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LABOR SUPPLY, based on Varian section 9.8 LABOR SUPPLY REAL WAGE (W/P) 20 15 Serie1 10 Serie2 5 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Hours worked Labor Supply: 3 possibilities: (1) Labor supply is unrelated to the real wage. (2) Labor supply increases when the real wage increases. (3) Labor supply decreases when the real wage increases: when the real wage increases the individual can afford to take more leisure, which she likes. Factors that increase aggregate labor supply at a given real wage: 1. Labor immigration. 2. Lower unemployment benefits should increase the labor supply of the domestic population. The Microeconomics behind labor supply The individual or household faces the choice between consumption and leisure. More consumption requires more hours worked and hence less leisure. The problem of the individual is to maximize: U = U(C,R) where C= consumption during a period of time, e.g. a day. R = hours of leisure enjoyed during a day. If C U(.), and if R U(.). The two constraints the individual faces are: (1) The time constraint: LR L where L = labor supply in hours, L is the time endowment which is 24 hours per day. (2) P C W L M where P= Price of the consumption good W = Nominal Hourly Wage M= non-labor income, e.g. government transfers Let M P C In other words, C is the quantity of goods that the individual receives that is not related to hours worked. P C W L P C P C W L P C P C W L W L P C W L P C W (L L) P C W L P C W R P C W L Now we have combined the two constraints that the individual faces, and the result is similar to the usual budget constraint: px x p y y I Thus, the goods that the individual derives utility from (C and R) are on the lefthand-side of the equation. And in front of the quantities of these goods are the respective prices of these goods W is the price of leisure: it is what the individual gives up by taking one hour of leisure. P C W L is called full or potential income. If R=0, then P C P C W L . The constraint can be rewritten in real terms: 1 C (W / P) R C (W / P) L where 1 = real price of consumption, W/P is the real price of leisure = the quantity of goods the individual gives up by consuming one more unit of leisure. Graphical illustration of the choice possibilities of the individual: Let C 0 , C (W / P) L (W / P) R Slopecoefficient Intercept An Increase of the Real Wage Consumption 20 15 Serie1 10 Serie2 5 0 1 2 3 4 5 6 7 8 9 10 Leisure (0.0-1.0) Note: The choice constraint cuts the x-axis where R= L . In the figure we assume that L =1, and that W/P increases from 10 to 20. The numbers on the x-axis are 0.0, 0.1, 0.2,…, 1.0. Note also that labor supply (L) = L - R: When R=0, then L= L . If W/P the intercept increases, and the slope becomes more negative. If W/P , the individual can afford more of both C and R. On the other hand, when W/P , R becomes more expensive in terms of the quantity of consumption goods the individual gives up by consuming one more unit (hour) of leisure. 3 hypothetical possibilities on demand for leisure and on labor supply (L= L -R) when W/P : 1.No effect on the demand for leisure and on the labor supply if the substitution (price) effect = income effect. The substitution effect is negative for the demand of leisure when the price of leisure (that is, the real wage) increases. The income effect for the demand of leisure is positive as a higher real wage means that the individual can afford and wants more leisure when income increases. 2.Negative effect on the demand for leisure (= positive effect on labor supply) if the substitution effect > income effect. 3. Positive effect on the demand for leisure (= negative effect on labor supply) if the substitution effect < income effect. The optimal choice with positive non-labor income ( C 0 ) C (W / P) R C (W / P) L C C (W / P) L (W / P) R Slopecoefficient Intercept An Increase of Non-Labor Income Consumption 20 15 Serie1 10 Serie2 5 0 1 2 3 4 5 6 7 8 9 10 LEISURE (0.0-1.0) In the figure we assume that L =1, W/P=10, and that C increases from 5 to 10. The numbers on the x-axis are 0.0, 0.1, 0.2,…, 1.0. When C increases the individual wants more of both goods as they are assumed to be so-called normal goods. You want more of normal goods when your income increases. An increase of C does not change the opportunity cost of enjoying leisure, and constitutes therefore a pure income effect. Summary: The effect of changes in the exogenous variables on optimal demand for C and R, and on optimal labor supply: If C C * , R * , L* L R* If W/P C * , R * ?, L* L R* ? MPL,W/P Employment and taxes 1.6 1.4 1.2 1 0.8 0.6 0.4 0.2 0 LS Eqb W/P:t=0 LD 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Employment (L) Introducing a tax creates a wedge between what the firm pays (producer real wage) and what the worker receives (consumer real wage). A tax decreases employment. L decreases in figure from 5 to about 3.5. The producer real wage increases to 0.8 (from 0.7 when tax is zero) and the consumer real wage drops to below 0.4. Taxes on labor include social insurance- and income taxes. A mathematical note on how to derive optimal demand-functions in case of a Cobb-Douglas (or a logarithmic) utility function: If the individual maximizes U ( x, y) x y subject to the budget constraint: px x p y y I where x = quantity of good x, y= quantity of good y, px = price of good x, p y = price of good y, and I= income. The optimal demand for x and y are such that the consumer chooses to spend a constant fraction of its income on these goods: p x x* I x* I px * py y I y* py I Note if 1 x* (1 ) I , px y* I py A mathematical example on the optimal choice of leisure (optimal labor supply): Assume that the individual has the following utility function: U C1/ 2 R1/ 2 The constraints of the individual are: (1) L R L 1 (2) C W / P L C Note: W, P and C can not be affected by the individual. Thus, they are exogenous from the point of view of the individual. Combining the constraints yields: 1 C (W / P) R C (W / P) L 1 C (W / P) R C (W / P) The result is similar to the usual budget constraint: px x p y y I Optimal demands for C and R, and optimal labor supply are: (W / P C) 0.5 (W / P C) C* 0.5 I 0.5 pc 1 (W / P C ) 0.5 0.5 C R* 0.5 I 0.5 pR W /P W /P L* 1 R* 0.5 0.5 C W /P When C 0 :If C C * , R * , L* L R* If W/P C * , R * , L* L R* : More labor is supplied when W/P . When C 0 : If W/P C * , R * =0.5 and L* L R* =0.5. That is, labor supply and optimal leisure are unrelated to W/P. Thus, the substitution effect equals the income effect.