Inter Macroecon ECON 3010
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This 33 page Class Notes was uploaded by Hallie Kuphal on Wednesday October 28, 2015. The Class Notes belongs to ECON 3010 at University of Wyoming taught by Robert Godby in Fall. Since its upload, it has received 8 views. For similar materials see /class/230356/econ-3010-university-of-wyoming in Economcs at University of Wyoming.
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Date Created: 10/28/15
Rob Godby University of Wyoming lA Av v Ll a Production functions describe how much output a set of given inputs K and L can create given technology a Production functions have the following general properties 0 no output without input 9 output is increasing in factor inputs used 0 as only one factor is increased output increases at a decreasing rate marginal products are diminishing in factors used a This is a specific mathematical functional form often used to describe production 1 Y AKO UW o where a K is the amount of capital used a L is the amount of labor used s A is a parameter describing technology Constant Returns to Scale CR8 1 CR8 technology refers to technology with the following property if by changing L and K by a constant factor of proportionality output also changes by the same proportion 9 Example double both L and K inputs then Y output doubles 3 Suppose both L and K increase by a factor CRS technology implies that output also increases by FZK 2L ZY a in a Cobb Douglas Function AZKOCZL1OC AZoc1ocKaL1oc AzKOCLlt10ltgt ZAKO L139O Marginal Products are decreasing in their own factor and increasing in the other factor 1 Since Y AKO LUO alabon o MPL 10cAK L39 10cAK L take a simple derivative 0 If L increases MPL falls 9 If K increases MPL rises 3 capital 0 MPK ocAK 1L13900 0cAL139 0K139 0 a this is the derivative of Y with respect to K or in plain English the change in output for a small change like one unit in K o If K increases MPK falls 9 If L increases MPK rises t 2 a Suppose we multiply the marginal product of labor by LL1 MPLxLL 1ocAK0ltL390 xLL using the rules for exponents MPL 1ocAK0 L390 1L MPL 1ocAK0 L1390 L Since Y AKOCLW MPL 1ocAK0 L1390 L 1ocYL a therefore MPL 1ocYL a Suppose we multiply the marginal product of capital by KK1 MPKxKK ocAKoc IUoquK using the rules for exponents MPK ocAKa11L0lt1K MPK aAKaLlaK Since Y AKOCLW MPK aAKaLlaK ocYK a therefore MPK ocYK To recap o MPL 1ocYL o MPK ocYK YL and WK are called the quot K respectively the marginal products of labor and capital are proportional to the their average productivities This function implies a constant proportion of total GDP is paid to each factor If factors of production earn the Y y Total factor payments to K are expressed as RPXKMPKXK OLYKXK0cY Similarly wP x L MPL x L 1 0cYL x L 1 0cY It is easy to show then that the total payments to factors are RP x K wP x L ocY 1 ocY oc1 ocY Y This is a general property of an economy with CRS technology I u 2 u i 7 r quotof 1 5 5147 my hi naive i ii J u H if i i r I quoth J 39Es quotA yr 5 r39quot Q i J M widL iii r r nigt ctdks IT 1 u tote ii pro ts must be zero 3 Imagine an exogenous change occurs in the economy Comparative statics evaluate such a change as it impacts the total economy Using comparative statics allows us to determine how the model predicts the economy will be affected by such a change For example suppose that the population decreases suddenly as it did during the Plague How does this impact the labor market How will this affect production How will this affect prices How will these in turn affect the labor market Z L K Y E if 7 Labor Capital Goods Market Market Market P MP P MPL K Y L K K Y W2 W1 Y MP 1 Y YFLI K YFL7K YZY L K Y R P L K Y Labor Capital Goods Market Market P2 Market L l 4 P MPL 4 P MPK P1 PT 4 4 4 AD Y a From the diagram we can see that the fall in L increases the nominal wage The fall in L also reduces output as a function of capital YFK L where L is fixed as there is less labor at all levels of capital Since production is increasing in factors of production the fall in L lowers output and the MPK 3 Since the capital market clears and all K is used the fall in L reduces output and lowers Aggregate Supply a This effect increases the price level a The increase in the price level effects the demand for K and L o P x MPLshifts upward increasing the nominal wage 0 Less L implies a higher MPL thus wP must rise 0 The same shift is occurring in the K market but it is offset by the fall in MPKdue to the fall in L o Diagrammatically this change cannot be determined 3 Overall then the fall in L caused o a fall in MPK o a fall in total output Y o and increase in P 9 an increase in MPL 9 an increase in nominal and real wages 9 An indeterminate change in nominal and real rental rates of K 3 Instead of using the diagram we can also use the equilibrium conditions that must be true afte the economy reacts to the exogenous change in L To do so we must identify the equilibrium conditions that are true in each market a In the factor markets the value of the wage a firm s marginal cost must be equal to the value of the benefit the firm gets from using that factor P x MP 5 F3 E f H llll s a In the labor market L available has fallen therefore MPL will rise 9 from the equilibrium condition in the labor market this implies the change in L results in an increase in the real wage D In the capital market L available has fallen therefore MPK will fall assuming CobbDouglas production 9 this implies RP must fall to maintain equilibrium a Reduced L implies reduced Y 3 Since E lquot f5r P AD must fall to maintain equilibrium 9 With no change in AD this implies an increase in Price level in the economy Using the equilibrium conditions we have now described all of the outcomes the diagram could tell us plus the indeterminant one in the K market a What if G is increased a To evaluate this change we consider the effect it has in the Goods market in equilibrium 47 g i J H i a i 39q quot39 n 1 w i hat Vii L lg L i j rquot t Previously we have show than this can be rearranged as 2 since all terms on the lefthand side are exogenously determined this implies that ifG increases lr must decrease by an equivalent amount to maintain equilibrium This is called m l u LEE a In the long run the classical model predicts that if government expenditure increases it will reduce private investment by an equivalent amount This makes sense because total output is determined only by the production technology and the amount of factors available not expenditure a This refers to the fact that the real side of the economy technology factors of production available determines the level of real output and real productivity Nominal values in the economy are determined by demand ie level of AD determines the price level given AS This is the basic model of the long run relationships in the economy It tells us real output is determined only by technology and the factors of production available It also tells us how income is distributed It tells us how price levels are determined in the economy 3 Because this is a long run model it cannot tell us how recessions and booms are caused why 1 It cannot explain business cycles why 1 It cannot explain persistent unemployment above the natural rate why Rob Godby University of Wyoming
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