Treasury
Publication

# 5  Returns to Capital

## 5.1  Theoretical Considerations

In a basic model of economic growth where capital is perfectly mobile, capital will flow to countries with the highest rates of return. With the assumption of diminishing returns to capital, these countries will be the ones which are relatively capital shallow. This can be shown with the help of Figure 11. If we assume that New Zealand and Australia have identical production functions, then New Zealand, with a lower capital-labour ratio than Australia, will lie at some point B. At this point it can be seen that there is a higher return to capital; that is, the slope of the tangential line at point B is higher than at point A.[6]

Alternatively, the different capital intensities might arise from differences in the underlying production functions, despite both countries facing the same relative prices for labour and capital. This case is illustrated in Figure 12. A country lying at any point along the lower production function has a lower multifactor productivity level, as any given amount of capital per unit of labour will produce less output per unit of labour. In this case, both countries may have the same return to capital (points A and C), but the country at point C has a relatively low capital-labour ratio due to its relatively low MFP. Alternatively, the country with a lower MFP level may also have a higher return to capital, thus lying at point D in the diagram. In this case there could be a “wedge” that impedes capital flows to the country at point D.

## 5.2  Empirical Evidence

Our previous investigation suggests that New Zealand may have a somewhat lower level of MFP compared to Australia (see Table 5). Therefore, the question which remains is whether New Zealand is at point C or point D in Figure 12. Both points C and D correspond to a lower capital intensity in New Zealand compared to Australia.

As a first step in this section we estimate the returns to capital in New Zealand and several other OECD countries by looking at the real operating surplus (converted to US dollars using PPPs) divided by the capital stock. Ideally, we would like to assess the rate of return which firms use when deciding whether to invest. That is, we want to look at an ex ante (expected) marginal return to capital investment. However, the Operating surplus divided by the capital stock is a realised rate of return and as such is only a proxy for the expected return. Also, the operating surplus divided by the capital stock is a measure of the average return, rather than the marginal return which arguably governs decisions to undertake additional capital investment. In a Cobb-Douglas production function, the average and marginal returns are the same so this is not an issue. In the case of the constant elasticity of substitution production function, the average return is directly related to the marginal return[7]; thus the measure of operating surplus to the capital stock provides us with a reasonably good proxy of the return to capital which firms are facing.

Figure 13 shows the rate of return to capital in New Zealand, Australia, the UK, and the US, together with the OECD average. Until the early 1990s, New Zealand had a relatively similar rate of return to that of Australia, the UK, the US and the OECD average. Since 1993 New Zealand has had a higher rate than Australia, the UK and the OECD average, and since 1999 higher than the US as well.[8] This suggests that New Zealand may lie at the point D in Figure 12 when compared with Australia.