Production1. The Technology of Production2. The Production Function with a Single Variable Input3. The Marginal Product of Labor4. Labor Productivity and the Wealth of Nations5. The Production Function with Two Variable Inputs6. Isoquants7. Marginal Rate of Technical Substitution8. Three Special Production Functions9. Returns to Scale1The Technology of Production• Production of goods and services involves transforming resources – suchas labor , raw materials, energy, and machines – into finished products.• Recall from lecture 2, the productive resources, such as labor and capitalequipment that a firm uses to manufacture goods and services are calledinputs or factors of production.• The amount of goods and services produced are called outputs.• Usually a firm can use different combinations of inputs to produce thesame level of output. Consider a restaurant that needs its 1000 disheswashed every night. It can use– one worker and a dishwasher or– five workers and no dishwashers2• A production function is a mathematical representation or varioustechnological recipes from which the firm can choose to configure itsproduction process. It shows the highest level of output that a firmcan produce for every specified combination of inputs.• Recall from the second lecture we wrote the production function as:Q = AF (K, L, R)whereQ = outputK = productive services of capitalL = laborR = natural resource inputs (land)A = level of technology.F is a function.A is sometimes called total factor productivity. It measures how effi-ciently one combines land, labor, and capital to produce an output.3• Outputs and inputs are measure per units of period of time. That is– Output is in number of units production per month, quarter, or year.– Labor is measured in hours per week, month or year or in workersper week, month or year• We will also in time want to make distinctions between the short-runand the long-run.– The short run is the period of time in which quantities of one or moreproduction factors cannot be changed. (i.e. firm can not engage innew investment or hire/fire workers, but change hours worked foreach existing worker)– The long run is the amount of time needed to make all productioninputs variable.4• Let’s also define: A fixed input as a production factor that cannot bevaried.• Let’s make our life easier for now by assuming A = 1, so we can ignoreit; let’s fix capital and land for now too.• We are just going to look at how the maximum of amount of output afirm can produce depends on just one input: labor.q = F (L)• Table 6.15• Fix capital at K and increase hours. In general output is increasing inhours worked until labor hits 7 hours. Then things output peaks andeven declines.• As output rises from a low level, a firm is capable of engaging in spe-cialization and division of labor, which lead to more output increasingat an increasing rate. At higher levels of output this effect goes awayand production is increasing as labor increases but at a decreasing rate.• Figure 6.1.• Average product of labor (APL)APL =outputlabor input=qLThe APL measures the productivity of the workforce on average.• Marginal product of labor (MPL)MPL =change in outputchange in labor input=∆q∆LThe MPL measure the productivity of the last incremental increase inlabor.6• The average product of labor at a point A on the production functionis the slope of the ray coming out of the origin and intersecting theproduction function at point A.• The marginal product of labor at point A is the slope of the productionat that point.• WhenMP L > AP L APL is decreasing• WhenMP L < AP L APL is decreasing7The Marginal Product of Labor• We usually find that the marginal product of labor faces the law ofdiminishing marginal returns.• This “law” states that as the use of an input increases holding all otherinputs fixed, the resulting additions to output will eventually decrease.• In other words, as you increase the labor input, output increases, butat a decreasing rate.• This is not to say that output is decreasing; just that each incrementaladdition of labor produces less output than the previous incrementaladdition.• Mathematically, the curve is concave.• At some point, the firm may face diminishing total returns to labor –that is the region along the production function where output decreaseswith additional labor.8Malthus and the Dismal Science• The idea of diminishing returns first became influential with ThomasMalthus in 1789 with his book An Essay on the Principle of Popu-lation.• Malthus argued as the population grew and the land area remainedfixed, a society would find it increasingly difficult to grow enough food.Though more intensive cultivation of the land could increase yields,each successive farmer would add less to the total than the last asthe marginal product of labor declined. Eventually per capita foodproduction would decline as the population grew.• Conclusion: Misery was the normal condition for humankind.– Image a country in which land was abundant and population low, sothat everyone had plenty to eat. Then families would be large andthe population would grow rapidly – until the pressure of populationon the land had reduced the condition of most people to the levelwhere starvation and disease held the population in check9• Led historian Thomas Carlyle to dub economics “the dismal science”• Fortunately Malthus was wrong– First, while 18th century European peasants did not live much betterthan ancient Egyptian peasants, scientific and technological progresshas been so rapid during the last 200 years than diminishing returnshave not been a problem.– Second, as countries have gotten wealthier, families have had fewer,not more, children.10Labor Productivity and the Wealth of Nations• A quote from Paul KrugmanProductivity isn’t everything, but in the long run it is almosteverything• This is really a macroeconomic topic, but what the heck ...• Average labor productivity is closely linked to per-capita output.• Think about an economy-wide production function.• Small changes in growth rate of productivity can have big affects in thelong-run.• How can a country increase its’ labor productivity?– perspiration theory – increase K, work more intensely.– inspiration theory – improve technology. Combine capital and laborin ways such that you get more output from the same level of inputs.• In 2005,