April 2nd, 2013 April 14 2015 Last part of “ Labor Supply” Labor Supply Over the Life-Cycle • “Static” model of Chapter 2 is not a complete depiction of how we allocate our time • We want to consider how individuals make labor supply decisions over their lifetimes. • Wage rates change over the worker’s life cycle in a predictable way – Wages are low when young – Wages rise with time and peak around age 50 – Wages decline or remain stable after the age of 50 • Changes in wages over the life cycle are “evolutionary”. Responses to Evolutionary Wage Changes • Evolutionary wage changes are predictable (cuz we know in ten years our wage is gonna go up) – don’t lead to a change in expected life income cuz you know they are happening – no income effect associated with them, just substitution effect • In life-cycle model, hours of work increase when wages are higher. • The profile of hours of work over the life cycle will have the same shape as the age-earnings profile • Intertemporal substitution hypothesis: people substitute their time over he life cycle to take advantage of changes in the price of leisure The Life Cycle Path of Wages and Hours for a Typical Worker !!ECON !139!!!SP !‘15 !!!An ton o vics!!!3!!!4/14/15!!!1!!!２of 15 Contrast with Static Model of Labor Supply (the distinct between predictable changes in wage v.s. unexpected change) • In a life-cycle model, wage changes are predictable and do not increase a worker’s opportunity set. • The two models complement rather than contradict each other. Case 1 à SE > IE Case 2 à IE >SE Compare Professor Antonovics and Bill Gates: If IE dominates: Bill Gates is working less at every age level If SE dominates: Bill Gats is working more at every age level Labor Force Participation Rates over the Life Cycle, 2005 (Inverted U shape)!!３of 15 Hours of Work Over the Life Cycle, 2005 Around age 45 – 50, you can see them hitting the peak and then decline Policy Application: LFP of Older Workers (No need for this slide) Labor Demand Labor Demand • A firm’s decision about how much labor to use in production is driven by the firm’s desire to maximize profits. Derived demand *** for employed it is always maximize profit • Firm’s thinking about whether to hire a worker (basic intuition) – Each worker produces a certain amount to output per hour – That output can be sold for money – So, each worker generates a certain amount of revenue per hour. – If that hourly revenue is greater than the hourly wage, then hire the worker. • Just another way of saying you will hire an additional worker whenever the marginal benefit of that worker is greater than marginal cost of that worker. The Production Function • The production function describes the technology that the firm uses to produce goods and service. • For simplicity, assume that there are only two inputs: employee-hours (E) and capital (K) • Production Function: q=f(E,K) • Example Cobb-Douglas production function: q = E1/2K1/3 As E goes up, q goes up; as K goes up, q goes up!!４of 15 Marginal Product • Marginal product of labor (MPE): change in output resulting from a hiring an additional worker, holding constant the quantities of all other inputs. • Marginal product of capital (MPK): change in output resulting from a one unit increase in the capital stock, holding constant the quantities of all other inputs. Output and MPE Assume K is fixed The derivative is the slope (Dq/DL) MPn = cost of the nth employee hours The value of the marginal product of labor • Value of the marginal product of labor: the dollar increase in revenue generated by an additional worker. • VMPE = p × MPE p = output price It means to hire one worker an additional hour, we get MPE The value this worker generates is gonna start to decline eventually as time passed.!!５of 15 Labor Demand in the Short Run • Profits = pf(E,K)-wE-rK w = wage rate r = price of capital p = price of output Total cost = wE+rK • In the short run, capital is fixed. • Value of the Marginal Product of Labor – VMPE = p × MPE • Marginal Cost of Labor – MCE = w Profit Maximization Decision making rule: VMPE > w à hire more workers VMPE < w à hire fewer workers VMPE = w à maximizing your profits w* = equilibrium wage rate!!６of 15 Derivation with Calculus (Optional) Choose E to Maximize Profits: Π=pf(E,K)-wE-rK f(E,K) à output change when labor change 0 = P*MPE – W 0 = VMPE – W W = VMPE Mathematical Example (How will this firm max its profit in the short run) q = 81/3E1/2 = 2E1/2 12E-1/2 = 2 6 = E1/2 E* = 36 Π = 12*81/3*361/2 – 2*36 – 1(8) Reconciling Different Conditions for Profit Maximization They are the same thing. It’s just two sides of the same point of view.!!７of 15 Labor Demand in the Long Run • Two conditions must hold in the long run: – VMPE =w -> p×MPE=w – VMPK=r -> p×MPK=r Mathematical Example Labor Demand in the Long Run • Two factors of production: capital and labor. • Both capital and labor can be varied. • Labor demand curve downward sloping in the long run too. • Demand for labor more responsive to wage changes in the long run. Why does the labor demand curve slope downward? • Substitution effect: Describes how input demand changes as the relative price of the inputs changes, holding output fixed.!!８of 15 – If wages increase, firms may want to substitute out of labor and into other inputs such as capital. Price of labor goes up à tend to substitute into other input like capital • Scale effect: Describes how input demand changes as output changes, holding the relative price of inputs fixed. – If wages increase, firms may want to scale back production (see next slide). Analogous to IE • Both of these effects cause the quantity of labor demanded to drop. Why wage changes lead to a scale effect: Price of labor goes up à MC of producing each unit of input goes up, holding capital constant Standard U-shape MC curve A wage increase will increase the marginal cost of producing an extra unit of output. This will lead the firm to produce less. Effect of Wage Change on the Quantity of Labor Demanded!!９of 15 April 16th 2015 Elasticity of Labor Demand How sensitive