Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization

Transcription

1 Consumer and Firm Behavior: The Work-Leisure Decision and Profit Maximization Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 1 Discussion So far: How to measure variables of macroeconomic relevance Now, we need a model to account for the stylized facts This week: study a simple model of the behaviour of consumers and firms in a static (one-period) environment taking into account the technology, preferences Static versus dynamic.. Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 2 1

2 A typical macroeconomics model A typical macroeconomics model contains Firms and consumers Goods to purchase Consumer preferences Production technology Resources, (K,L,N) Sometimes policymakers Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 3 A typical macroeconomics model We have to identify the objectives of consumers, firms and governments They may optimize subject to tastes, preferences, resources and constraints Consistency is important: Final outcome should be an equilibrium concept (maybe competitive or noncompetitive eq m. [imperfect competition]) Run experiments (what happens to the equilibrium if there is a shock to say government expenditures, oil prices, monetary policy etc.) Experiments on issues that you know the answer (fitting the data) Experiments on issues that you don t know the answer Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 4 2

3 Discussion Consumers: trade off between working and leisure How are the preferences affected by this trade-off How are the preferences affected by constraints Wages, non-wage income always affect decision to work hard or less hard Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 5 Discussion Firms: production decisions Production technology Market environment profits influence how much labour is needed to engage in production Equilibrium in the goods and labour market!! Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 6 3

4 Optimizing Agents (Firms & Consumers) Both consumers and firms optimize!! Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 7 Representative Consumer Represents all consumers in the economy Has preferences (Indifference Curves) Faces constraints (Budget and time constraints) Optimizes her utility She can consume two types of goods 1.a (physical) consumption good. 2.leisure Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 8 4

5 Utility Function (Consumption bundles) UC (, l) > UC (, l) UC (, l) < UC (, l) UC (, l) = UC (, l) Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 9 Assumptions: Useful to frame our mind! A1. More is always preferred than less! A2. Diversity is important A3. We are talking about normal goods! (dc/dy>0, dl/dy>0) Indifference Curve: Graphical representation of preferences Def: An indifference curve connects a set of points representing preferred consumption bundles among which the consumer is indifferent Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 10 5

6 Indifference Curves Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 11 Properties of Indifference Curves downward sloping because of A1 (amount) Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 12 6

7 Figure 4-2 Properties of Indifference Curves Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 13 Properties of Indifference Curves convex (bowed in towards the origin) because of A2 (diversity) Marginal Rate of Substitution Def: MRS of leisure for consumption is the rate at which the consumer is just willing to substitute leisure for consumption goods MRS l,c = -(slope of the indifference curve passing through (C,l)) Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 14 7

8 Diversity implies diminishing marginal rate of substitution Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 15 Constraints Rep. Agent is competitive (price taker) Price are taken as given, then decisions on consumption are taken Suppose (for the moment) barter economy Two goods: consumption and time Trade for leisure time Time constraint s l+ N = h (1) Where h: hours available l: leisure N s : time spent working (labour supply) Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 16 8

9 Constraints (Cont d) Assume that rep. Agent s (consumer s) real disposable income is: S wn + π T w: real wage rate π: dividend (profit of firms are distributed to rep. Agent T: lump-sum taxes (2) Consumer has no saving motive remember it is a one-period economy, so spend it (consume all!) Budget Constraint S C = wn + π T Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 17 (3) Some manipulations Substitute for N s from time constraint ( l+ N s = h) C = w( h l) + π T (4) i.e. total market expenditure equal to real disposable income Alternatively C+ wl = wh+ π T (5) RHS: implicit quantity of real disposable income LHS: expenditure on two goods (C, l) Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 18 9

10 Graph Consumer s Budget Constraint Write in slope-intercept form C = wl+ wh+ π T And graph according to T>π Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 19 Figure 4-3 Representative Consumer s Budget Constraint (T > π) Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 20 10

11 Graph Consumer s Budget Constraint What if π>t? Budget constraint is kinked Slope of the BC is w over its upper portion Constraint is vertical in the lower portion There is a kink in the budget constraint because consumer can not consume more than h hours of leisure Points along BD: l=h, number of hours worked is 0! Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 21 Figure 4-4 Representative Consumer s Budget Constraint (T < π) Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 22 11

12 In sum Rep. agent Budget Constraint tells us what consumption bundles are feasible given the market real wage, dividend income and taxes! Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 23 Putting Budget Constraint and Indifference Curves together: Consumer Optimization Assume rational agent (knows its preferences, budget constraint and is ABLE to evaluate feasible consumption bundle for itself!) Def: The optimal consumption bundle is the point representing a consumption-leisure pair that is on the highest possible indifference curve, and on or inside the consumer s budget constraint M RS l, C = w Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 24 12

13 Figure 4-5 Consumer Optimization (MRS l,c =w) Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 25 Optimal Consumption bundle I 1 is optimal (indifference curve is tangent to budget constraint) Why? 1. Any point inside the Budget Constraint violates the assumption of more is preferred to less! 2. At a point along the Budget Constraint: Point H is preferred to a Point F since the slope of the indifference curve at F > slope of the BC (that is w) i.e. at F the rate at which the consumer is willing to trade leisure for consumption > the rate at which the consumer can trade leisure for consumption (i.e. MRS l,c > w) Consumer would be better off if she gives up a bit of consumption for leisure (moves into higher indifference curve!) MRS l,c =w i.e. optimizing condition makes SURE that MRS l,c equals the RELATIVE PRICE of leisure in terms of consumption goods (C: numeraire) Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 26 13

