CONSUMPTION-LABOR FRAMEWORK (aka CONSUMPTION-LEISURE FRAMEWORK) SEPTEMBER 19, 2011 The Three Maro Markets THE THREE MACRO (AGGREGATE) MARKETS Goods Markets P Labor Markets Finanial/Capital/Savings/Asset Markets interest rate labor Will put miro-foundations under all three September 19, 2011 2 apital 1
The Three Maro Markets THE THREE MACRO (AGGREGATE) MARKETS Goods Markets P Labor Markets labor September 19, 2011 3 Introdution BASICS n + l 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 19, 2011 4 2
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) September 19, 2011 5 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 19, 2011 6 3
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 - l P (1 t) W( l) Rearrange P+ (1 t) Wl (1 t) W Spending on onsumption 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 A onstant from the point on 2 of view of the individual September 19, 2011 7 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 - l P (1 t) W( l) Rearrange P+ (1 t) Wl (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 framework 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 A onstant from the point on 2 of view of the individual September 19, 2011 8 4
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 (1 t) W Plot budget line optimal hoie (*,l*) Superimpose indifferene map slope -(1-t)W/P IMPORTANT: the larger is (1-t)W/P, the steeper is the budget line September 19, 2011 9 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 (1 t) W Plot budget line optimal hoie (*,l*) Superimpose indifferene map At the optimal hoie 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 19, 2011 10 5
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 September 19, 2011 11 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 19, 2011 12 6
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 (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 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 19, 2011 13 The Mathematis of the Consumption-Leisure Model LAGRANGE ANALYSIS Apply Lagrange tools to onsumption- optimization Objetive funtion: u(,l) Constraint: g(,l) (1-t)W P (1-t)Wl 0 Step 1: Construt Lagrange funtion [ ] L(,, lλ) ul (,) + λ (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 ) * * u (, l ) P CONSUMPTION-LEISURE OPTIMALITY CONDITION MRS (between After-tax real onsumption and ) September 19, 2011 14 7
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 slope -(W/P) 1 September 19, 2011 15 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 September 19, 2011 16 8
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 * 3 * 2 slope -(W/P) 3 * 1 slope -(W/P) 2 slope -(W/P) 1 l* 3 l* 2 l* 1 September 19, 2011 17 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 * 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 September 19, 2011 18 9
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 September 19, 2011 19 Labor Supply in the Miro MICRO-LEVEL LABOR SUPPLY Using the relation n - l real Bakward-bending labor supply urve at the miro level Inome effet dominates the substitution effet Inome effet and substitution effet roughly anel Substitution effet dominates the inome effet n* 1 n* 2 n* 3 n* 4 labor n* 5 September 19, 2011 20 10
Labor Supply in the Miro and the Maro LABOR SUPPLY Using the relation n - 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 n* 5 Individual-level labor supply funtion labor Why the differene? Problem Set 2, Q3 Aggregate-level labor supply funtion labor September 19, 2011 21 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 measure this September 19, 2011 22 11
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 measure this Intensive margin Extensive margin Standard rep-agent framework offers an aggregate theory of employment But not neessarily of unemployment Searh theory is a theory of unemployment September 19, 2011 23 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 19, 2011 24 12
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 Finanial/Capital/Savings/Asset Markets interest rate September 19, 2011 25 apital 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 framework (Chapters 3 and 4) the simplest possible multi-period 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 framework (Chapter 8) Allows a riher quantitative desription of the maroeonomy Highlights the role of assets and the intersetion between finane and maroeonomis September 19, 2011 26 13