RDP 2025-05: How Costly are Mark-ups in Australia? The Effect of Declining Competition on Misallocation and Productivity 6. Cost of Mark-ups – Oligopoly Model

One final question is: How much does the assumption of monopolistic competition drive the findings? Many sectors in Australia are highly concentrated with a few small dominant firms. As such, a model of oligopoly might be better description of the economy. To explore this we use the oligopolistic version of the model which is also outlined in EMX.

6.1 Set-up

For the oligopoly model, we follow EMX and assume Cournot competition within industry, with standard CES demand within each industry.

More precisely, we assume that each industry s consists of n firms. Output is aggregated within an industry s using a CES aggregator that is a power function:

where $\gamma$ is the elasticity of substitution within the industry and q_it (s) is again the share of output accruing to firm i in industry s. This implies that the inverse demand function takes on the following form:

Under Cournot competition, this will mean the elasticity of demand facing each firm is:

where $\eta$ is the elasticity of substitution between industries, $\gamma >\eta >1$ and ${\omega }_{it}\left(s\right)=q_{it}{\left(s\right)}^{\frac{\gamma -1}{\gamma }}$ is the market share of the firm within the industry in terms of sales (rather than output).

This implies the mark-up takes the form:

so the inverse of the mark-up is related to the market share. The strength of the relationship between the mark-up and market share depends on the gap between the within and between sector elasticities of substitution. Intuitively, when households are just as willing to switch consumption between industries as they are between firms within an industry, a firm's market share in its industry doesn't really matter in terms of their market power and mark-up.

Multiplying Equation (20) by ${\omega }_{it}\left(s\right)$ and summing over all firms in an industry gives us the following relationship between industry mark-ups and the sum of squared market shares:

So there is a linear relationship between the inverse mark-up in the industry and the sum of the squared sales shares in the industry. This latter measure is often referred to as a Herfindahl-Hirschman index (HHI), and it is a common measure of market concentration. As the labour share is linearly related to the inverse mark-up too, this means that there should be a linear relationship between the industry labour share and the HHI, where the slope of this relationship can tell us about the gap between the within- and across-industry elasticity of substitution parameters $\gamma$ and $\eta$.^[14]

6.2 Calibration

Again for this model we need to pin down the shape of the productivity distribution. In this case as well as pinning down the within-industry elasticity of substitution, we also need to pin down the across-industry elasticity.

To calibrate the parameters we again target a number of moments. To pin down the shape of the productivity distribution (i.e. the tail of the Pareto distribution $\xi$) we again target measures of industry concentration. In this case we target the top 4 and top 20 share of firm sales within industries, taking the unweighted average across industries (Table 8). This is similar to the approach taken in the monopolistic model, but using two moments in the firm size distribution instead of one. The top 4 share is similar to the EMX calibration, but the top 20 share is a bit lower at around 60 per cent, compared to 75 per cent. This reflects, at least in part, the use of the whole economy, rather than the manufacturing sector as in EMX.

To pin down the elasticities we target two moments. One is again the observed mark-ups. We focus on the harmonic sales-weighted measures for parsimony. The second is the coefficient from a regression of the labour share of income in the industry on the sector HHI. As discussed above, this helps to pin down the difference between the within- and between-industry elasticities of substitution. Under our preferred specification (run on an annual rather than long-difference model) the coefficient is around –0.15. This is slightly lower than the value used in EMX of –0.21.

One other notable difference in the calibration compared to EMX is that the average number of firms in each industry is much larger in our sample, closer to 3,500 compared to around 350 in EMX. In part this likely reflects the use of slightly more aggregated industries (4-digit ANZSIC instead of 6-digit NAICS industry definitions). It also likely reflects again the use of the entire economy, rather than the manufacturing industry, as the average number of firms per industry in the manufacturing sector in our data is closer to EMX.

Table 9 shows the calibrated parameters to meet these targets. We can see that to meet the higher mark-ups in the later period, the demand elasticity declines moderately.

6.3 Cost of mark-ups

Turning now to the misallocation costs, we can see that the results under the oligopoly model are actually extremely similar to those under the equivalent monopolistic competition model (Table 10). This indicates that the earlier findings are not particularity sensitive to the choice of competitive structure for the economy.

Footnote

In practice, mark-ups could increase without the labour share declining if the share of income accruing to capital declines. As discussed in Barkai (2020), while people tend to measure the capital share as the residual from the labour share, this calculation actually captures two components: the true return to capital and excess profits (or mark-ups). [14]