Component supply responses in dairy production

1. Introduction

Since the introduction of the Babcock and Gerber tests in 1890 and 1891, milk processors have been able to adjust the price of raw milk according to its composition. Such component pricing schemes were initially based on fat content, and prices were adjusted according to deviations from the expected content. However, several developments in dairy markets since the 1960s have increased the need for pricing schemes that consider other components too. First, the use of milk as an input by the dairy processing industry has increased relative to its use as a beverage. For example, the percentage of milk sold as beverage within the US federal milk marketing orders declined from 64.2 per cent in 1960 to 42.7 per cent in 1990 (Cropp and Wasserman, 1993). The value of milk in dairy processing, however, depends on the content of multiple components. Second, consumer preferences in many developed countries have been changing towards low- and non-fat dairy products, resulting in a lower relative value of fat in the dairy market.¹ Given these two trends, milk pricing based on the fat content only became inefficient and inequitable (Cropp and Wasserman, 1993). As a result, multiple component pricing (MCP) schemes began to evolve in the 1960s, and currently they operate in different forms in, for example, New Zealand, Denmark, Netherlands, Australia, Norway, Iceland, six out of ten federal milk marketing orders in the United States (Dairy Policy Analysis Alliance, 2010),² and several provinces in Canada.

Milk composition can vary for many reasons, including the breed of cattle, seasonal factors, the stage of lactation and management decisions (Manchester and Blayney, 2001). The effects on component supply of many of these factors are mainly observable in the intermediate- or long-run. However, management practices like the choice of feed affect milk composition in the short-run. Few studies have analysed the responsiveness of component supply to price changes under MCP schemes. Kirkland and Mittelhammer (1986) investigated the effects of fat-based milk pricing in the United States by treating the pricing system as a MCP scheme after deriving implicit prices for non-fat solids. They used a nonlinear programming model and found that a 1 per cent price increase resulted in a 0.07 per cent increase in the supply of fat and a 0.01 per cent increase in the supply of non-fat solids. Iizuka (1995) used non-statistical inverse marginal cost functions to calculate the price responsiveness of component supply in many states of the United States.³ While some of the calculated elasticities have unexpected signs (e.g. for fat and milk), the marginal cost elasticities indicated inelastic supply response. Other studies have investigated the component production technology itself (e.g. Buccola and Iizuka, 1997; Cho, Nakane and Tauer, 2009; Roibas and Alvarez, 2012), the returns of MCP schemes to the farm (e.g. Bailey, Jones and Heinrichs, 2005), by breed (e.g. Elbehri et al., 1994) and to society (Lenz, Mittelhammer and Hillers, 1991).

Our objective is to estimate the responsiveness of short-run component supply functions to changes in component and input prices as well as quantities of quasi-fixed inputs under a MCP scheme, where the value of milk is primarily determined by the content of fat and protein. To do so, we develop a theoretical model for the short-run supply of different components by a dairy farm that operates under a tradable quota regime. We use data from a panel of 311 Icelandic dairy farms between 1997 and 2006. This study is different when compared with Kirkland and Mittelhammer (1986) in several respects: (i) methodology (i.e. programming versus econometric), (ii) data (i.e. farm level versus experimental, time period, breed and country) and (iii) incentive scheme (i.e. multiple versus single component pricing). These differences may have implications for the estimated component supply responses. For example, experimental data are generated by agents that are unlikely to behave as profit maximisers and, consequently, estimated supply responses may differ from what would be observed on actual farms.⁴ Such differences in responses attributed to data type have been observed for the productivity effects of breeding (e.g. Byerlee, 1993).

The rest of the article is organised as follows. In Section 2, some information about the dairy sector in Iceland is provided. The theoretical model is developed in Section 3, and in Section 4 the econometric model is described. In Section 5, the data are presented and in Section 6 some estimation issues are discussed. In Section 7, the empirical results are presented and discussed before we conclude in Section 8.

2. Milk production and pricing in Iceland

Icelandic dairy farms have traditionally been small family-owned enterprises. Milk production has on average provided more than 85 per cent of the sales revenue, and meat output has largely been a by-product of milk production. During the 1970s, milk production increased significantly, and by the late 1970s production exceeded domestic demand. To balance supply with domestic demand, non-tradable production quotas were introduced in 1980 (Agnarsson, 2007). Such non-tradable quotas are likely to slow productivity growth by preventing farms from operating at an optimal size and thereby hindering the efficient utilisation of available resources (e.g. Richards and Jeffrey, 1997). To reduce the efficiency losses associated with non-tradable quotas, the quota regime evolved to a system with freely tradable quotas in 1992.

