## Modeling Wage Increase Using Market with Asymmetric Information

CNN Money reported on December 3, 2015 that American wages “may finally go up”.

The article cites the need for better, more talented workers as the reason for the potential increase. North Carolina restaurant owner Greg Hatem says, “We’re fine paying more to bring in better people.”

Furthermore, the article reports, “This year Hatem bumped up pay for all employees to \$10.15 an hour in an effort to recruit and retain the best workers. Some workers had been making \$8.50 an hour previously.”

We attempt to model the current situation by examining the equilibria in a market where there is asymmetric information between buyers and sellers. The asymmetry arises from the fact that employers are unsure from the outset whether an jobseeker is talented or not. Furthermore, employers are unsure of the number of talented jobseekers versus untalented jobseekers, and may hold different expectations of the job market.

We make the model more concrete by classifying employers as buyers of labor in the job market and jobseekers as sellers of labor in the job market. In this situation, we may even use the numbers from the article to represent the buyers’ value of labor. We take \$10.15 as the buyers’ value of good labor and \$8.50 as the buyers’ value of bad labor. We can presume that good workers value their labor at \$8.75 and bad workers value their labor at \$8.25.

We need an estimate of the percentage of talented (“good”) workers versus the percentage of untalented (“bad”) workers. The article suggests that talented workers are difficult to find, and unemployed yet talented workers are intuitively not abundant. Let us say that employers believe that 80% of the unemployed are bad and 20% are good.

Previously to the recent increase in demand for good workers, buyers disregarded good workers and assumed all jobseekers were bad. The expected value to buyers is \$8.50 for bad labor, which is higher than the \$8.25 wage asked by bad workers. This is an equilibrium situation where the price of labor is between \$8.25 and \$8.50. This models the previous jobs of the workers described in the article now looking to find a job at a restaurant such as Hatem’s.

As buyers begin to seek good workers, buyers assume both good and bad workers are on the market. Since 20% of them are good and 80% of them are bad, the expected value to buyers is \$10.15 * 20% + \$8.50 * 80% = \$8.83. This expected value is greater than the value of both good and bad to sellers, and so all members of society are employed in an equilibrium situation. The price of labor is somewhere between this value, \$8.83, and the buyer’s valuation of \$10.15. This models the current situation: as restaurants (and other businesses) seek more talented workers, the price of labor increases.

Note also that the price of labor increases not gradually but more abruptly. This is due to the movement between two somewhat discrete equilibrium states – one where the expectation is that there is only bad labor to one where the expectation is that there should be good labor as well as bad labor.

Admittedly, this is not a perfect model of the labor market. The changes differ between types of businesses and jobseeker skills, and are of course influenced by far more factors. However, this model does offer some insight into the all-of-a-suddenness of changes in wage levels – they rest on endogenous views that sharply impact the equilibrium of the market.

CNN Money, “Why American wages may finally go up”, found online at http://money.cnn.com/2015/12/03/news/economy/wage-growth-jobs-us-economy/index.html.