CONSUMPTION-LEISURE FRAMEWORK SEPTEMBER 20, 2010 The Three Maro Markets THE THREE MACRO (AGGREGATE) MARKETS Goods Markets P Labor Markets Capital/Savings/Funds/Asset Markets interest rate labor Will put miro-foundations under all three September 20, 2010 2 apital 1
Introdution BASICS n + l 168 Consumption-Leisure Framework provides foundation for Labor-market supply funtion Goods-market demand funtion An appliation of the basi onsumer theory model we will put a maro interpretation on it Only one time period no future for whih to save Notation : onsumption ( all stuff ) n: number of hours spent working per week l: number of hours per week (time spent not working) P: dollar prie of one unit of onsumption (a nominal variable) W: hourly rate in terms of dollars (a nominal variable) t: tax rate on labor inome Weekly model a detail Could have alled it a daily model, a monthly model, a yearly model, Just need to take SOME stand on the length of a period September 20, 2010 3 Model Struture UTILITY Preferenes u(, l) with all the usual properties Stritly inreasing in Stritly inreasing in l Diminishing marginal utility in Diminishing marginal utility in l Plotted in good-by-good spaes: u(,l) u(,l) Plotted as indifferene urves Utility side of onsumption- framework idential to Chapter 1 framework September 20, 2010 4 2
Model Struture BUDGET CONSTRAINT Consumer must work for his inome Y no longer falls from the sky P Y Y (1-t)Wn (all inome is after-tax labor inome) P (1 t) Wn n 168 - l P (1 t) W(168 l) Rearrange P+ (1 t) Wl 168(1 t) W Simply an appliation/reinterpretation of our basi onsumer theory model Spending on Spending onsumption on P 1 1+ P 2 2 Y A onstant from the point of view of the individual (prietaker) Chapter 1 budget onstraint Spending on 1 Spending on 2 A onstant from the point of view of the individual September 20, 2010 5 Model Struture BUDGET CONSTRAINT Consumer must work for his inome Y no longer falls from the sky P Y Y (1-t)Wn (all inome is after-tax labor inome) P (1 t) Wn n 168 - l P (1 t) W(168 l) Rearrange P+ (1 t) Wl 168(1 t) W (After-tax) is opportunity ost of, hene the prie of - opportunity osts are real eonomi osts/pries Simply an appliation/reinterpretation of our basi onsumer theory model Spending on Spending onsumption on P 1 1+ P 2 2 Y A onstant from the point of view of the individual (prietaker) Chapter 1 budget onstraint Spending on 1 Spending on 2 A onstant from the point of view of the individual September 20, 2010 6 3
Model Struture CONSUMER OPTIMZATION Consumer s deision problem: maximize utility subjet to budget onstraint bring together both ost side and benefit side Choose and l subjet to P+ (1 t) Wl 168(1 t) W Plot budget line optimal hoie (*,l*) Superimpose indifferene map At the optimal hoie 168 CONSUMPTION-LEISURE OPTIMALITY CONDITION - A key building blok of modern maro models ul (*,*) l (1 tw ) u (*,*) l P slope -(1-t)W/P IMPORTANT: the larger is (1-t)W/P, the steeper is the budget line MRS (between onsumption and ) prie ratio (inlusive of taxes) September 20, 2010 7 Maro Fundamentals REAL WAGE W/P a key variable for maroeonomi analysis Unit Analysis (i.e., analyze algebrai units of variables) Units(W) $/hour of work Units(P) $/unit of onsumption $ Units(W/P) hour of work $ unit of onsumption $ hour of work $ unit of onsumption unit of onsumption hour of work Will sometimes denote using w (lower-ase ) Eonomi deisions depend on real s (W/P), not nominal s (W) Measures the purhasing power of (nominal) earnings whih is presumably what people most are about September 20, 2010 8 4
The Graphis of the Consumption-Leisure Model CONSUMER OPTIMIZATION Consumer s deision problem: maximize utility subjet to budget onstraint bring together both ost side and benefit side Choose and l subjet to P+ (1 t) Wl 168(1 t) W Plot budget line optimal hoie (*,l*) Superimpose indifferene map At the optimal hoie CONSUMPTION-LEISURE OPTIMALITY CONDITION - key building blok of modern maro models ul (*,*) l (1 tw ) u (*,*) l P MRS (between onsumption and ) After-tax real 168 slope -(1-t)W/P IMPORTANT: the larger is (1-t)W/P, the steeper is the budget line Derive onsumption- optimality ondition using Lagrange analysis September 20, 2010 9 The Mathematis of the Consumption-Leisure Model LAGRANGE ANALYSIS Apply Lagrange tools to onsumption- optimization Objetive funtion: u(,l) Constraint: g(,l) 168(1-t)W P (1-t)Wl 0 Step 1: Construt Lagrange funtion [ ] L(,, lλ) ul (,) + λ 168(1 tw ) P (1 twl ) Step 2: Compute first-order onditions with respet to, l, λ September 20, 2010 10 5
