Unit 1 The supply side of the macroeconomy: Unemployment and real wages

1.7 The price-setting real wage (PS curve)

The price-setting curve, PS, is a horizontal line that shows the split in output per worker between wages and profits that arises when firms set their prices to maximize profits. This split will depend on the extent of competition in the markets for goods and services, and in the labour market. More market power for firms in either or both these markets reduces the real wage, which shifts the PS curve down.

If firms face little competition in the product market, it will be in their interest to set a higher price, with the result that their profit margins will be higher. The higher price pushes down the real wage. Likewise, if they face little competition for workers in the labour market, their wages will be low. In both cases, the PS curve is lower—workers get a lower share of output per worker and the real wage they get is lower. Equally, if competition in the economy is more intense, then profit margins will be lower and the real wage higher.

In this section, we analyse price setting and the PS curve more closely. Remember that we are making a simplifying assumption: the intensity of competition in both product and labour markets is constant (it does not depend on the firm’s output and employment).

A single firm’s price-setting decision

To understand the key ideas on which the price-setting real wage is based, think first of a single firm.

• It employs many workers, paying them a nominal wage, W: The firm’s HR department determines the wage to be set, which depends on the desired number of employees (as explained in the previous section). Remember that all workers are equally productive and are paid the same wage.
• It sells its product at a price, P: This is set by the firm to maximize profits.

How will the marketing department find the profit-maximizing price? First, it needs to consider the demand for the product: the price it chooses will determine how many items it can sell, and hence the firm’s revenue. Then, it can calculate the production costs by working out how many workers are needed to produce that amount of output, and—following the advice of HR—the wage that will be required. Putting all these things together, it can work out how much profit will be made at a given price. Then it can choose the price that maximizes profits.

Product demand

When the firm raises its price, demand for its product falls—in other words, fewer people will want to buy it. If it has competitors producing quite similar products to its own, demand will fall a lot when the price rises, because customers can easily find what they are seeking elsewhere.

price elasticity of demand

The percentage change in demand that would occur in response to a 1% increase in price. We express this as a positive number. Demand is elastic if this is greater than 1, and inelastic if less than 1.

profit margin

The difference between the price of a product and its marginal production cost.

We measure how much demand falls when price rises by calculating the price elasticity of demand (PED): the percentage fall in the quantity demanded in response to a 1% increase in price. We say that demand is more elastic when the percentage fall is large, and less elastic if it is small. The more competition the firm faces from other firms selling similar products, the more elastic its demand will be.

When demand is more elastic, the firm will have to set a lower price, relative to the production cost of the product. Its profit margin will be low.

The profit-maximizing price

At the profit-maximizing price, the markup is equal to the inverse of the price elasticity of demand, \(1/\text{PED}\). Our assumption that the intensity of competition faced by the firm in the product market is constant means that the PED does not vary with the firm’s output. So the profit-maximizing markup is a constant too. We will use the Greek letter \(\mu\) (pronounced ‘mu’) for the profit-maximizing value of the markup: \(\mu = 1/\text{PED}\). Then we can say that the firm sets its price so that:

\[\frac{P-\text{MC}}{P}=\mu\]

Rearranging this expression:

\[P = \frac{1}{1 - \mu} \text{MC}\]

This tells us that the profit-maximizing price is proportional to the marginal cost of production.

The factor \(1/(1-\mu)\) is a number greater than 1. If the firm faces little competition in the product market, the demand elasticity is low, so the markup, \(\mu\), is high, and the price is a higher multiple of marginal cost.

The marginal cost

average cost

The total cost of producing the firm’s output divided by the total number of units of output produced.

In our model, labour is the firm’s only cost, and output per worker, \(λ = Y/N\), is constant (it doesn’t depend on employment, N). This means that the average cost of a unit of output, AC, is proportional to the wage:

\[\text{AC} = \frac{\text{total cost of labour}}{\text{units of output}} = \frac{WN}{Y} = \frac{W}{\lambda}\]

However, the wage (determined by HR) depends on the number of workers the firm wants to employ. To increase output, the firm will not only have to increase employment, but also pay a higher wage to all its workers. Remember that the reservation wage curve (and therefore also the no shirking wage curve) is upward sloping. As we explain further in the extension to this section, the marginal cost (MC, the additional cost of producing one more unit of output) is given by:

\[\text{MC} = (1+\eta)\frac{W}{\lambda}\]

In this expression, the term \(η\) (pronounced ‘eta’) is a measure of how much wages have to be increased, which depends on competition in the labour market. Our assumption that the intensity of labour market competition is constant means that \(η\) is constant and the firm’s marginal cost is proportional to the wage.

wage markdown

When employers have labour market power they ‘mark down’ the wage. In our model with constant output per worker, the markdown is equal to the difference between the marginal cost of output and the average wage cost of a unit of output, as a proportion of the average wage cost of a unit of output.

