ECON 3020 Intermediate Macroeconomics

ECON 3020 Intermediate Macroeconomics Chapter 4 Consumer and Firm Behavior The Work-Leisure Decision and Profit Maximization 1 Instructor: Xiaohui Huang Department of Economics University of Virginia 1 Some content in the slides is borrowed from Alice Schoonbroodt. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 1 / 57

A One-Period Model of the Macroeconomy Chapter 4: Microeconomic behavior of consumers and firms Consumer: work-leisure decision Firm: profit maximization Chapter 5: Macroeconomic analysis: government and competitive equilibrium. Under what conditions are free market outcomes efficient? Effects of changes in government spending. Effects of changes in total factor productivity (TFP). c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 2 / 57

Model Ingredients and Features One-period model Static decisions (no dynamics, e.g. no saving decision) Dynamic decisions: plans over more than one period. Many consumers and firms, but we assume that all consumers are identical and all firms are identical Study a representative consumer and a representative firm c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 3 / 57

Main Topics of Chapter 4 Representative consumer: Given: market prices Preferences and budget constraint Choose: consumption, working hours/leisure hours Goal: maximize utility Representative Firm: Given: market prices Available technology Choose: labor input Goal: maximize profit Next chapter: market clearing and competitive equilibrium Economics is all about optimization. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 4 / 57

The Representative Consumer s Preferences Suppose the consumer cares about two goods: Consumption good Physical good Aggregation of all consumer goods Measurement: aggregate consumption Leisure Time spent not working in the market Measurement: total number of hours available minus total hours worked c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 6 / 57

The Representative Consumer s Preferences Preferences can be represented by a utility function. What is an utility function? It assigns a value to every consumption bundle. The value is called "utility". Mathematical expression: U(C, l) C: quantity of consumption goods l: quantity of leisure A consumption bundle is a particular pair of quantities of consumption goods and leisure. E.g. (C 1, l 1 ). c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 7 / 57

The Representative Consumer s Preferences Utility function represents how the consumer ranks different consumption bundles. Bundle (C 1, l 1 ) is strictly preferred to bundle (C 2, l 2 ) if U(C 1, l 1 ) > U(C 2, l 2 ) Bundle (C 2, l 2 ) is strictly preferred to bundle (C 1, l 1 ) if U(C 1, l 1 ) < U(C 2, l 2 ) The consumer is indifferent between bundle (C 1, l 1 ) and bundle (C 2, l 2 ) if U(C 1, l 1 ) = U(C 2, l 2 ) Remark: the actual level of utility is irrelevant all that matters is the relative utility level of one bundle to another. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 8 / 57

Assumptions on Consumer s Preferences 1 More is always preferred to less. 2 Diversity is good. 3 Consumption goods and leisure are normal goods Normal good: the quantity of the good purchased increases when income increases. Example: meals at fine restaurant. Inferior good: the quantity of the good purchased decreases when income increases. Example: fast food. In our model, if income C, l c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 9 / 57

Indifference Curves An indifference curve connects a set of points, with these points representing consumption bundles among which the consumer is indifferent. Figure 4.1 Indifference Curves c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 10 / 57

Indifference Curves In Figure 4.1: B(C 1, l 1 ) and D(C 2, l 2 ) are on the same indifference curve U(C 1, l 1 ) = U(C 2, l 2 ). A is strictly preferred to B I 2 is an indifference curve representing a higher utility level than I 1. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 11 / 57

Indifference Curves Two key properties of indifference curves: An indifference curve is downward-sloping. An indifference curve is convex, i.e. bowed-in toward the origin point. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 12 / 57

Property 1: Indifference Curves Slope Downward Figure 4.2 Properties of Indifference Curves Because more is preferred to less. Compare points A, D and B. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 13 / 57

Property 2: Indifference Curves Are Convex Figure 4.2 Properties of Indifference Curves Because diversity is a good thing. Compare combinations of A and B with A or B. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 14 / 57

Marginal Rate of Substitution (MRS) The marginal rate of substitution of leisure for consumption, MRS l,c, is the rate at which the consumer is just willing to substitute leisure for consumption goods. MRS = slope of indifference curve at a cetain point. (See Figure 4.2) For example: MRS l,c (moving from A to B) = slope of AB = C 2 C 1 l 2 l 1. How much consumption we need to take away for each unit of leisure added as we move from A to B. As B getting closer to A, MRS l,c becomes the negative of the slope of the tangent line to the indifference curve at A. Note: MRS l,c is different at different points c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 15 / 57

