to scale need not be uniform across all possible levels of output • Example: at lower levels of output, the firm could have increasing returns to scale, but constant and eventually decreasing returns at higher levels of output • Returns to scale vary considerably across firms and industries • Other things being equal, the greater the returns to scale, the larger the firms in an industry are likely to be SUMMARY 1. A production function describes the maximum output that a firm can produce for each specified combination of inputs. 
 2. In the short run, one or more inputs to the production process are fixed. In the long run, all inputs are potentially variable. 
 3. Production with one variable input, labor, can be usefully described in terms of the average product of labor (which measures output per unit of labor input) and the marginal product of labor (which measures the additional output as labor is increased by 1 unit). 
 4. According to the law of diminishing marginal returns, when one or more inputs are fixed, a variable input (usually labor) is likely to have a marginal product that eventually diminishes as the level of input increases. 
 5. An isoquant is a curve that shows all combinations of inputs that yield a given level of output. A firm’s production function can be represented by a series of isoquants associated with different levels of output. 
 6. Isoquants always slope downward because the marginal product of all inputs is positive. The shape of each isoquant can be described by the marginal rate of technical substitution at each point on the isoquant. The marginal rate of technical substitution of labor for capital (MRTS) is the amount by which the input of capital can be reduced when one extra unit of labor is used so that output remains constant. 7. The possibilities for substitution among inputs in the production process range from a production function in which inputs are perfect substitutes to one in which the proportions of inputs to be used are fixed (a fixed-proportions production function). 8. In long-run analysis, focus on the firm’s choice of its scale or size of operation. Constant returns to scale means that doubling all inputs leads to doubling output. Increasing returns to scale occurs when output more than doubles when inputs are doubled; decreasing returns to scale applies when output less than doubles. CHAPTER 7: The Cost of Production 7.1 Measuring Cost: Which Costs Matter? Economic Cost versus Accounting Cost • Accounting cost: actual expenses plus depreciation charges for capital equipment • Economistsand we hope managerstake a forward-looking view • they are concerned with the allocation of scarce resources • therefore, they care about what cost is likely to be in the future and about ways in which the firm might be able to rearrange its resources to lower its costs and improve its profitability • Economic cost: cost to a firm of utilizing economic resources in production • The word economic tells us to distinguish between the costs the firm can control and those it cannot • It also tells us to consider all costs relevant to production • Clearly capital, labor, and raw materials are resources whose costs should be included • But the firm might use other resources with costs that are less obvious, but equally important Opportunity Cost • Opportunity cost: cost associated with opportunities forgone when a firm’s resources are not put to their best alternative use • Example: o a firm that owns a building and therefore pays no rent for office space o Does this mean the cost of office space is zero? o The firm’s managers and accountant might say yes, but an economist would disagree o The economist would note that the firm could have earned rent on the office space by leasing it to another company o Leasing the office space would mean putting this resource to an alternative use that would have provided the firm with rental income o This forgone rent is the opportunity cost of utilizing the office space o because the office space is a resource that the firm is utilizing, this opportunity cost is also an economic cost of doing business o What about the wages and salaries paid to the firm’s workers? o This is clearly an economic cost of doing business, but if you think about it, you will see that it is also an opportunity cost o The reason is that the money paid to the workers could have been put to some alternative use instead o Perhaps the firm could have used some or all of that money to buy more labor-saving machines, or even to produce a different product altogether o As long as we account for and measure all of the firm’s resources properly, we will find that: 𝐸𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝐶𝑜𝑠𝑡 = 𝑂𝑝𝑝𝑜𝑟𝑡𝑢𝑛𝑖𝑡𝑦 𝐶𝑜𝑠𝑡 • Example: o Consider an owner that manages her own retail toy store and does not pay her-self a salary (We’ll put aside the rent that she pays for the office space just to simplify the discussion.) o Had our toy store owner chosen to work elsewhere she would have been able to find a job that paid $60,000 per year for essentially the same effort o In this case the opportunity cost of the time she spends working in her toy store business is $60,000. o Now suppose that last year she acquired an inventory of toys for which she paid $1 million o She hopes to be able to sell those toys during the holiday season for a substantial markup over her acquisition cost o However, early in the fall she receives an offer from another toy retailer to acquire her inventory for $1.5 million o Should she sell her inventory or not? The answer depends in part on her business prospects, but it also depends on the opportunity cost of acquiring a toy inventory o Assuming that it would cost $1.5 million to acquire the new inventory all over again, the opportunity cost of
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