Chapter 3 - GDP

8/20/2019 Chapter 3 - GDP

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The circular flow diagram

Let’s look at the flow of dollars from the viewpoints of these economicactors. Households receive income and use it to pay taxes to thegovernment, to consume goods and services, and to save through thefinancial markets. Firms receive revenue from the sale of goods andservices and use it to pay for the factors of production. Households andfirms borrow in financial markets to buy investment goods, such as housesand factories. The government receives revenue from taxes and uses it topay for government purchases. ny excess of tax revenue over governmentspending is called public saving, which can be either positive !a budgetsurplus" or negative !a budget deficit".

What Determines the Total Production of Goods and Services?

n economy’s output of goods and services#its $%depends on !'" its(uantity of inputs, called the factors of production, and !)" its ability to turninputs into output, as represented by the production function.Factors of production are the inputs used to produce goods and services.The two most important factors of production are capital and labor. *apitalis the set of tools that workers use. Labor is the time people spend working.+e use the symbol to denote the amount of capital and the symbol L todenote the amount of labor.-n this chapter we take the economy’s factors of production as given. +ealso assume here that the factors of production are fully utilied.

The available production technology determines how much output isproduced from given amounts of capital and labor. /conomists express thisrelationship using a production function. Letting 0 denote the amount of


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output, we write the production function as 01F!, L". The productionfunction reflects the available technology for turning capital and labor intooutput. 2any production functions have a property called constant returnsto scale. production function has constant returns to scale if an increaseof an e(ual percentage in all factors of production causes an increase in

output of the same percentage3 01F!, L".

+e can now see that the factors of production and the production functiontogether determine the (uantity of goods and services supplied, which inturn e(uals the economy’s output. 4ecause we assume that the supplies of capital and labor and the technology are fixed, output is also fixed. +henwe discuss economic growth in *hapters 5 and 6, we will examine howincreases in capital and labor and advances in technology lead to growth inthe economy’s output.

How Is National Income Distributed to the Factors of Production

4ecause the factors of production and the production function togetherdetermine the total output of goods and services, they also determinenational income.Here we examine the modern theory of how national income is dividedamong the factors of production. -t is based on the classical !eighteenth7century" idea that prices ad8ust to balance supply and demand, applied hereto the markets for the factors of production, together with the more recent!nineteenth7century" idea that the demand for each factor of productiondepends on the marginal productivity of that factor. This theory, called theneoclassical theory of distribution, is accepted by most economists today asthe best place to start in understanding how the economy’s income is

distributed from firms to households.The distribution of national income is determined by factor prices. -n aneconomy wherethe two factors of production are capital and labor, the two factor prices arethe wage workers earn and the rent the owners of capital collect. 4ecausewe have assumed that the economy’s factors of production are fixed, thefactor supply curve is vertical.


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To understand factor prices and the distribution of income, we mustexamine the demand for the factors of production. 4ecause factor demandarises from the thousands of firms that use capital and labor, we start byexamining the decisions a typical firm makes about how much of thesefactors to employ.

The simplest assumption to make about a typical firm is that it iscompetitive. competitive firm is small relative to the markets in which ittrades, so it has little influence on market prices. 9imilarly, our firm cannotinfluence the wages of the workers it employs because many other localfirms also employ workers.The firm sells its output at a price &, hires workers at a wage +, and rentscapital at a rate :. ;otice that when we speak of firms renting capital, weare assuming that households own the economy’s stock of capital. -n thisanalysis, households rent out their capital, 8ust as they sell their labor.The goal of the firm is to maximie profit. &rofit is e(ual to revenue minuscosts< it is what the owners of the firm keep after paying for the costs of

production.&rofit 1 :evenue = Labor *osts = *apital *osts&rofit 1 &0 = +L = :&rofit 1 &F!, L" = +L = :.The competitive firm takes the product price and the factor prices as givenand chooses the amounts of labor and capital that maximie profit. 4utwhat are those profit7maximiing (uantities>The more labor the firm employs, the more output it produces. Themarginal roduct of labor !2&L" is the extra amount of output the firmgets from one extra unit of labor, holding the amount of capital fixed.2&L 1 F!, L ? '" = F!, L ".

