Dynamic and Static Behaviour with Respect to Energy Use and Investment of Dutch Greenhouse Firms

Abstract

Dutch greenhouse horticulture firms are energy-intensive and major emitters of greenhouse gases. This paper develops a theoretically consistent model that is able to describe the greenhouse firms’ behaviour regarding energy use and investments in energy technology. The behaviour of the firm is modelled using a combination of a dynamic cost function and a static profit function framework. The optimal quantity of energy is derived from the link between these two functions. The model is applied to a panel of 97 Dutch greenhouse firms over the period 2001–2008. The results show that most Dutch greenhouse firms shift from being net electricity users to net electricity producers in the long term. Investing in energy capital contributes to reducing net energy use, however it increases the quantity of carbon dioxide emissions due to an increase in electricity production. A 1 % increase of the price of gas reduces carbon dioxide emissions by 1.6 %.

Appendices

Appendix A

1.1 Estimation results

Parameter	Estimate	SE	Parameter	Estimate	SE
$a_{11}$	268.877	91.05**	$g_{4}$	5.561	7.232
$a_{12}$	$-$25.891	101.6	$g_{5}$	0.01129	0.018
$a_{22}$	96.732	308.6	$g_{6}$	$-$880.968	1958.2
$\beta _{1}$	$-$211.088	46.44**	$g_{11}$	$-$1866.29	2448.4
$\beta _{2}$	117.744	37.65**	$g_{12}$	2891.196	2405.3
$\beta _{3}$	0.276	0.079**	$g_{13}$	$-$14464.2	20014.1
$\beta _{4}$	0.763	0.12**	$g_{22}$	$-$4633.74	2465.9*
$\beta _{11}$	16.465	13.299	$g_{23}$	17777.23	10471.9*
$\beta _{22}$	$-$25.789	6.55**	$g_{33}$	$-$136522	429762
$\beta _{33}$	$-$0.00006	0.00003*	$Q_{11}$	0.003126	0.00409
$\beta _{44}$	0.00007	0.000019**	$Q_{12}$	$-$0.00006	0.000039
$\beta _{55}$	$-$7.238	4.72	$Q_{13}$	0.1694	0.2684
$\beta _{12}$	13.829	6.45**	$Q_{22}$	$4.129^{-6}$	$6.472^{-6}$
$\beta _{13}$	0.0000158	0.018	$Q_{23}$	0.000713	0.00383
$\beta _{14}$	0.004219	0.01	$Q_{33}$	$-$30.7669	69.527
$\beta _{15}$	$-$19.625	6.06**	$R_{11}$	21.7229	2.3388**
$\beta _{23}$	$-$0.0299	0.013**	$R_{12}$	7.408	2.1766**
$\beta _{24}$	0.0078	0.0036**	$R_{13}$	$-$4.0637	7.516
$\beta _{25}$	2.438	2.98	$R_{21}$	$-$0.09834	0.0319**
$\beta _{34}$	$2.01^{-6}$	$-9.68^{-6}$	$R_{22}$	0.11279	0.0349**
$\beta _{35}$	$-$0.00398	0.01	$R_{31}$	$-$52.947	248.9
$\beta _{45}$	0.0117	0.010	$R_{32}$	$-$115.443	270.3
$\gamma _{11}$	296.03	25.95**	$D_{1}$	$-$195.057	63.307**
$\gamma _{12}$	$-$69.609	20.272**	$D_{2}$	238.703	64.27**
$\gamma _{13}$	$-$0.0289	0.043	$R_{33}$	$-$2.33484	55.17
$\gamma _{14}$	0.226	0.087**	$R_{23}$	$-$0.288817	0.0603**
$\gamma _{21}$	60.9398	23.26**	$\sigma$	269.77	128.3**
$\gamma _{22}$	139.87	17.955**
$\gamma _{23}$	$-$0.023	0.038
$\gamma _{24}$	0.269	0.1408*

1. Asterisk (*) and double asterisk (**) denote significance at 10 and 5 %, respectively

Appendix B

1.1 Elasticities for CO$_{2}$

Using both the direct and the indirect effects, one can derive the responses of CO$_{2}$ emissions quantity to a change in an energy input price. In the short term, the CO$_{2}$ emission elasticities show the effect of a price change before adjustments in energy capital or energy quantity have taken place. The short-term CO$_{2}$ emission elasticity is:

$$\begin{aligned} \varepsilon _{E^{*}gas}^{SR} =\left[ {\frac{dGas}{dw_m }+\frac{dGas}{dE^{*SR}}\frac{dE^{*SR}}{dw_m }} \right] \frac{w_m }{Gas}. \end{aligned}$$

The first term between the brackets corresponds to the direct effect to a change in price $w_{m}$, and indicates the response of the quantity of gas to the change in price. The second term between the brackets is the indirect effect that corresponds to the response of gas quantity to a change in the price when the quasi-fixed input energy quantity is optimal in the short term.

In the long term, energy output and the quasi-fixed input energy capital could adjust to their optimal levels. Now the responses of the specific quantity to a gas price change when energy capital and the output energy quantity fully have adjusted to their long-term equilibrium level, are taken into account. In the long term, the responses of gas quantity to a change in optimal energy quantity or optimal energy capital are derived from Eqs. (25a) and (26). The long term CO$_{2}$ emission elasticity is expressed as:

$$\begin{aligned} \varepsilon _{E^{*}gas}^{LR} =\left[ {\frac{dGas}{dw_m }+\frac{dGas}{dE^{*LR}}\frac{dE^{*LR}}{dw_m }+\frac{dGas}{dK^{*}}\frac{dK^{*}}{dw_m }} \right] \frac{w_m }{Gas}. \end{aligned}$$