Subsidy strategies of grain supply chain considering stakeholder efforts on post-harvest loss reduction and pollution emission reduction

Figures & data

Table 1. The description about the related variate

Parameter	Explanation
$e_0$	The unit PE of food producer.
$\gamma$	The effort level of PE reduction of the producer.
$k$	The cost coefficient of pollution abatement.
${\lambda }_1$	The unit quantity loss of the producer before adopting the GPHL reduction technology.
${\lambda }_2$	The unit quantity loss of the retailer before adopting the GPHL reduction technology.
$m$	The unit yield of food.
${\delta }_1$	The quantity loss discount rate of the producer after adopting the GPHL reduction technology, $0\le {\delta }_1\le 1$.
$k_1$	The cost coefficient of the loss reduction from the producer.
$m_1$	The unit quantity of the cargo received by the retailer.
${\delta }_2$	The quantity loss discount rate of the retailer after adopting the GPHL reduction technology, $0\le {\delta }_2\le 1$.
$k_4$	The cost coefficient of the loss reduction from the retailer.
$q_0$	The initial quality of food in the harvest stage.
${\alpha }_1$	The quality attenuation coefficient of food in the producer, $1\ge {\alpha }_1\ge 0$.
${\beta }_1$	The quality loss reduction coefficient of the producer. ${\beta }_1>;1$, in this paper, we used ${\beta }_1$ and ${\delta }_1$ to reflect the loss reduction effort level of the producer.
${\alpha }_2$	the quality attenuation coefficient in the retailer, $1\ge {\alpha }_2\ge 0$
${\beta }_2$	The retailer’s loss reduction coefficient about food quality, ${\beta }_2>;1$, in this paper, we used ${\beta }_2$ and ${\delta }_2$ to reflect the loss reduction effort level of the retailer.
${\kappa }_2$	The cost coefficient of the quality loss reduction from the producer.
${\kappa }_3$	The cost coefficient of the quality loss reduction from the retailer.
$M$	A constant and indicates the maximum value of the allowable PE.
$i$	$i=\left\{NEL,ENL,EL,ELB\right\}$
$p_i$	The retail price of food in the $i$ model.
$p_{max}$	The price when the market demand equals to zero.
$s$	The environmental innovation subsidy coefficient.
$s_1$	The GPHL reduction subsidy coefficient for the producer.
$s_2$	The GPHL reduction subsidy coefficient for the retailer.
$\beta$	The yield subsidy coefficient.

Figure 1. Deterioration situation of food quality in the two loss reduction backgrounds.

Figure 2. Variation trends of equilibrium prices and benefits with $s$ in the NEL model.

Figure 3. Variation trends of equilibrium prices and benefits with $\gamma$ in the NEL model.

Figure 4. Variation trends of equilibrium prices and benefits with $\gamma$ and $s$ in the EL model.

Figure 5. Variation trends of equilibrium prices and benefits with ${\beta }_1$, ${\delta }_1$ and $s$ in the EL model.

Figure 6. AVariation trends of equilibrium prices and benefits with ${\beta }_1$, ${\delta }_1$, $\gamma$ and $s$ in the ELB model.

Figure 7. Variation trends of equilibrium prices and benefits with ${\beta }_2$, ${\delta }_2$, $s_1$ and $s_2$ in the ELB model.

Figure 8. Investment and subsidy conditions of PE technology for the producer.

Figure 9. Investment and subsidy conditions of the GPHL reduction technology for the producer.

Figure 10. Investment and subsidy conditions of the GPHL reduction technology for the retailer.

Figure 11. Relationships between government subsidy and the efforts of producer (the loss reduction effort.

Figure 12. Relationships between government subsidy and the retailer’s efforts (the loss reduction effort).