2ost production functions have the property of diminishing marginalproduct3 holding the amount of capital fixed, the marginal product of labordecreases as the amount of labor increases.


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4ecause an extra unit of labor produces 2&L units of output and each unitof output sells for & dollars, the extra revenue is & @ 2&L. The extra cost of hiring one more unit of labor is the wage +. Thus, the change in profit fromhiring an additional unit of labor is

A&rofit 1 A:evenue = Acost 1 !& @ 2&L" = +.The firm continues to hire labor until the next unit would no longer beprofitable#that is, until the 2&L falls to the point where the extra revenuee(uals the wage. The competitive firm’s demand for labor is determined by& @ 2&L 1 +. +e can also write this as 2&L 1 +B&.+B& is the real wage#the payment to labor measured in units of outputrather than in dollars. To maximie profit, the firm hires up to the point atwhich the marginal product of labor e(uals the real wage.4ecause the 2&L diminishes as the amount of labor increases, this curveslopes downward. For any given real wage, the firm hires up to the point atwhich the 2&L e(uals the real wage. Hence, the 2&L schedule is also the

firm’s labor demand curve.

The firm decides how much capital to rent in the same way it decides howmuch labor to hire, using the marginal product of capital !2&".To sum up, the competitive, profit7maximiing firm follows a simple ruleabout how much labor to hire and how much capital to rent. The firmdemands each factor of production until that factor’s marginal product fallsto e(ual its real factor price.

Having analyed how a firm decides how much of each factor to employ, wecan now explain how the markets for the factors of production distribute the

economy’s total income. -f all firms in the economy are competitive and


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profit maximiing, then each factor of production is paid its marginalcontribution to the production process.The total real wages paid to labor are therefore 2&L@ L, and the total realreturn paid to capital owners is 2&@ .The income that remains after the firms have paid the factors of production

is the economic profit of the owners of the firms. :eal economic profit is/conomic &rofit 1 0 = !2&L @ L" = !2&@ ".How large is economic profit> The answer is surprising3 if each factor of production is paid its marginal product, then the sum of these factorpayments e(uals total output. -n other words, constant returns to scale,profit maximiation, and competition together imply that economic profit isero.-f economic profit is ero, how can we explain the existence of CprofitD in theeconomy> -n the real world, however, most firms own rather than rent thecapital they use. 4ecause firm owners and capital owners are the samepeople, economic profit and the return to capital are often lumped together.

-f we call this alternative definition accounting profit, we can say thatccounting &rofit 1 /conomic &rofit ? !2&@ ".+e can now answer the (uestion posed at the beginning of this chapterabout how the income of the economy is distributed from firms tohouseholds. /ach factor of production is paid its marginal product, andthese factor payments exhaust total output. Total output is divided betweenthe payments to capital and the payments to labor, depending on theirmarginal productivities.

!"emles

ccording to the neoclassical theory of distribution, factor prices e(ual the

mar7ginal products of the factors of production. 4ecause the marginalproducts depend on the (uantities of the factors, a change in the (uantity of any one fac7tor alters the marginal products of all the factors. Therefore, achange in the sup7ply of a factor alters e(uilibrium factor prices and thedistribution of income.The outbreak of the bubonic plague#the 4lack %eath#in 'E6 reduced thepopulation of /urope by about one7third within a few years. 4ecause themarginal product of labor increases as the amount of labor falls, thismassive reduction in the labor force should have raised the marginalproduct of labor and e(uilibrium real wages. The evidence confirms thetheory3 real wages approximately doubled during the plague years. Thevertical supply curve shifts to the left.The reduction in the labor force caused by the plague should also haveaffected the return to land, the other ma8or factor of production in medieval/urope. +ith fewer workers available to farm the land, an additional unit of land would have produced less additional output, and so land rents shouldhave fallen. Gnce again, the theory is confirmed3 real rents fell I percentor more during this period.