We can call \(η\) ‘the markdown’. Just as the markup, \(\mu\), indicates how far the price is ‘marked up’ above the marginal cost, the wage markdown, \(η\), indicates how far the wage is marked down so that the wage cost per unit, \(W/λ\), is below the marginal cost. And both depend on the degree of competition. The markup, \(\mu\), is high when product market competition is low; likewise the markdown, \(η\), is high when labour market competition is low. In the extreme case of one seller, a monopoly firm sets a higher price than when there are competing sellers; similarly, in the case of a single firm in a labour market (think of a ‘company town’), the firm sets a lower wage than when jobseekers have more choice of employers. This is the case of monopsony.

The price-setting real wage

The profit-maximizing price, P, is proportional to MC, and MC is proportional to the nominal wage, W.

We can deduce that—whatever the level of output and employment—the firm will set a price proportional to its nominal wage, W. In other words, the ratio between W and P—the price-setting real wage—is constant.

In the extension, we show how to rearrange the equations above for P and MC to get a simple expression for the real wage. It is:

\[\frac{W}{P} = (1 - \sigma) \lambda\]

where \(σ\) (pronounced ‘sigma’) is a constant between 0 and 1.

This equation tells us that the firm sets its price so that each worker is paid a real wage that is a constant share (\(1 – σ\)) of the output per worker, \(λ\). The firm gets the remaining share of \(λ\)—that is, it makes a profit of \(σλ\) on each worker.

We also show in the extension that the profit share, \(σ\), depends on competition in the product and labour markets (that is, on \(\mu\) and \(η\)). If both markets are highly competitive, the profit share, \(σ\), will be low and the wage share (\(1 – σ\)) will be close to 1. If there is less competition in either market, the firm will get a higher share of output and wages will be lower.

The economy’s price-setting curve

Since all firms are identical and make the same choices, the aggregate price-setting real wage, \(w = W/P\), is a constant share of output per worker, whatever the level of aggregate employment:

\[w = (1 - \sigma) \lambda\]

Figure 1.22 shows the price-setting curve, and the shares of output that go to workers and firms.

What shifts the price-setting curve?

Both the diagram in Figure 1.22 and the equation show that the price-setting real wage will increase if productivity increases or if the profit share, \(σ\), falls. But what mechanisms bring this about?

• Higher labour productivity: Higher productivity reduces costs and firms cut their prices. The result is a higher real wage.

\[\begin{align*} \uparrow \text{productivity} \text{ }\Rightarrow \text{ } \downarrow \text{ }\text{MC} \text{ }\Rightarrow \text{ }\downarrow P \text{ }\Rightarrow \text{ }\uparrow \frac{\displaystyle W}{\displaystyle P} \end{align*}\]

• More competition for goods resulting in a lower markup: More intense competition among sellers in the economy reduces the markup firms can incorporate in their prices; the share of profits will be lower and real wages will rise.

\[\begin{align*} \downarrow \text{markup}\text{ } \Rightarrow \text{ }\downarrow P \text{ }\Rightarrow\text{ } \uparrow \frac{\displaystyle W}{\displaystyle P} \text{ } \Rightarrow \text{ } \downarrow \sigma \end{align*}\]

• More competition for labour resulting in a lower markdown: More intense competition among employers seeking to hire workers reduces the markdown in the wages firms set: the share of profits is lower and real wages rise.

\[\begin{align*} \downarrow \text{markdown}\text{ } \Rightarrow \text{ }\uparrow W \text{ }\Rightarrow\text{ } \uparrow \frac{\displaystyle W}{\displaystyle P} \text{ } \Rightarrow \text{ } \downarrow \sigma \end{align*}\]

What determines the height of the price-setting curve?

We now summarize what determines the height of the price-setting curve. In Unit 2, we will analyse how government policy can affect this.

• Labour productivity: For any given markup and markdown, the level of labour productivity—how much a worker produces in an hour—determines the real wage on the price-setting curve. The greater the level of labour productivity (or equivalently, the average product of labour, called lambda, \(λ\)), the higher the real wage that is consistent with the given profit share.

Higher productivity pushes the price-setting curve upwards. Shares stay the same; the price-setting real wage is higher.

labour market power

A firm has labour market power (sometimes called monopsony power) if it can reduce the wage it needs to pay its workers by lowering the number of workers that it employs.

• Competition: You know that the intensity of competition facing firms determines the extent to which they can profit by charging a price that exceeds their costs, that is, their markup. The more intense the competition, the lower the markup. Since this leads to lower prices across the whole economy, it implies higher real wages, which pushes the price-setting curve upwards. Similarly, if employers have less labour market power (a lower markdown) then the wage is higher and the price-setting curve shifts upward.

More competition means workers get a bigger share; the price-setting real wage is higher.