MRS and Convexity of Indifference Curves Indifference curve is convex MRS is diminishing. Because diversity is preferred. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 16 / 57

Representative Consumer s Budget Constraint Assumptions: The consumer is a price-taker (competitive behavior). Barter economy: no money in the economy. Exchanges of labor time for consumption, or vice versa. Time constraint: l }{{} leisure + N s }{{} labor supply Budget constraint: C }{{} consumption goods = wn s }{{} real wage income = h }{{} total amount of time available + π }{{} dividends from firms T }{{} lump-sum tax Real wage: in terms of C, C is the "numeraire". wn s + π T : real disposable income. No motive to save + the more the better consume all. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 17 / 57

Lump-Sum Tax Lump-sum tax does not depend in any way on the actions of the economic agent being taxed. In practice, no taxes are lump sum. Lump-sum tax is non-distorting: does not change consumer s behavior. Distorting taxes: sales tax. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 18 / 57

Mathematical Representation of Budget Constraint Put the time constraint into the budget constraint Add wl to both sides C + wl }{{} Implicit expenditures C = w(h l) + π T = wh + π T }{{} Implicit real disposable income To graph the budget constraint in C l plane, rewrite it as C = w }{{} Slope l + wh + π T }{{} Intercept c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 19 / 57

Graphical Representation of Budget Constraint Figure 4.3 Representative Consumer s Budget Constraint when (T > π) c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 20 / 57

Graphical Representation of Budget Constraint Figure 4.4 Representative Consumer s Budget Constraint when (T < π) c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 21 / 57

Consumer Optimization Assumption: the representative consumer is rational. The consumer knows his or her own preferences and budget constraint and can evaluate which feasible consumption bundle is best for him or her. The optimal consumption bundle is the point representing a consumption-leisure pair that is on the highest possible indifference curve and is on or inside the consumer s budget constraint. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 22 / 57

Consumer Optimization Figure 4.5 Consumer Optimization when (T < π) The consumer will choose the best bundle that is budget feasible. Rule out impossible candidates: Points below the budget line would never be chosen (e.g. J). Why? Any points along BD other than B would never be chosen. Why? Restrict attention to points on AB. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 23 / 57

Consumer Optimization Figure 4.5 Consumer Optimization when (T < π) The market pays w units of consumption goods for each unit of leisure time you give up. Point F: MRS l,c > w, willing to have more leisure. Point E: MRS l,c < w, willing to have more consumption goods. Point H: MRS l,c = w, optimal. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 24 / 57

Consumer s Optimizing Condition A consumption bundle (C, l) is optimal when MRS l,c = w The rate at which the consumer is willing to trade leisure for consumption (MRS l,c ) is the same as the rate at which the consumer can trade leisure for consumption in the market (w). Generally, a consumption bundle (x, y) is optimal when MRS x,y = P x P y Sets the marginal rate of substitution of good x for good y equal to the relative price of x in terms of y. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 25 / 57

Interior Solution vs. Corner Solution Interior solution Tangency condition MRS x,y = P x P y holds. Optimal choices of both goods are strictly inside their boundaries. 0 < l < h and C > 0. Corner solution Optimal choice of either good is just on the boundaries l = 0 or l = h or C = 0. In our example, point H stands for an interior solution. Is a corner solution possible in our model? Is it possible for the consumer to choose not working at all (i.e. l = h)? c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 26 / 57

Extreme case: l = h (not working at all) Figure 4.6 The Representative Consumer Chooses Not to Work If consumer chooses not working at all, i.e. point B with N s = 0. This will not be possible when consumers and firms interact. Why? Also, point A cannot be the optimal choice. Why? c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 27 / 57

Is It Plausible to Assume Rationality? Do we always make optimizing decisions? Why do people make non-optimal choices? Is it safe to assume that consumers are always optimizing? c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 28 / 57

Recall: Income Effect vs. Substitution Effect Income effect: changes in consumer s wealth. Substitution effect: changes in relative prices. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 29 / 57