&aul %ouglas noticed a surprising fact3 the division of national incomebetween capital and labor had been roughly constant over a long period. -nother words, as the economy grew more prosperous over time, the totalincome of workers and the total income of capital owners grew at almostexactly the same rate. %ouglas asked *harles *obb, a mathematician, whatproduction function, if any, would produce constant factor shares if factors


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always earned their marginal products. This function became known as the*obbJ%ouglas production function3F!,L" 1 K L!'7K"

K is a constant between ero and one that measures capital’s share of income. That is, '7K determines what share of income goes to labor.

is a parameter greater than ero that measures the productivity of theavailable technology. n increase in the amount of capital raises the 2&Land reduces the 2&. 9imilarly, an increase in the amount of labor reducesthe 2&L and raises the 2&. technological advance that increases theparameter raises the marginal product of both factors proportionately.The 2&L is proportional to output per worker, and the 2& is proportional tooutput per unit of capital. 0BL is called average labor productivity, and 0B iscalled average capital productivity.The neoclassical theory of distribution tells us that the real wage +B& e(ualsthe marginal product of labor. The *obbJ%ouglas production function tellsus that the marginal product of labor is proportional to average labor

productivity 0BL.-f this theory is right, then workers should en8oy rapidly rising livingstandards when labor productivity is growing robustly. -s this true>Theory and history both confirm the close link between labor productivityand real wages. This lesson is the key to understanding why workers todayare better off than workers in previous generations.

9i millora la productivitat, les empreses contractaran a cada +B& mstreballadors !es desplaMarN la demanda de treball a la dreta". /n desplaMar7se la demanda hi harurN un excs de demanda de treballadors i els sou realtendirN a pu8ar. /n el nou e(uilibri el sou real serN ms alt per(uO hamillorat la productivitat.

What Determines the Demand for Goods and Services?

+e now continue our tour of the circular flow diagram and examine how theoutput from production is used.For now, to simplify the analysis, we assume our economy is a closedeconomy. closed economy has three uses for the goods and services itproduces. These three components of $%& are expressed in the nationalincome accounts identity3 01*?-?$.

Households consume some of the economy’s output< firms and householdsuse some of the output for investment< and the government buys some of the output for public purposes.Households receive income from their labor and their ownership of capital,pay taxes to the government, and then decide how much of their after7taxincome to consume and how much to save. The income that households


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receive e(uals the output of the economy 0. The government then taxeshouseholds an amount T. +e define income after the payment of all taxes,0= T, to be disosable income. Households divide their disposable incomebetween consumption and saving.The relationship between consumption and disposable income is called the

consumtion function3 *1*!0=T". This e(uation states that consumptionis a function of disposable income.

4oth firms and households purchase investment goods. Firms buyinvestment goods to add to their stock of capital and to replace existingcapital. Households buy new houses, which are also part of investment.Total investment in the Pnited 9tates averages about ' percent of $%&.The (uantity of investment goods demanded depends on the interest rate,which measures the cost of the funds used to finance investment.-f the interest rate rises, fewer investment pro8ects are profitable, and the(uantity of investment goods demanded falls.

+hen studying the role of interest rates in the economy, economistsdistinguish between the nominal interest rate and the real interest rate.The nominal interest rate is the interest rate as usually reported3 it is therate of interest that investors pay to borrow money. The real interest rate isthe nominal interest rate corrected for the effects of inflation. The realinterest rate measures the true cost of borrowing and, thus, determines the(uantity of investment.+e can summarie this discussion with an e(uation relating investment - tothe real interest rate r3 -1-!r".