The late 1990s were characterised by considerable quota trading and subsequent reductions in the number of farms. From 1995 to 2007, the number of dairy farms declined by 50 per cent, and the average milk production per farm more than doubled (Bjarnadottir and Kristofersson, 2008). In addition to scale economies (Atsbeha, Kristofersson, and Rickertsen, 2012), several changes in the dairy sector enabled this large increase in output (The Farmers Association of Iceland, 2009). For example, feed quality improved significantly because of better feed processing and storage methods, including the introduction of round hay bales in the late 1980s. Furthermore, the widespread cultivation of high-quality forage (e.g. timothy grass), increased local production of concentrates (primarily barley), mechanisation of feeding and the introduction of automated milk parlours contributed to the growth in output.

Dairy production in Iceland is based on native Icelandic dairy cattle. The average annual yield is approximately 5,000 kg per cow with an average composition of 3.4 per cent protein and 4.0 per cent fat. Despite relatively low milk yields, Icelandic dairy cows have desirable characteristics such as a good adaptation to difficult geographic and climate conditions and a milk composition that is favourable to cheese production (Johannesson, 2010).

The Icelandic MCP scheme is based on the content of fat and protein in the milk, and the price of milk is the sum of the value of fat and protein whereas there is no payment for lactose or the fluid carrier itself. However, there are lower prices for milk that does not meet the required standards concerning somatic cell count and antibiotic residues. Furthermore, the component prices are different for milk that is delivered within and outside the quota. Each year, a pricing committee appointed by the government determines the component prices for milk that is delivered within the quota. These prices are effective from dates that are published well in advance. The component prices in the surplus milk market are determined late in the spring for the remainder of the year. The prices in the surplus milk market are mainly determined by developments in domestic demand. However, if the world market prices for protein or fat allow for profitable exports, the world market prices will determine the prices in the surplus milk market. The component prices are typically lower in the surplus than the quota milk market (Johannesson and Agnarsson, 2004). Consistent with demand for dairy products, the Icelandic MCP scheme has valued protein three times more than fat in the quota milk market and thirteen times more in the surplus milk market during the study period. However, after a recent butter shortage, fat prices in the surplus milk market have increased.

3. Theoretical model

Consider a dairy farm in a quota-regulated dairy market.⁵ Let y^q and y^o be milk output delivered within and outside of the quota. The total output of milk is $y=yq+yo$⁠. Furthermore, assume milk is priced according to its content, and the prices of components are different for milk delivered within and outside of the quota. Let b_i be the proportion of component i = 1, … , I per kilogram of milk, let $piq$ be the price per kilogram of component i in milk delivered within the quota, and let $pio$ be the price per kilogram of component i in milk delivered outside of the quota. The unit value of milk delivered within and outside of the quota will then be $∑i=1Ipiqbi$ and $∑i=1Ipiobi$⁠, respectively. The quantity of component i delivered within the quota is $ciq=yqbi$⁠, the quantity of component i delivered outside of the quota is $cio=yobi$ and the gross revenue of milk produced within and outside of the quota is $∑i=1Ipiqciq+∑i=1Ipiocio$⁠.

The dairy farm uses a vector of variable inputs $x=(x1,…,xM)$ with input prices $w=(w1,…,wM)$ and a vector of services from quasi-fixed inputs $z=(z1,…,zK)$ to produce the component vector $c=(c1,…,cI),$ where $ci=ybi$⁠. As a by-product of milk production, meat m is produced and sold for a price of p_m per kilogram. The associated variable cost function is $C(w,c,m;z)$⁠.⁶ Each year a farm will have an initial quota $y¯$⁠, and we assume that there is a leasing market in which the farm can lease in or out quotas for a price r. Let the quota lease be $Δy¯$⁠. Then the net quota holding y^q satisfies $y¯=yq+Δy¯$ and the revenue (i.e. $Δy¯>0$⁠) or cost (i.e. $Δy¯<0$⁠) from quota transactions will be $rΔy¯$⁠.

Solving the first-order conditions, we get choice functions for component supply within quota, component supply outside of quota, meat supply, variable input demand and net quota lease. The associated restricted profit function $π(piq,pio,pm,w,r;z)$ is assumed to be continuous, convex, monotonic and linearly homogeneous in output, input and quota lease prices.⁸

The first term on the right-hand side is the quantity effect, and the second term on the right-hand side is the composition effect.

