Higher minimum wage – higher employment?

Over at Not Sneaky they are discussing how a higher minimum wage may lead to higher employment when we have a firm that has market power in the labour market (hat-tip CPW). The argument is a very interesting one as economists often view a minimum wage as a way of placing a price floor, which leads to a lower level of employment and social ‘surplus’.

On the blog he uses this fine graph to explain the result. The purple line illustrates the path of wages and employment. According to that, there is a range where higher wages create greater employment in the labour market. Let me attempt to explain this.

In the case with no minimum wage, after choosing a business structure the firm sets marginal cost (MC) equal to the marginal revenue product (VMPL) to choose the labour market quanitity. However, as the firm has market power (and employees have none), it only pays the wage required to get the target quantity of workers working.

Now, the introduction of a minimum wage changes the marginal cost curve. The marginal cost curve will be flat up until it hits the point where a higher wage is required to increase the quantity supplied in the market, so where it hits the labour supply curve. Once it hits the labour supply curve it discontinuously leaps up to the old marginal cost curve, and then continues to rise.

How does this work?

Well, the marginal cost is the additional cost the firm must pay to hire one more labour unit. We are assuming that if the firm wants one more employee they have to pay a little more (upward sloping supply curve), however they have to pay this wage to everyone, not just the new person they are hiring (no price discrimination/perfect contract information amongst employees). As a result, without a minimum wage they have to pay the new worker, and increase wages to everyone. When there is a minimum wage, and it is binding, the firm does not have to increase the wage of all its other workers when they hire a new employee, reducing the marginal cost of that employee.

The reason that the purple line Not-Sneaky draws is the choice of the firm is because of the fact that introducing a minimum wage lowers the marginal cost over some range above the market wage. As the marginal cost curve jumps discontinuously when it hits the supply curve (as from this point they must pay all the employees a higher wage to increase the number of workers), the firm chooses to hire at the point where the marginal cost curve hits the supply curve (as any additional labour will cost more to hire than it will add value to the firm).

The next question we need to ask is how this influences the goods market?

The firm produces goods with a combination of capital and labour. However, in the short run capital is fixed. As labour has risen, this must imply that output rises. How does this work?

Well, the minimum wage reduces the marginal cost of labour, which in turn reduces the marginal cost of producing the good. As a result, the firms short run supply curve becomes flatter (and lower at each quantity), implying that output will rise, and price will fall.

In the long-run, the firm can adjust capital, so next we have to ask, will employment be higher in the long-run?

The first point to take into account is that an increase in the minimum wage may put firms out of business. However, a firm that acts as a monopoly in the labour market is probably operating at a margin significant enough such that a minimum wage will not put them out of business. As a result, we will assume that the firm continues to operate in the long-run.

Given this, we need to know about the relationship between capital and labour. For simplicity I will first assume that they are separable (eg capital+labour=ouptut), in other words they are perfect substitutes. In this case the firm chooses capital and labour such that the marginal cost (MCl and MCk) and marginal revenue product (VMPL and VMPK) of both products are all equal (MCl=VMPL=VMPK=MCk).

Looking at our initial equilibrium, the minimum wage has lowered the marginal cost of labour implying that the firm will need to increase labour to lower VMPL and VMPK, and decrease capital in order to decrease MCk (all towards the constant MCl).

As a result, when they are separable we know that labour will rise and capital will fall. Also output will rise as the shift will make the marginal cost lower for every level of output.

If we move to the more realistic case where an increase in capital (labour) increases the marginal product of labour (capital), but they are still substitutes in output. In this case, the increase in employment from a reduction in the MCl will have an ambiguous impact on capital and output will definitely rise.

So what does all this gibberish mean?

Well, if we assume:

1. Firm has market power in the labour market
2. Workers have no market power
3. Everyone must get an increasing wage as employment rises
4. Firm will not be put out of business by increase in average costs

Then there is a situation where a minimum wage may increase employment! Very interesting.