Do minimum wages strictly reduce employment?
The costs and benefits of legislated minimum wages are a venerable topic in economics—and area of ongoing controversy and active policymaking (e.g., President Obama tried to raise the national minimum wage from $7.25 to $10.10 per hour, a substantial increase. President Trump’s top economic advisor called a higher federal minimum wage “a terrible idea” that would “damage” small businesses. In general, the Republican party vehemently opposes minimum wage regulations. Arkansas and Missouri had successful ballot measures in November 2018 to raise the minimum wage, and in recent years, several cities have enacted minimum wage regulations).
In the case of a textbook competitive market - as wages go up the supply of labor goes up – a binding minimum wage (meaning it’s set above the equilibrium wage) reduces employment. A case can be made that such policy can still benefit workers; if the price elasticity of demand (how much a change in price affects the changes in wages) is larger than -1, then per unit gain in wage leads to proportionally less reduction in employment number, and in this case the total society wage sum for workers improved after the policy. In other words, if the proportional increase in wages is larger than the (induced) proportional decline in employment. Specifically, if σ > −1 (i.e., |σ| < 1), then a 1% rise in wages reduces employment by less than 1%, so total wages paid (wages × workers) rises. {elasticity is calculated as σ = – delta q / delta $}.
Before we challenge this notion, let’s take a moment to revisit why the above is so. In a competitive market, a firm’s hiring behavior does not impact the labor market. This is true for most companies hiring most roles. What is the primary assumption in the textbook model that yields the prediction that (binding) minimum wages always and everywhere reduce employment? The answer is price-taking behavior, both in labor and product markets. That is, the price of the good the firm is producing does not fall if the firm makes a few more, and the prevailing wage the firm faces does not rise if it hires a few more workers. Formally, product demand and labor supply are both perfectly elastic as the far as the firm is concerned. MRPL = Marginal Revenue Product of Labor ⇒ “What the marginal worker produces”.
We normally assume that at any given firm, MRPL is decreasing in employment due to decreasing returns in the production function. All else equal, the next worker produces marginally less than the prior hire. This could be because the most important tasks are always done first; hence, adding more workers means that some less important tasks are also accomplished.
Recall the firm’s profit maximization problem, which is to maximize the difference between revenues and costs (i.e, profits). Assume that the firm’s only input is labor. Denote the first derivative of a function f (·) by f′ (·) and the second by f′′ (·). The firm’s problem is: max π = p · f (L) − w(L) · L, where p is the product price, w(L) is the wage necessary to “call forth” L workers, and f (L) is the amount of output produced. We assume that f′ (·) > 0 and f′′ (·) < 0, so an additional worker always raises output, but marginal productivity declines as we add workers. Note that p is not a function of L, meaning we assume that the price of output is taken as given (it’s exogenous).
Differentiate this expression with respect to L and set it equal to zero. (Why zero? At the optimum, this derivative must equal zero. If not, the firm would want to adjust L further. If the marginal profit were positive, the firm would want to hire more labor. If the marginal profit were negative, the firm would want to hire less labor.)
Now you have pf′(L) = w(L) + w′(L)L, where:
– pf′(L) is the marginal revenue product of labor (MRPL)
– w(L) is the equilibrium wage
– w′(L)L is an additional change in total labor costs caused by hiring an extra worker. It is equal to the product of the firm’s entire work force and the marginal wage increase.
This third term is potentially important. It says that each additional worker hired (each “marginal” worker) could potentially raise the cost of all of the previous workers hired (“inframarginal” workers). Why? If all workers are paid a single wage (w (L)), and calling forth an additional worker raises that wage, then the cost of the additional worker is not simply w but w + w′ (L)L. So the key assumption of the competitive model is: w′ (L) = 0 ⇐⇒ Price taking firms. No firm is large enough to raise the market wage simply by hiring a few more workers. If the firm is a price taker in the labor market, it chooses employment so that: pf′(L) = w∗, where w∗ is the market wage, which the firm takes as given.
How does firm choose employment when it is not price taker? According to the FOC above: pf′(L) = w(L) + w′(L)L. If w′(L) does not equal to zero, then firms must pay all of its workers higher wages with each additional worker it hires. Here’s one convenient way to express this result, MRPL = w(1+1/η). η is the elasticity of labor supply (the percent change in labor supply for a 1 percent change in the wage) as experienced by the single firm. For a price-taking firm, η → ∞, meaning that 1/η → 0. So, if a firm is a price taker, the wage is exactly equal to MRPL (since the denominator of the above expression is equal to one). If the firm is not a price taker in the labor market, then the wage it pays is strictly less than MRPL.
If you’re a monopsonist employer
Monopsony. “One buyer, many sellers.” More generally, monopsony is a case where an agent (firm or consumer) is not a price taker in a market in which it is a buyer. Its own demand affects the price it pays. (Conversely, monopoly is a case where a firm is not a price taker in a market in which it is a seller. Its own supply affects the price it commands in the market.)
• The labor supply curve for a monopsonist is upward sloping. To obtain one more worker, the monopsonist must raise the wage by a small amount.
• Assuming that all workers receive the same pay (i.e., the late-comers don’t get paid more), the marginal cost of the next worker is not simply her wage but also the wage increase given to all of the other inframarginal workers.
• Thus, the marginal cost of labor curve for a monopsonist firm is even more upward sloping than its labor supply curve. The additional cost for each worker is given by the higher wage of that worker and by the increase in wage given to the entire pool of workers.
What happens if we impose a binding minimum wage on a monopsonist employer? One case is illustrated above. In this example, implementation of a binding minimum wage raises wages and employment. Why does that happen? The firm is now a price-taker for labor at W_min. That is, it is required by law to pay at least W_min, although it would like to set a lower wage. At this wage, the firms only want to hire Q_min workers since if it hires more, then the MRPL (the amount a marginal worker produces) exceeds the wage. Therefore the firms chooses Q_min so that: w = MRPL. Note that the number of workers that would like to be employed is larger than Qmin – it is given by QL. So, although more workers try to get employed, the monopsonist only gives a job to fewer.
Thus, paradoxically, raising the minimum wage can raise both wages and employment in a monopsonist labor market. ■