4. Econometric model

The symmetric normalised quadratic (SNQ) functional form (Diewert and Wales, 1987; Kohli, 1993) is used to approximate the restricted profit function. This flexible functional form allows for negative profits and the global imposition of curvature properties without destroying flexibility.

Equation (3) allows for unobserved farm heterogeneity, since the first-order price coefficients α_nh are farm-specific. Furthermore, following Diewert and Wales (1992), ω_n is a fixed weight for each price constructed as $ωn=vnt∗|q¯n|⋅∑n=1Nvnt∗|q¯n| −1,$ where $vnt∗$ is a price in a reference price vector and $q¯n$ is the mean quantity of the nth netput. Following Diewert and Wales (1992), we choose a vector of ones as the reference price vector and this vector is created by scaling all prices with their respective mean values.

The SNQ is homogeneous of degree one by construction and symmetry is imposed by requiring α_np = α_pn and β_kl = β_lk. Furthermore, convexity with respect to prices is satisfied when the matrix A consisting of parameters α_np is positive semidefinite, and concavity with respect to quasi-fixed inputs is satisfied when the matrix B consisting of parameters β_kl is negative semidefinite (Diewert and Wales, 1987). These conditions do not necessarily hold, and when violations occur, they can be imposed globally by using a method due to Wiley, Schmidt and Bramble (1973). As shown by Diewert and Wales (1987), convexity with respect to prices can be imposed by setting A= ΓΓ′, where the elements of the N × N matrix Γ are d_np for $∀n≥p$ and 0 for $∀n<p$⁠.⁹ In a similar manner, concavity with respect to quasi-fixed inputs can be imposed by setting B=−EE′, where E is a lower triangular matrix with the same structure as Γ. Finally, local flexibility of the SNQ at $vnt∗$ requires the restriction Av* = 0 (Diewert and Wales, 1987). This restriction implies that all row sums of A are zero at the selected reference point.

The elasticity form of Equation (7) is then computed as $ent=(∂qnht/∂t)⋅1/q¯n$⁠, which is equivalent to a logarithmic differentiation of Equation (4) with respect to t. Therefore, it can be interpreted as a growth rate of the respective variables.

The parameters of Equation (3) are found by estimating a stochastic version of the system of equations (Equation (4)). An advantage of estimating this system of netput equations is that the farm-specific intercepts disappear after the within transformation of the variables. A random error term ε_nht is added to each of the netput equations (Equation (4)). We allow for different variances across netputs. The variances are assumed to be constant across farms and over time, i.e. $ϵnht∼N(0,σnn2)$ where $σnn2=var(ϵnht,ϵnht).$ Furthermore, we allow for non-zero covariances across netputs (contemporaneous correlation). However, the covariances are assumed to be constant across farms and over time (serially uncorrelated), i.e. $σnp2=var(ϵnht,ϵpht)$ for n ≠ p and var(ε_nht, ε_nht′) = 0 for t ≠ t′.

5. Data

The sample is an unbalanced panel consisting of 311 Icelandic dairy farms with 1,177 observations for the period from 1997 to 2006. All farms with only one observation were removed from the sample before the within transformation was performed to remove time-invariant heterogeneity across farms. A total of 1,127 observations from 261 farms were used for the estimation, and these farms had been observed for 4.3 years on average.

Data for the quantities and costs of variable inputs, except for quota leases, were provided by the Agricultural Economics Institute (Hagþjónusta landbúnaðarins). They also provided the data for the stocks of quasi-fixed inputs, quantities of milk and meat as well as income from milk and meat sales.¹⁰ According to analysis by the Agricultural Economics Institute, the dataset is representative for Icelandic farms (Hagþjónusta landbúnaðarins, 2010). The variable inputs included in our model are fertiliser, concentrates and leased in quota. As in most small scale farming systems, forage is an intermediate output produced on the farm using input such as fertiliser, land, capital and labour. We assume all inputs in forage production except fertiliser as quasi-fixed and forage production can only be affected by changing fertiliser application. The prices of meat, fertiliser and concentrates were calculated as unit values from value and quantity data. To correct for outliers in the quantity data, unit values that deviated by more than 50 per cent from the median were replaced by the median itself.¹¹ Then input quantities are recovered from the value data and the adjusted unit values.