Government urchases are the third component of the demand for goods

and services. These purchases are only one type of government spending.The other type is transfer payments to households, such as welfare for thepoor and 9ocial 9ecurity payments. Pnlike government purchases, transferpayments are not made in exchange for some of the economy’s output of goods and services. Therefore, they are not included in the variable $.Transfer payments are the opposite of taxes3 they increase households’ disposable income, 8ust as taxes reduce disposable income. Thus, anincrease in transfer payments financed by an increase in taxes leavesdisposable income unchanged. +e can now revise our definition of T toe(ual taxes minus transfer payments. %isposable income, 0=T, includesboth the negative impact of taxes and the positive impact of transferpayments.-f $ exceeds T,the government runs a budget deficit, which it funds byissuing government debt#that is, by borrowing in the financial markets. -f $ is less than T, the government runs a budget surplus, which it can use torepay some of its outstanding debt.

What #rings the Sul$ and Demand for Goods and Services Into!%uilibrium?

+hat ensures that the sum of consumption, investment, and governmentpurchases e(uals the amount of output produced> +e will see that in thisclassical model, the interest rate is the price that has the crucial role of e(uilibrating supply and demand.There are two ways to think about the role of the interest rate in theeconomy. +e can consider how the interest rate affects the supply and


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demand for goods or services. Gr we can consider how the interest rateaffects the supply and demand for loanable funds. s we will see, these twoapproaches are two sides of the same coin.

Equilibrium in the Market for Goods and Services: The Supply and

Demand for the Economy’s Output The factors of production and the production function determine the(uantity of output supplied to the economy3 01F!,L".4ecause the variables $ and T are fixed by policy, and the level of output 0is fixed by the factors of production and the production function, we canwrite 0 1 *!0=T" ? -!r" ? $. The right side of the e(uation is demand andde left side suply. The left side is output and the left side the use of thisoutput.This e(uation states that the supply of output e(uals its demand, which isthe sum of consumption, investment, and government purchases.;otice that the interest rate r is the only variable not already determined in

the last e(uation. This is because the interest rate still has a key role toplay3 it must ad8ust to ensure that the demand for goods e(uals the supply.The greater the interest rate, the lower the level of investment, and thusthe lower the demand for goods and services, *?-?$. -f the interest rate istoo high, then investment is too low and the demand for output falls shortof the supply. -f the interest rate is too low, then investment is too high andthe demand exceeds the supply. t the e(uilibrium interest rate, thedemand for goods and services e(uals the supply.

Equilibrium in the inancial Markets: The Supply and Demand for !oanable unds

0=*=$ 1 -.The term 0=*=$ is the output that remains after the demands of consumers and the government have been satisfied< it is called nationalsaving or simply saving !9". -n this form, the national income accountsidentity shows that saving e(uals investment.To understand this identity more fully, we can split national saving into twoparts#one part representing the saving of the private sector and the otherrepresenting the saving of the government39 1 !0=T=*" ? !T=$" 1 -.The term !0=T=*" is disposable income minus consumption, which isprivate saving.The term !T=$" is government revenue minus governmentspending, which is public saving.The circular flow diagram reveals an interpretation of this e(uation3 thise(uation states that the flows into the financial markets !private and publicsaving" must balance the flows out of the financial markets !investment".To see how the interest rate brings financial markets into e(uilibrium,substitute the consumption function and the investment function into thenational income accounts identity. ;ext, note that $ and T are fixed bypolicy and 0 is fixed by the factors of production and the productionfunction30= *!0=T" = $ 1 -!r".9 1 -!r".The left7hand side of this e(uation shows that national saving depends onincome 0 and the fiscal7policy variables $ and T. For fixed values of 0, $,and


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T, national saving 9 is also fixed. The right7hand side of the e(uation showsthat investment depends on the interest rate.

