Topic 4.3 - 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 370 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 370 3 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 370 4
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 370 5 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 370 6
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 370 7 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 370 8
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 Points inside the offer curve Firm 1 will be dominated by points on the offer curve Example: B 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 370 9 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 370 10
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 370 11 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 370 12
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 iso-profit) To the right the worker is not willing to give up enough wage If the firm tries to reach a lower iso profit (higher profits) workers will go to another firm Professor Schuetze - Econ 370 13 Equilibria 2. Single Worker, 2 Types of Firms: W W B Firm 1 (Costly) Firm 2 (Cheap) B U U B With preferences as drawn, maximum utility with Firm 1 is U Could reach a higher indifference curve (U B ) with Firm 2 at point B S S B This can t be an equilibrium ll workers would work at Firm 2 Professor Schuetze - Econ 370 14
djustment to Equilibrium Suppose that Firm 1 is able to raise the price of its product when the good becomes in short supply The firm s iso-profit will shift out The 0 profit iso profit curve allows the firm to offer higher wages and safety 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 370 15 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 The differences between the combinations of wages and safety tells us how workers value safety Professor Schuetze - Econ 370 16
Equilibria 3. 1 Type of Firm, 2 Types of Workers: W W B S B S B U L Less Risk verse U M Here, a cross-section on wages and safety traces out the isoprofit curve tells us how firms are able to trade wages for safety More Risk verse The less risk averse worker will accept less safety (more risk) for a higher wage The more risk averse worker prefers higher safety (less risk) at a lower wage Professor Schuetze - Econ 370 17 Different Individuals (Risk Preferences) 4. Many Firms and Individuals: F 1 F 2 U L Less Risk verse *- Locus* F 3 U verage Risk verse U M More Risk verse Workers will sort themselves into firms (occupation, industries) of different risks along the employer s offer curve They will receive different wages for the different levels of risk(the least risk averse person will enter the highest risk occupation, etc.) Professor Schuetze - Econ 370 18
- Locus Gives the change in the wage premium the market yields for differences in risk 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) firms ability to provide safety (ii) workers preferences The slope will always be negative - compensation is required for reductions in safety Professor Schuetze - Econ 370 19 - 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 You are not being told how much you are being paid for additional risk Professor Schuetze - Econ 370 20
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 W E 0 0 U 0 Suppose the competitive equilibrium is at E 0 It is efficient in that neither the worker nor the firm can be made better off without making at least one of them worse off. S 0 Professor Schuetze - Econ 370 21 Effects of Regulation W E 0 0 U 0 W r E r U r S 0 S r Suppose regulatory board requires the level of safety to increase to s r This will leave the firm, the worker or both worse off Clearly the worker is worse off in the diagram (lower indifference curve) The firm appears to be no worse off Professor Schuetze - Econ 370 22
Effects of Regulation Suppose instead the firm is able to absorb the cost - excess profits - all firms increase price, etc. E 0 W 0 U 0 W E 1 r The iso profit would shift out (lower profit) The worker stays on the same indifference curve Decrease in wage exactly offset by increase in safety S 0 S r In this case the firm is worse off In reality we would expect the costs to be divided between the workers and firms Professor Schuetze - Econ 370 23 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 Firm 1 would go out of business iso profit curve is below Firm 2 in the relevant region (s r and up) Workers in Firm 1 would go to Firm 2 Professor Schuetze - Econ 370 24
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. latency period before disease shows up In this case the worker thinks she has higher safety and compensating wage than she really does Professor Schuetze - Econ 370 25 Imperfect Information W a E 0 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) U o (optimal) U a (actual) S a S 0 S p S r In fact, she is only getting S a safety with the wage W a (U a ) ny imposed safety standard between S a and S r could improve the workers utility without making employers worse off The optimal standard would be at S o Giving workers full information would also make them better off (move to U o ) Professor Schuetze - Econ 370 26
Why Regulation? Workers and firms are worse off so why? 1. Could be imperfect information 2. Competition may not prevail in all job markets thus, workers have no choice 3. Workers who choose risky jobs may not pay the full costs of the risk e.g - medical costs and worker s compensation 4. Society may feel workers should not have to sell their health/safety to make a living 5. Willingness to accept risk may be a function of risk already exposed to - Legislation could lower risk for all workers (new eqm) Professor Schuetze - Econ 370 27 Empirical Evidence Difficult to estimate compensating differentials (i) Hard to isolate one job characteristic (ii) Some workers have stronger bargaining power and therefore, wages (unions) Can be explicit: e.g. premium for night shift or underground mining Can be implicit: -need to compare similar jobs with the exception of one characteristic Studies have looked at premiums for: risk of unemployment mandatory overtime commuting time risk of injury and death (most) Professor Schuetze - Econ 370 28
Problems 1. Increase wage due to increase risk may work the other way could be increased risk because of low wages low wage workers cannot afford a safe environment (income effect) foregone income from an accident is less (substitution effect) 2. errors in variables aggregate risk measure could be flawed 3. Sample selection bias only include those in risky occupations Professor Schuetze - Econ 370 29 Results 1. The more serious the risk the higher the premium. risk of death pays more than risk of injury 2. The wage premiums are reduced if covered by worker s compensation. Professor Schuetze - Econ 370 30