Table 1 shows that the average farm used approximately 21,000 kg of chemical fertilisers and nearly 36,000 feed units of concentrates each year. The quasi-fixed inputs are labour, capital, land and the number of cows.¹² The average farm used approximately 25 man months of labour annually, farmed approximately 47 hectares of land, and had approximately 32 cows.

Data on milk quota transactions were collected by The Farmers' Association of Iceland. The average net seller sold quota rights for approximately 6,000 l, while the average net buyer purchased three times as much. As shown in Table 1, the average farm is a net buyer, and its annual purchase of quota rights is for 5,027 l. The excess purchase of quota rights is explained by farms leaving the sample by selling all of their quota holdings. For legal reasons, a quota lease market does not exist in Iceland, while a quota sale market exists (Bjarnadottir and Kristofersson, 2008). However, since a quota represents the right to sell in a preferred market currently as well as in the future, it is perceived as an asset (Moschini, 1989). We therefore used the reported sales prices to construct the quota lease price. Following Newell, Papps and Sanchirico (2007: 260), we assume that the quota sales price is equal to the present value of all the future earnings from the quota, and the corresponding lease price is equal to the expected annual earnings from holding the quota.¹³ Assuming constant discount rates, we set the annual quota lease price to 5 per cent of the sales price. This discount rate was also used in Bjarnadottir and Kristofersson (2008). As shown in Table 1, the resulting average annual lease price for quota is approximately ISK 11 per litre.¹⁴

Data on milk composition and component prices were collected by the dairy cooperative in Iceland, MS Icelandic Dairies, which controlled the entire dairy market during the period. The composition data are based on weekly measurements for each farm. Figure 1 shows the development of protein and fat percentages in a kilogram of milk during the study period. The linear trend lines indicate that the percentage of components per kilogram of milk has been growing during the study period and the growth appears to be stronger for protein.

Table 1 also shows that the average Icelandic dairy farm delivered 5,323 kg of fat and 4,436 kg of protein annually to the quota milk market and 323 kg of fat and 269 kg of protein to the surplus milk market. As shown in Table 1, the average price per kilogram of fat and protein in the quota milk market were ISK 242 and ISK 873, respectively. The corresponding prices in the surplus milk market were ISK 57 and ISK 748 per kilogram of fat and protein, respectively. The difference in price between fat and protein is due to high demand for protein in Iceland, while the demand for fat has traditionally been quite low. However, recently the price of fat in the surplus milk market has increased on the back of fat shortages. Finally, the average farm delivered nearly 2 tons of meat.

6. Estimation

An initial set of parameters was obtained by using iterative seemingly unrelated regression (IT-SUR). The estimated function was checked for monotonicity by looking at the signs of the predicted netput quantities. The average predicted quantities of all netputs have the expected signs, which suggest that the estimated profit function is monotonic with respect to netput prices at the mean. Three eigenvalues of the A matrix were negative, and two eigenvalues of the B matrix were positive. This suggests that curvature conditions with respect to prices and quasi-fixed inputs are not satisfied by the estimated function, and it cannot be treated as a valid profit function. Consequently, we imposed curvature conditions globally by using the procedure described above.

The re-parameterised model is nonlinear in parameters and convergence problems were encountered as commonly found in similar specifications (Diewert and Wales, 1988; Moschini, 1998). As noted by Moschini (1998), imposing curvature conditions on the fully flexible model is likely to force the wrongly signed eigenvalues of the relevant matrices to zero and cause estimation to break down. In such cases, Diewert and Wales (1988) suggested to specify a semiflexible model by reducing the ranks of A and B. There are several alternative ways to specify such a model and we followed the rule-of-thumb recommended by Moschini (1998). It is recommended that the rank of the relevant matrix in the specified semiflexible model should not exceed the number of eigenvalues from the fully flexible model with the correct sign required to meet curvature conditions. Accordingly, we reduced the ranks of A and B to five and two, respectively. However, this model also did not converge and we had to further reduce the rank of A to four before the model converged.¹⁵ The Stata routine nlsur (StataCorp, 2009) was used to estimate the model using iterative nonlinear seemingly unrelated regression (IT-NLSUR).¹⁶ The estimated parameters are provided in Appendix.

7. Results

Based on the parameter estimates, the own- and cross-price elasticities of netputs and the elasticities of intensity are discussed in the following sub-sections.

