3 The production block (continued)

3.1.2  The input decisions

1. The mix of capital and labour

The profit-maximising firm in NZTM seeks to choose the amount of capital (k) and labour (hours paid, n) that minimises the cost of production for a given use of domestic factors.[9] The functional form of the production function is a CES (constant elasticity of substitution) equation. This means the rate of response to the relative price changes is constant, regardless of the level of the capital/labour ratio. The current estimation of the production block means a 1 percent increase (decrease) in the price of labour (w) relative to the price of capital leads to 0.55 percent decrease (increase) in labour/capital ratio.

Figure 5 shows how the input decisions are made, and therefore how medium-run variables are determined in the model. In Figure 5, c₀(y₀) represents the isocost curve. In the medium run, the amount of capital is “exogenous” to the block, as capital accumulation takes time, and the wage and the demand for “other goods” are also determined outside (or exogenous to) the production block. Given the level of capital is fixed, the medium-run value of labour input (n₀^mr) is determined by the intersection of a vertical line drawn at the given level of capital (k₀). The rental/wage ratio (ar⁰) is also determined by the slope of the isocost curve where the firm uses k₀ units of capital. Given the wage rate, the medium-run value of the rental price of capital can be found by the factor-price ratio.

Figure 6 shows the impact that an increase in labour productivity has on the input decisions in the model in both the medium run and steady state respectively. In the medium run, an increase in labour productivity will lead to the inward movement of the isocost function from c₀(y₀) to c₁(y₀), which implies less labour needed to produce the same amount of output for a given level of capital. Given the level of capital is fixed in the medium run at k_0, higher labour productivity sees the medium-run value of labour input fall from n₀^mrto n₁^mr.

However, in the steady state, both wages and capital are no longer exogenous to the production block. On the other hand, hours paid become exogenous (based on working-age population) as does the rate of return on capital. The rental price of capital is determined mainly by the neutral long-term interest rate and the risk premium for investment. In the steady state, firms will employ more capital (k₁-k₀) to increase their output from y₀ to y₁ because of higher labour productivity. The new steady-state value of capital is equal to k₁. Given the factor-price ratio (ar₁), hours paid, and the rental price of capital, we can work out the new steady-state wage.

The production function in NZTM incorporates a labour-augmenting technological process. Labour-augmenting technological progress is technological innovation that makes labour more productive. Solow (1956) showed that a production function with labour-augmenting technological process implies the growth rate of the capital to labour ratio equals the rate of technological progress. In other words, if the technology is assumed to improve over time, it implies the capital-to-labour ratio is also increasing over time. Figure 7 shows that this is consistent with the New Zealand data and therefore the labour-augmented production function is a reasonable assumption in the New Zealand context. Furthermore, Barro and Sala-i-Martin (1995) show that labour-augmenting technological change is consistent with the existence of a steady state in the neoclassical growth model.

Figure 5: Determination of employment and wages

Figure 6: Impact of higher labour productivity

Figure 7: Ratio of business capital stock to private sector hours paid

Source: Statistics New Zealand, Treasury

2. The mix of domestic factors and imported intermediates they use

Similar to the first decision, the firm determines its split between domestic factors and imported intermediate goods that minimises the cost of producing a given level of gross output (t) based on the relative price of domestic factors to imported intermediates. In the current estimation of the production block, a 1 percent increase (decrease) in the price of domestic factor inputs (py) relative to imported intermediates (pmo) leads to a 0.40 percent decrease (increase) in the ratio of domestic factors to imported intermediates. Again, the functional form implies a constant elasticity of substitution, so again the ratio of domestic factors to imported intermediates does not matter.

In the past, the model allowed for the increasing real share of imported intermediates in the production process. However, the results of the current estimation suggest that the increasing trend is very small, reflecting that imported intermediates no longer include all imports. There is an equivalent term in the exporting equation and the new estimate is very close to zero.

3.1.3  The output decisions

Firms in NZTM choose to produce either commodity exports or “other goods”. The “other goods” production is then split into non-commodity exports and domestically consumed goods and services (this occurs outside the production block and is discussed more fully in Section 4.4). The rationale for having two distinct outputs in the model is that commodity exports and “other goods” are not easily transformable in production because a significant proportion of New Zealand's commodity goods are primary-based.

An increase in the relative price of commodity exports to “other goods” will result in an increase in commodity export production relative to “other goods” production. The current estimation of the production block means a 1 percent increase (decrease) in the relative price of commodity exports to “other goods” leads to a 0.29 percent increase (decrease) in the supply of commodity exports relative to “other goods”. Similar to the input equations, the functional form of this equation is such that it implies a constant elasticity of transformation − this means that regardless of the ratio of commodity export production to “other goods” production, the proportionate rate of change of the output ratio to the proportionate rate of change of the relative price changes is constant. For a more detailed description of the production block, refer to Powell and Murphy (1997).