Two Experiments Using the Model 1 Increase in after-tax dividend income, i.e. π T. Results from π or T or both. Holding real wage rate (w) constant. Pure income effect: consumer is richer. No substitution effect: relative price of l to C remains the same. 2 Increase in the real wage rate, i.e. w. Holding π and T constant. Income effect: the consumer is richer. Substitution effect: relative price of l to C is higher. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 30 / 57

Experiment 1: π T Figure 4.7 An Increase in π T for the Consumer Before: Budget constraint: ABD. Optimal choice: H. After: Budget constraint: FJD. Optimal choice: K. Effects on C and l: Richer l (normal good) Two opposing effects on C: Nonwage income C Wage income C Net effect: C (normal good) c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 31 / 57

Experiment 2: w Figure 4.8 Increase in the Real Wage Rate Before: Budget constraint: ABD. Optimal choice: F. After: Budget constraint: EBD. Optimal choice: H Effects on C and l: Richer C (normal good) Two opposing effects on l: Richer l Leisure is more expensive l Net effect on l is unclear. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 32 / 57

Decompose: Substitution Effect and Income effect How to decompose? Remove the pure income effect. Start from the new budget constraint. Shift it parallelly until tangent to the old indifference curve. Pure Substitution effect: F O. l, C, N s. Pure income effect: O H. l, C, N s. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 33 / 57

Net Effect: Substitution Effect + Income Effect For consumption goods C: Substitution effect: C (relatively cheaper); Income effect: C (richer); Net effect: C. We always have w C. For leisure l: Substitution effect: l (relatively more expensive); Income effect: l (richer); Net effect: unclear. In Figure 4.8, both effects just cancel out with each other. Remark: w may lead to N s. Labor supply curve may be backward-bended! c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 34 / 57

Labor Supply Curve N s (w) Figure 4.9 Labor Supply Curve To obtain labor supply curve: For any given w, find the optimal bundle (C(w), l(w)). Labor supply under w: N s (w) = h l(w). Connect all pairs (w, N s (w)). Assume: substitution effect dominates. N s (w) is upward sloping. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 35 / 57

Shifts of Labor Supply Curve: π T Figure 4.10 Effect of an Increase in Dividend Income or a Decrease in Taxes π T l (pure income effect) N s Labor supply is lower at any wage rate. Labor supply curve shifts to the left. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 36 / 57

Example: Perfect Complements Figure 4.11 Perfect Complements A specific type of preferences: consumer can be better off only if receives more of both goods. (The assumption "the more the better" is not satisfied!) Indifference curves are L-shaped (MRS = or 0). The optimal bundle is always along the line C = al, a > 0. C and l are always consumed in fixed proportions. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 37 / 57

Example: Perfect Complements Optimal bundle (C, l) must satisfy two conditions: Budget constraint: C = w(h l) + π T Optimizing condition: C = al Solve for C and l: l = wh + π T a + w Repeat our two experiments: π T C, l, N s w C, l, N s, C = a(wh + π T ) a + w With perfect complements, there are no substitution effects! How to see this? Change in the preferences: a C, l. Practice on your own: perfect substitutes. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 38 / 57

The Representative Firm s Production Function A production function describes how factor inputs are converted into outputs. Y }{{} output = z }{{} total factor productivity F( K }{{} capital, N d ) }{{} labor N d : measured as total hours worked by workers F(K, N d ): the production function Assume capital input is fixed firm cannot vary the quantity of plant and equipment in the short run. Labor input is variable firm can hire and lay off workers. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 40 / 57

Marginal Product of Labor (MP N ) Figure 4.12 Production Function, Fixing K and Varying N d Marginal product of labor: additional output that can be produced with one additional unit of labor holding capital constant. MP N = slope of F(K, N d ) c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 41 / 57

Marginal Product of Capital (MP K ) Figure 4.13 Production Function, Fixing N d and Varying K Marginal product of capital: additional output that can be produced with one additional unit of capital holding labor constant. MP K = slope of F(K, N ) c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 42 / 57

Assumptions on Production Technology 1 The size of firm is irrelevant. 2 Both capital and labor are useful for production. 3 Input factors become less and less productive as they accumulate over time. 4 Increasing one factor input makes the other factor more productive. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 43 / 57