7.1. Effects of changes in output prices

Table 2 shows that all own-price elasticities are positive for outputs and negative for inputs. Except for fat supply to the surplus milk market and quota lease, they are significantly different from zero at the 5 per cent level of significance.¹⁷ In the quota milk market, the own-price elasticity for fat and protein are 0.26 and 0.23, respectively. These elasticities are substantially higher than those reported in Kirkland and Mittelhammer (1986). As discussed above, several factors related to data, methodology, breed and characteristics of the pricing schemes may explain the difference. In contrast, the own-price elasticities of fat and protein supply in the surplus milk market are quite different. A 1 per cent increase in the price of protein results in a 0.25 per cent increase in protein supply, while a 1 per cent increase in the price of fat only results in a 0.02 per cent increase in fat supply. Furthermore, the latter is significant only at the 10 per cent level of significance.

The low price responsiveness of fat supply in the surplus milk market can mainly be explained by the low price of fat as measured in both absolute and relative terms in this market. According to Table 1, protein was valued 13 times as much as fat in the surplus milk market, while it was valued only 3.6 times more in the quota milk market. Furthermore, the mean price of fat in the surplus milk market was less than 25 per cent of the mean price in the quota milk market. Given the low value of fat in the surplus milk market, a small price change for fat will have negligible effects on profitability and provides weak incentives to change management practices to produce more or less fat. On the other hand, price changes of protein in both markets and fat in the quota milk market provide much stronger incentives to change management practices. In the short-run, the change in management practice to influence component supply is likely to be in the form of changing feed composition. Jenkins and McGuire (2006) showed that high concentrate intensity in the feeding regime boosts protein content and milk output while it tends to depress fat content. On the other hand, low concentrate intensity boosts fat content while it depresses protein content and milk output. For example, an increased price of fat in the quota milk market increases the demand for fertilisers more proportionally than for concentrates, suggesting an attempt to lower the concentrate intensity to boost the fat content. This, however, comes at the cost of reducing protein content and milk output, which is reflected in a statistically significant reduction in the supply of fat and protein to the surplus milk market.

The nature of the shift in feed composition also provides another subtle reason for the low price responsiveness of fat supply in the surplus milk market. As seen in Table 2, an increase in the price of fat in the surplus milk market motivates a shift towards a more concentrate intensive feeding regime. This implies that farmers respond to the price change by increasing milk quantity. Given the price of concentrates, however, the cost of producing each kilogram of fat also increases with concentrate intensity. The generally inverse relationship between fat content and concentrate intensity further strengthens the cost implication of the concentrate intensive feeding regime on fat production. Therefore, the price responsiveness of fat supply in the surplus milk market is likely to be small.

The difference in own-price elasticity of protein between the two markets is statistically insignificant. This indicates that the effect of an almost 17 per cent higher price of protein in the quota milk market is balanced by the additional cost of leasing the quota required to sell in this market. Finally, the own-price elasticity of meat is 0.09.

There are 20 cross-price elasticities between output prices and quantities, and eight of them are significant at the 5 per cent level. Several cross-price effects may be noted. First, the supply of fat to one market responds negatively to changes in the price of fat in the other market. The effect is strongest for a price change in the quota milk market. A 1 per cent increase in the price of fat in the surplus milk market reduces the supply of fat to the quota milk market by only 0.004 per cent, while a 1 per cent increase in the price of fat in the quota milk market reduces the supply of fat to the surplus milk market by 0.26 per cent. The strong supply response in the surplus milk market to a fat price change in the quota milk market can be a consequence of a reduction in concentrate intensity to boost milk fat content, which also reduces milk output and thereby the fat delivered to the surplus milk market. The weak fat supply response in the quota milk market to a fat price change in the surplus milk market is likely due to the very low price of fat in the surplus milk market.

Second, an increase in the price of fat in the quota milk market has a negative effect on protein supply to the surplus milk market. As explained above, this reduction is likely to be a consequence of reducing concentrate intensity to boost the fat content.

Third, an increase in the price of protein in the surplus milk market has a negative effect on fat supply to the quota milk market. This reduction is likely to be composition driven. A price increase for protein gives incentive to increase protein content of the milk output by using high concentrate intensity feeding regimes. Although such a regime is also favourable to milk output, it will reduce fat content. Since the average farm produces slightly above its quota, the implication of the positive quantity effect for fat supply to the quota milk market will only be minor, and the negative composition effect will dominate.