14 Figure 4-6 The Representative Consumer Chooses not to Work Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 27 Comparative Statics Let s conduct some experiments!! Assume some exogenous changes in parameters of our model! (changes in the economic environment) See what happens to the consumption leisure decisions of our RepAg Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 28 14

15 Two Experiments A change in the π-t (an income change, that does not depend on wages) Both π and T can change Pure income effect (prices do not change, thus real wage w remains constant) A change in the w Income and substitution effects Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 29 Figure 4-7 An Increase in the Consumer s Dividend Income Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 30 15

16 An Increase in the Consumer s Dividend Income Move from H to K Why not some other point on Budget Constraint 2 An artefact of the assumption of normal goods Implies that as income increases, consumption increases but labour supply decreases!! income increases by AF but consumption only by C 2 -C 1 Working less means less wage income Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 31 Figure 4-8 Increase in the real Wage Rate-Income and Substitution Effects Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 32 16

17 Increase in the real Wage Rate-Income & Substitution Effects An increase in w Remember -w represents the slope of the BC Keep π-t constant (isolate pure income effect) C 1 C 2 But l may increase or decrease (in the example it remains constant) Why? Income versus substitution effects! Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 33 Substitution effect: w increases, suppose we take away dividend income or increase taxes such that we stay on the initial indifference curve When real wages increase leisure becomes more expensive relative to consumption goods RepAg substitutes away from the more expensive good (leisure) to relatively cheaper good i.e. C increases l drops Labour supply increases (N s =h-l) Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 34 17

18 Income Effect Give back the π-t income Normal goods! Pure income effect (both consumption and income increases) final effect C increases l may increase/decrease, labour supply N s may increase/decrease Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 35 Figure 4-9 Labor Supply Curve Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 36 18

19 Figure 4-10 Effect of an Increase in Dividend Income or a Decrease in Taxes Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 37 Example: Consumption and Leisure are Perfect Complements Goods are perfect complements for the consumer if she always wishes to consume these goods in fixed proportions Tires/cars Left shoe/right shoe Toothbrush/paste etc Suppose C=al Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 38 19

20 Figure 4-11 Perfect Complements Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 39 Algebraically Perfect complements C = a l ( 7 ) C = w ( h l ) + π T ( 8 ) s o l v e f o r C, l w h + π T l = a + w a n d a ( w h + π T ) C = a + w Note that there is no substitution effects Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 40 20

21 Empirical Evidence in the US ( ) 1. An upward trend in real wages 2. A downward trend in average weekly hours worked (employment) income effect seems to dominate substitution effect in recent time periods in earlier time periods it was not necessarily so.. Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 41 The Representative Firm Firms and consumers exchange labour to produce consumption goods Production technology Y = d zf( K, N ) z: total factor productivity Assume that K is fixed (static model), z, N d are variable Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 42 21

22 The Representative Firm Def: The marginal product of a factor of production is the additional output that can be purchased with one additional unit of that factor input, holding constant the quantities of the other factor inputs Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 43 Properties of prod n function 1. constant returns to scale 2. output increases when either capital or labour input increases (MP N >0, MP K >0) 3. MP N decreases as quantity of labour increases 4. MP K decreases as quantity of capital increases 5. MP N increases as the quantity of capital input increases Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 44 22

23 Figure 4-14 Production Function, Fixing the Quantity of Capital and Varying the Quantity of Labor Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 45 Figure 4-15 Production Function, Fixing the Quantity of Labor and Varying the Quantity of Capital Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 46 23

24 Figure 4-16 Marginal Product of Labor Schedule for the Representative Firm Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 47 Figure 4-17 Adding Capital Increases the Marginal Product of Labor Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 48 24

25 An increase in total factor productivity z Technological innovations (e.g. assembly line) Weather Government regulations (e.g. pollution control, do you remember Kyoto protocol?) Oil/energy prices Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 49 Figure 4-18 Total Factor Productivity Increases Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 50 25

26 Figure 4-19 Effect of an Increase in Total Factor Productivity on the Marginal Product of Labor Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 51 Cobb Douglas Prod n Function and Solow Residual ( d ) α Y = zk N ==> z = K α 1 α Y ( d N ) 1 α Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 52 26

27 Figure 4-20 The Solow Residual for the United States Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 53 Profit Maximization Determinants of the firm s demand for labour Like the Rep. consumer, firm is competitive (it takes real wages as given) Maximize profits π=y-wn d Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 54 27

28 Profit Maximization K fixed Choose N d to maximize the profits d π = zf ( K, N ) w N d π = 0 d d N d d F ( K, N ) = z w = d d N N M P N M P = w d 0 Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 55 Figure 4-21 Revenue, Variable Costs, and Profit Maximization Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 56 28

29 Figure 4-22 The Marginal Product of Labor Curve Is the Labor Demand Curve of the Profit-Maximizing Firm Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 57 In Sum Representative consumer Representative firm Both optimizing some well specified objective Need of bringing these into a coherent framework Copyright 2002 Pearson Education, Inc. and Dr Yunus Aksoy Slide 58 29