The Mathematis of the Consumption-Leisure Model LAGRANGE ANALYSIS Apply Lagrange tools to onsumption- optimization Objetive funtion: u(,l) Constraint: g(,l) 168(1-t)W P (1-t)Wl 0 Step 1: Construt Lagrange funtion [ ] L(,, lλ) ul (,) + λ 168(1 tw ) P (1 twl ) Step 2: Compute first-order onditions with respet to, l, λ Step 3: Solve (with fous on eliminating multiplier) * * ul (, l ) (1 tw ) * * ul (, l ) P CONSUMPTION-LEISURE OPTIMALITY CONDITION MRS (between After-tax real onsumption and ) September 20, 2010 11 Labor Supply in the Miro MICRO-LEVEL LABOR SUPPLY An experiment: how do miro-level onsumption/ hoies hange as the real hanges (assume t 0 here for simpliity) * 1 l* 1 168 slope -(W/P) 1 September 20, 2010 12 6
Labor Supply in the Miro MICRO-LEVEL LABOR SUPPLY An experiment: how do miro-level onsumption/ hoies hange as the real hanges (assume t 0 here for simpliity) REAL WAGES: (W/P) 1 < (W/P) 2 * 2 * 1 slope -(W/P) 2 slope -(W/P) 1 l* 2 l* 1 168 September 20, 2010 13 Labor Supply in the Miro MICRO-LEVEL LABOR SUPPLY An experiment: how do miro-level onsumption/ hoies hange as the real hanges (assume t 0 here for simpliity) REAL WAGES: (W/P) 1 < (W/P) 2 < (W/P) 3 < (W/P) 4 < (W/P) 5 SUMMARY 1. For low levels of real s, a rise in the real auses optimal to derease 2. For intermediate levels of real s, a rise in the real auses optimal to remain unhanged 3. For high levels of real s, a rise in the real auses optimal to inrease * 4 * 4 slope -(W/P) 5 * 3 slope -(W/P)4 * 2 slope -(W/P) 3 * 1 slope -(W/P) 2 slope -(W/P) 1 l* 5 l* 3 l* 4 l* 2 l* 1 168 September 20, 2010 14 7
Labor Supply in the Miro and the Maro LABOR SUPPLY Using the relation n 168 - l real Bakward-bending labor supply urve at the miro level n* 1 n* 2 n* 3 n* 4 labor n* 5 Individual-level labor supply funtion September 20, 2010 15 Miro Fundamentals DECOMPOSING EFFECTS OF PRICE CHANGES Substitution effet General two-good ase: if relative prie of good 1 inreases (i.e., P 1 /P 2 inreases), purhases of good 1 derease Good 1 more expensive buy less of it Appliation to onsumption- framework: if real W/P inreases (i.e., the relative prie (opportunity ost) of ), hoose less hoose to work more Work in opposite diretions in C-L Inome effet framework General two-good ase: if total inome inreases (i.e., Y inreases), purhases of all goods inreases Riher buy more of everything Appliation to onsumption- framework: if real W/P inreases total inome inreases (holding all else onstant ) hoose more ( is a good) hoose to work less September 20, 2010 16 8
Labor Supply in the Miro and the Maro LABOR SUPPLY Using the relation n 168 - l real Bakward-bending labor supply urve at the miro level real but not at the maro level S Inome effet dominates the substitution effet Inome effet and substitution effet roughly anel Sum over all individuals Substitution effet dominates the inome effet n* 1 n* 2 n* 3 n* 4 labor labor n* 5 Individual-level labor supply funtion Aggregate-level labor supply funtion September 20, 2010 17 Miro-Maro Connetions MACRO VS. MICRO LABOR QUANTITIES Average hours per worker Aggregate Hours Worked Number of individuals working Aggregate Hours Worked Average hours per worker x Number of individuals working Maro/representative-agent framework has typially been most onerned with this Miro studies are piking up this Intensive margin Extensive margin Standard rep-agent framework offers an aggregate theory of employment But not neessarily of unemployment Tratably inorporating both intensive and extensive margins of labormarket adjustment in full maro models only a reent development September 20, 2010 18 9
Consumption Demand in the Miro and the Maro CONSUMPTION DEMAND Optimal hoie of onsumption was always rising as real was rising Could have onduted the entire analysis assuming nominal W was held fixed and nominal P was falling Whih means real W/P is rising Result: Fall in P rise in optimal always Implies downward-sloping onsumption demand funtion at the miro level and at the aggregate level Consumption demand over two-thirds of aggregate demand in developed ountries September 20, 2010 19 The Three Maro Markets THE THREE MACRO (AGGREGATE) MARKETS Goods Markets Demand derived from C-L framework P D Labor Markets Supply derived from C-L framework S labor Capital/Savings/Funds/Asset Markets (aka Finanial Markets) interest rate September 20, 2010 20 apital 10
THE MACROECONOMICS OF TIME Consumption- model a stati (i.e., one time period) model Dynami models the ore of modern maroeonomi theory Expliit onsideration of how eonomi deisions/behaviors/outomes unfold over multiple time periods Two-period model (Chapters 3 and 4) the simplest possible multiperiod framework Will allow us to begin analyzing issues regarding interest rates and inflation (phenomena that our aross time) Will allow us to think about redit restritions and the redit runh Infinite-period model (Chapter 8) Allows a riher quantitative desription of the maroeonomy Highlights the role of assets and the intersetion between finane and maroeonomis September 20, 2010 21 11