Fourth, all the significant cross-effects of a change in meat price are with component supplies to the quota milk market. An increase in the price of meat has small and positive effects on the supply of fat and protein to the quota milk market. One possible explanation for these positive effects is that higher meat price results in increased culling rates. The best cows with the most profitable milk output and composition will remain. The overall result may be an increase of component supply to the quota milk market but a reduction in component supply to the surplus milk market due to the smaller herd size and the consequent reduction in overall production. In our case, however, the negative effects on component supply to the surplus milk market are statistically insignificant.

Fifth, component price increases in the quota milk market apparently have positive effects on meat supply. A 1 per cent increase in the price of fat results in a 0.1 per cent increase in meat supply while an equivalent increase in the price of protein results in a 0.3 per cent increase in meat supply. One possible explanation for these effects is the relationship between optimal feeding for component production and the associated effects on milk output. For example, a higher protein price in the quota milk market will encourage increasing concentrate intensity to boost the protein content. However, milk output will also increase and some of the milk output may have to be sold in the surplus milk market at lower prices. To counteract the positive quantity effect of the change in feeding regime, farmers may increase their culling rates and thereby the meat supply.

There are 10 cross-price elasticities between output prices and input quantities. All of these elasticities are significant at the 5 per cent level. Eight cross-price elasticities are positive, which suggests that increasing output prices increases input demand. Contrary to the quota milk market, the cross-price elasticities between component prices in the surplus milk market and the demand for fertiliser are negative. These negative cross-price elasticities can be caused by a change in the feeding regime towards higher concentrate intensity to increase milk quantity and supply the surplus milk market. Finally, the only output price that affects the quantity of quota leases is the price of fat in the quota milk market.¹⁸ A 1 per cent price increase for fat in the quota milk market decreases the demand for quota by 0.80 per cent.

7.2. Effects of changes in input prices

All the cross-price elasticities between input prices and output quantities are significant at the 5 per cent level. As expected, eight of these cross-price elasticities are negative, which suggests that increasing input prices decreases output supply. The two exceptions are the positive cross-price elasticities of fat and protein supply to the surplus milk market with respect to fertiliser price. This is likely the consequence of high fertiliser prices leading to substitution of concentrates for forage. The resulting increase in the concentrate intensity will increase milk output and hence increases component supply to the surplus milk market.

The cross-price elasticities between fertiliser and concentrates are positive and statistically significant at the 5 per cent level. This suggests that fertiliser and concentrates are substitutes in milk production.

Only one cross-price elasticity of netput quantities with respect to a change in the quota lease price is statistically significant at the 5 per cent level. The supply of fat to the quota milk market increases slightly as the quota lease price increases. An increase in quota price may motivate some farmers who decide to leave dairy farming to sell their entire quota holding. Given the lower fat than protein prices in the surplus milk market, the quotas are likely to be purchased by farmers who are aiming to produce milk with a higher fat content.

7.3. Effects of changes in quasi-fixed inputs

Table 3 shows elasticities of intensity and the percentage growth in the supply or use of each netput. Eleven out of twenty elasticities of intensity for output supply are statistically significant at the 5 per cent level. An increase in number of cows has a positive effect on the supply of all outputs. As expected, the supplies of components to the surplus milk market are more affected than the supplies to the quota milk market. An increase in the use of capital increases component supply to the quota milk market, but reduces component supply to the surplus milk market. This implies that capital intensive farms find the surplus milk market relatively more unattractive. An increase in the quantity of land also has a similar effect. However, this latter effect is likely to be the result of increased production and use of forage that tends to depress milk output. Finally, we find that an increase in labour supply has no effect on component supply.

Four out of eight elasticities of intensity for feed demand are statistically significant at the 5 per cent level. As expected, an increase in herd size leads to an increase in the demand for fertiliser and concentrates, and the demand for concentrates increases twice as much as the increase for fertiliser. On the other hand, an increase in capital has a negative effect on fertiliser demand, which suggests that concentrate intensity is likely to be higher on farms with high capital intensity. Finally, increased labour supply is associated with higher demand for fertiliser. This could be the result of increased production of forage that additional labour facilitates.

Only one out of four elasticities of intensity for quota lease is statistically significant at the 5 per cent level. As can be expected, an increase in herd size results in increased demand for milk quota. For a 1 per cent increase in herd size, the demand for quota increases by 3.8 per cent.