The saving function is a vertical line because in this model saving does notdepend on the interest rate !we relax this assumption later". Theinvestment function slopes downward3 as the interest rate decreases, moreinvestment pro8ects become profitable.-n fact, saving and investment can be interpreted in terms of supply anddemand. -n this case, the CgoodD is loanable funds, and its CpriceD is theinterest rate. 9aving is the supply of loanable funds#households lend theirsaving to investors or deposit their saving in a bank that then loans thefunds out. -nvestment is the demand for loanable funds#investors borrowfrom the public directly by selling bonds or indirectly by borrowing frombanks. 4ecause investment depends on the interest rate, the (uantity of loanable funds demanded also depends on the interest rate.The interest rate ad8usts until the amount that firms want to invest e(ualsthe amount that households want to save. -f the interest rate is too low,investors want more of the economy’s output than households want to save./(uivalently, the (uantity of loanable funds demanded exceeds the (uantitysupplied. +hen this happens, the interest rate rises. *onversely, if theinterest rate is too high, households want to save more than firms want toinvest< because the (uantity of loanable funds supplied is greater than the(uantity demanded, the interest rate falls.The e(uilibrium interest rate is found where the two curves cross. t thee(uilibrium interest rate, households’ desire to save balances firms’ desireto invest, and the (uantity of loanable funds supplied e(uals the (uantitydemanded.

&hanges in Saving' The !ffects of Fiscal Polic$

*onsider first the effects of an increase in government urchases by anamount A$.-n the market for goods and services3 4ecause total output is fixed by the

factors of production, the increase in government purchases must be metby a decrease in some other category of demand. %isposable income 0 = T


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is unchanged, so consumption * is unchanged as well. Therefore, theincrease in government purchases must be met by an e(ual decrease ininvestment. To induce investment to fall, the interest rate must rise.$overnment purchases are said to crowd out investment.

-n the market for loanable funds3 4ecause the increase in governmentpurchases is not accompanied by an increase in taxes, the governmentfinances the additional spending by borrowing#that is, by reducing public

saving. +ith private saving unchanged, this government borrowing reducesnational saving. s Figure shows, a reduction in national saving isrepresented by a leftward shift in the supply of loanable funds available forinvestment. t the initial interest rate, the demand for loanable fundsexceeds the supply. The e(uilibrium interest rate rises to the point wherethe investment schedule crosses the new saving schedule.

;ow consider a reduction in ta"es of (T. %isposable income rises by AT,and consumption rises. The increase in consumption must be met by adecrease in investment. For investment to fall, the interest rate must rise.Hence, a reduction in taxes, like an increase in government purchases,

crowds out investment and raises the interest rate.;ational saving 9, which e(uals 0 = * = $, falls by the same amount asconsumption rises. s in above figure, the reduction in saving shifts thesupply of loanable funds to the left, which increases the e(uilibrium interestrate and crowds out investment.M

9o far, we have discussed how fiscal policy can change national saving. +ecan also use our model to examine the other side of the market#thedemand for investment. Gne reason investment demand might increase istechnological innovation. 9uppose, for example, that someone invents anew technology, such as the rail7road or the computer. -nvestment demand

may also change because the government encourages or discouragesinvestment through the tax laws.


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Figure E7'' shows the effects of an increase in investment demand. t anygiven interest rate, the demand for investment goods !and also for loanablefunds" is higher.

The surprising implication of Figure E7'' is that the e(uilibrium amount of investment is unchanged. Pnder our assumptions, the fixed level of savingdeter7mines the amount of investment< in other words, there is a fixedsupply of loanable funds. n increase in investment demand merely raisesthe e(uilibrium interest rate.

+e would reach a different conclusion, however, if we modified our simpleconsumption function and allowed consumption !and its flip side, saving" todepend on the interest rate. 4ecause the interest rate is the return tosaving !as well as the cost of borrowing", a higher interest rate mightreduce consumption and increase saving. -f so, the saving schedule wouldbe upward sloping rather than vertical.+ith an upward7sloping saving schedule, an increase in investment demandwould raise both the e(uilibrium interest rate and the e(uilibrium (uantityof investment. Figure E7') shows such a change. The increase in theinterest rate causes households to consume less and save more. Thedecrease in consumption frees resources for investment.


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Chapter 3 - GDP

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