Topic Compensating Differentials. Professor H.J. Schuetze Economics 370. Compensating Wage Differentials
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1 Topic Compensating Differentials Professor H.J. Schuetze Economics 370 Compensating Differentials Refers to the wage differentials that exist in equilibrium to compensate workers for undesirable job characteristics Examples: Unpleasant/unsafe working conditions Desirable attributes like non-wage benefits Long commute time Thus, wages can also reflect compensation to workers for undesirable job characteristics not just productivity Let s work through the theory thinking about compensating wages for the risk of injury that can result from an unsafe or unhealthy work environment Professor Schuetze - Econ
2 The Firm s Iso-Profit Curve The various combinations of wages and safety the firm can provide while maintaining the same level of profit I 1 I 0 Downward Sloping: Both wages and safety are costly for the firm Firm can maintain profit and increase safety only if it can pay a lower wage B Concave: There is a diminishing marginal rate of transformation between wages and safety Professor Schuetze - Econ Concavity of Iso-Profit Curve t : little safety and high wages With little safety the firm can increase safety inexpensively better lighting signs guard rails The firm is at a stage of increasing returns with respect to the provision of safety The iso-profit is relatively flat Professor Schuetze - Econ
3 Concavity of Iso-Profit Curve t B: lots of safety, low wage The firm can only increase safety with more sophisticated and costly safety procedures Stage of diminishing returns in the provision of safety The iso-profit is relatively steep Left to right: The firm starts with the cheapest forms of safety provision and moves to more expensive forms I 0 to I 1 : Implies a higher level of profits. Iso-profit curves with both lower wages and safety are higher because both are costly Professor Schuetze - Econ Different Firms/ Technology Different firms can have different abilities to provide safety at a given cost Thus, different firms can have differently shaped iso profit curves for the same level of profits Firm 1 (High Costs) Firm 2 (Low Costs) Professor Schuetze - Econ
4 Different Firms/ Technology Firm 1: is costly Can provide additional safety only if wages drop rapidly to compensate for safety costs and maintain profits rapidly diminishing returns to providing safety e.g. inherently dangerous sectors mining logging Professor Schuetze - Econ Different Firms/ Technology Firm 2: Low safety costs Can provide additional safety at a relatively cheaper price e.g. inherently safe industry office manager professor Competition implies that in equilibrium both firms will earn zero economic profits so that I 1 = I 2 = 0 Professor Schuetze - Econ
5 Employer s Offer Curve W* W 1 The maximum compensating wage that will be offered in the market for the different levels of safety Therefore, it is the outer limits of the two iso profit curves Firm 1 B Points inside the offer curve will be dominated by points on the offer curve Example: Worker can receive S* safety Firm 2 and a wage of W 1 from Firm 1 (Point ) S* Firm 2 can provide safety relatively cheaper and therefore can offer W* > W 1 wage along with the same amount of safety Professor Schuetze - Econ Individual s Preferences Workers have preferences for wages and safety Can illustrate using indifference curves B U 0 U 1 The level of utility is the same along the indifference curve. Utility increases up and to the right Convexity illustrates a diminishing marginal rate of substitution between wages and safety : willing to give up a lot of wages to get small increase in safety (curve is steep) B: not willing to give up wages for safety (curve is flat) Professor Schuetze - Econ
6 Different Individuals (Risk Preferences) Different workers may be more or less willing to give up safety in return for higher wages (a risk premium) The individual with preferences U L is less risk averse while U M is more risk averse U M U L Person L requires less of a compensating wage increase to give up safety at point than person M L s indifference curve is flatter than M s Professor Schuetze - Econ Equilibria 1. Single Firm, Single Individual: W* E U 0 S* For a single type of firm and single type of worker the equilibrium occurs at a point of tangency like E This gives maximum utility given the firms ability to trade safety for wages at perfectly competitive profit = 0 Professor Schuetze - Econ
7 Single Firm, Single Individual To the left of E: dditional wage required by the worker to accept more risk (slope of IC) is greater than the firm is able to offer (slope isoprofit) To the right: The worker is not willing to give up enough risk If the firm tries to reach a lower iso profit (higher profits) workers will go to another firm Professor Schuetze - Econ Equilibria 2. Single Worker, 2 Types of Firms: W W B Firm 1 (Costly) Firm 2 (Cheap) B With preferences as drawn, maximum utility with Firm 1 is U U S S B Professor Schuetze - Econ
8 djustment to Equilibrium Suppose that Firm 1 is able to raise the price of its product when the good becomes in short supply Firm 1 B Now in equilibrium The homogeneous workers would be indifferent between working at either Firm 1 or Firm 2 Firm 2 Professor Schuetze - Econ Equilibrium We could measure how much workers value safety if we could measure safety In a cross section of workers the various combinations of wages and safety traces out an indifference curve Professor Schuetze - Econ
9 Equilibria 3. 1 Type of Firm, 2 Types of Workers: W W B B U L Less Risk verse Here, a cross-section on wages and safety traces out the isoprofit curve tells us how firms are able to trade wages for safety S S B U M More Risk verse Professor Schuetze - Econ Different Individuals (Risk Preferences) 4. Many Firms and Individuals: F 1 F 2 U L Less Risk verse F 3 U verage Risk verse U M More Risk verse Professor Schuetze - Econ
10 Locus The set of tangencies between iso profits and indifference curves (combination of wage and safety that will prevail in the market) The wage safety locus can change depending upon: (i) (ii) Professor Schuetze - Econ Locus The wage premium paid for risk is often called a shadow price This is because the price is embedded in the market wage rather than being attached explicitly to a job characteristic Professor Schuetze - Econ
11 Effects of Regulation Might expect the effects of safety regulation to be negative Workers and firms efficiently allocate themselves in terms of worker s risk aversion and employers adopting cost effective safety standards Single Firm, Single Worker Suppose the competitive equilibrium is at E 0 W E 0 0 U 0 S 0 Professor Schuetze - Econ Effects of Regulation W E 0 0 U 0 S 0 Suppose regulatory board requires the level of safety to increase to s r Professor Schuetze - Econ
12 Effects of Regulation Suppose instead the firm is able to absorb the cost E 0 W 0 U 0 S 0 S r In this case the firm is worse off Professor Schuetze - Econ Not ll Firms Will Be ffected The Same F 1 F 2 U L Less Risk verse F 3 U verage Risk verse U M More Risk verse s a s r For Firm 3 the safety regulation is redundant Firm 2 could meet the standard only if workers are willing to give up wages for safety or if the firm can absorb some costs Professor Schuetze - Econ
13 Imperfect Information The safety standard weeds out firms whose safety technology cannot meet the standard t a cost to workers and firms Imperfect Information: Could be that firms have more information about risks than workers e.g. Professor Schuetze - Econ Imperfect Information W a The worker perceives that she is getting S p safety and knows she gets the actual wage (w a ) (on U p ) U p (perceived) E 0 U a (actual) S a S p In fact, she is only getting S a safety with the wage W a (U a ) Professor Schuetze - Econ
14 Why Regulation? Workers and firms are worse off so why? Professor Schuetze - Econ Empirical Evidence Difficult to estimate compensating differentials (i) (ii) Can be explicit: Can be implicit: Studies have looked at premiums for: risk of unemployment mandatory overtime commuting time risk of injury and death (most) Professor Schuetze - Econ
15 Problems 1. Increase wage due to increase risk may work the other way 2. errors in variables 3. Sample selection bias Professor Schuetze - Econ Results 1. risk of death pays more than risk of injury 2. Professor Schuetze - Econ
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