Table 3 also shows the percentage growth rates of the respective netputs over time. Component supply to the quota milk market increased by 0.1 per cent per year, while it increased by about 0.3 per cent in the surplus milk market. Furthermore, fertiliser use has declined by 0.3 per cent per year and concentrates use has increased by 0.2 per cent per year.

8. Conclusions

Following an increase in the demand for milk as an input in dairy processing, milk is increasingly being considered as a heterogeneous product that consists of several components. MCP schemes channel component value information to farmers and provide direct incentives for the supply of milk with more of the components the market is willing to pay for. We propose a model for milk component supply under a MCP scheme for a profit-maximising dairy farm operating under a tradable quota regime. The model can easily be modified to situations without quotas or with non-tradable quotas. We derive a system of component supply and input demand functions that was estimated for a panel of Icelandic dairy farms for the period 1997–2006.

Our results show that component supplies respond to price changes in the short-run. A 1 per cent increase in the price of fat in the quota milk market increases the supply of fat to the quota milk market by 0.26 per cent. Similarly, a 1 per cent increase in the price of protein in the quota milk market increases the supply of protein by 0.23 per cent. In the surplus milk market, a 1 per cent increase in the price of fat and protein results in a 0.02 per cent increase in the supply of fat and a 0.25 per cent increase in the supply of protein. The difference in supply response for fat between the two markets is likely to be caused by differences in price levels of fat in the two markets.

There are several significant within and between components cross-price effects. First, the supply of fat to one market responds negatively to changes in the price of fat in the other market. This negative effect is strongest for a price change in the quota milk market. A 1 per cent increase in the price of fat in the surplus milk market reduces the supply of fat to the quota milk market by 0.004 per cent, while a 1 per cent increase in the price of fat in the quota milk market reduces the supply of fat to the surplus milk market by 0.26 per cent. The relatively strong supply response in the surplus milk market can be an effect of reducing concentrate intensity to boost milk fat content, which also reduces milk output and thereby the quantity of fat that is delivered to the surplus milk market. Second, fat supply to the quota milk market is negatively affected by changes in the price of protein in the surplus milk market, and protein supply to the surplus milk market is negatively affected by changes in the price of fat in the quota milk market. The former effect is explained as a composition driven response generated by shifts in feeding regimes towards mixes that are favourable for protein content and milk output but are unfavourable for fat content. The latter effect is explained as a composition and quantity driven response generated by feeding regimes that boost fat content but reduce milk output and protein content.

With respect to quasi-fixed inputs, a change in the number of cows has positive effects on the supply of all outputs with larger effects on component supply to the surplus milk market. This is likely to be driven by strong milk quantity effects of a large herd size. We also find that capital intensity on the farm is positively related to component supply to the quota milk market and negatively related to component supply to the surplus milk market. Finally, we find that component supply to both markets has increased over time and the growth in components supply to the surplus milk market has been stronger.

One can draw some policy implications based on our results. First, our results indicate that price incentives do affect milk composition in the short-run and component supply is more price responsive than previously found. Given changes in consumer preferences towards different milk components over time, a MCP scheme is therefore better suited to respond to changes in consumers' demand and processors' need than pricing schemes that mainly are based on a price per litre of milk. However, we find that the effect of price changes on component supply can be quite complex with several interactions that need to be taken into account. An incentive to increase protein supply may adversely affect fat supply and vice versa. This is due to the different strategies farmers use to change protein and fat supply. For example, protein production can be increased by more intensive feeding, but that may also lead to a reduction in fat supply. Increasing both fat and protein supply simultaneously may therefore require a balanced increase in prices for fat and protein.

Second, there are limits on how much component supply can be adjusted in the short-run. Dairy policy must allow for as much flexibility as possible to ensure that the dairy industry can respond to changes in component demand, for example, new trends towards low-carb and high-fat diets. The ambition must be on facilitating adjustments that are needed to supply components according to consumer demand. An obvious suggestion is to liberalise the markets for dairy products and facilitate structural changes in dairy farming by, for example, lifting restrictions on quota lease and sales or abolishing quotas all together. Such liberalisation is also likely to reduce consumer prices for dairy products and promote efficiency in milk production.

Acknowledgements

The authors thank the Agricultural Economics Institute of Iceland, the Farmers Association of Iceland and the dairy cooperative MS Icelandic dairies for providing the data used in this article. The authors also thank Professor Iain Fraser, Co-Editor of the European Review of Agricultural Economics and three anonymous referees for valuable comments.

References