Properties of Production Function Four important properties of production function: 1 Constant returns to scale. 2 Marginal products are positive, production function is upward-sloping. 3 Diminishing marginal products, production function is concave. 4 Additional capital increases marginal product of labor. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 44 / 57

Property 1: Constant Returns to Scale Production function exhibits constant returns to scale (CRS). If all factor inputs double, then output also doubles. Generally, given any constant x > 0, we have zf (xk, xn d ) = xzf(k, N d ) With CRS technology, the size of firms is irrelevant: one large firm is equivalent to many small ones. Compared with IRS and DRS. With CRS, all we need is a representative firm. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 45 / 57

Property 2: Marginal Products Are Positive Output increases when either labor or capital increases. N d Y and K Y Alternatively, MP N > 0 and MP K > 0. Production function is upward-sloping with respect to N d and K. (See Figure 4.12 and Figure 4.13) c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 46 / 57

Property 3: Diminishing Marginal Products MP N as N d, holding K fixed. (MP NN < 0) MP K as K, holding N d fixed. (MP KK < 0) Y = zf(k, N d ) is concave in N d and K. (See Figure 4.12 and Figure 4.13) Figure 4.14 MP N for the Representative Firm c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 47 / 57

Property 4: Additional Capital Increases MP N Figure 4.15 Additional Capital Increases MP N MP N as K (i.e. MP NK > 0) MPN 1 corresponds to K = K 1. MPN 2 corresponds to K = K 2 > K 1. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 48 / 57

Total Factor Productivity (TFP) We have discussed properties of F(K, N d ). F(xK, xn d ) = xf (K, N d ), for any x > 0. F N > 0, F K > 0. F NN < 0, F KK < 0. F NK > 0. Now we study the total factor productivity, z. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 49 / 57

What Causes TFP Changes? Technological innovation Example: automobile manufacturing industry (z ) Good weather Example: agriculture, construction sector (z ) Government regulation Example: pollution control (z ) Relative price of energy Example: increase in oil price (z ) c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 50 / 57

Effects of An increase in TFP Two effects of z : Higher output level: z Y = zf (K, N d ). Higher marginal product of labor: z MP N (K, N d ). Effect of z on output Effect of z on MP N c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 51 / 57

Measurement for TFP TFP is not directly observed in any data. Look at our production function Y = zf(k, N d ) What factors make contributions to output? Which variables can we observe in data? How to measure TFP? c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 52 / 57

Measurement for TFP: An Empirical Example Commonly used Cobb-Douglas production function Y = zk a (N d ) 1 a, 0 < a < 1 Consistent with data: capital and labor shares of national income have been roughly constant in U.S. Does this function satisfy all of our assumptions? Check. Empirical estimate for a is 0.3 using U.S. data. Y = zk 0.3 (N d ) 0.7 Y : measured by real GDP. K : measured as total quantity of capital in existence, built up from expenditures on capital goods in NIPA. N d : measured by total employment. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 53 / 57

Measurement for TFP: An Empirical Example z is measured by Solow residual: z = Y K 0.3 (N d ) 0.7 Figure 4.18 The Solow Residual for the U.S., 1948-2010 c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 54 / 57

Firm Optimization Figure 4.19 Revenue, Variable Costs, and Profit Maximization Firm s profits (K is fixed): π = Y wn d = zf(k, N d ) wn d Optimum: N d = N, where the production function is tangent to labor cost curve. π = AB = ED. Optimizing condition: MP N = w. Why? c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 55 / 57

Firm s Optimizing Condition Benefit-cost analysis: Benefit of an extra unit of labor: MP N Cost of an extra unit of labor: w To the left of N, MP N > w, firm wants to hire more. To the right of N, MP N < w, firm wants to hire less. Eventually, the firm will set N d = N, where MP N = w. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 56 / 57

Labor Demand Curve N d (w) Figure 4.20 Labor Demand Curve To obtain labor demand curve For any given w, find optimal labor input: MP N (K, N d ) = w N d Connect all pairs (w, N d (w)) The MP N curve is also the labor demand curve. c Copyright 2014 Xiaohui Huang. All Rights Reserved. Macroeconomics, Williamson 5/E, Chapter 4 57 / 57