Intuitively, this limits the firm’s growth rate such that it can at most double its capacity in one year. As shown below, the firm will choose not to grow for all values of up to .951, after which g it will always choose the maximum growth rate of 1. This is the smallest at which the firm will g be able to profit; in our further analysis, we will call this point the optimal g. The result indicates that perhaps our assumption of = 1 is unrealistic; this defines a α production function with constant returns to scale. Instead, we want to understand the relationship between and under a production function with decreasing returns to scale. Thus, n g we take the perspective of the government and search for the optimal for each level of The g α. graph below describes the relationship between optimal and the dotted exponential trend line g α; has an R2 of almost exactly 1, indicating a nearly perfect fit. Intuitively, higher levels of have α higher returns to scale of the production function. In our model, our constraints define that the production function must have decreasing returns to scale. This means that as approaches 1, α doubling capacity will nearly, but not quite, double generation. As decreases, the production α function has lower returns to scale. From the government’s perspective, it is optimal to provide subsidy at the optimal in other words, the government wants to stimulate solar capacity growth g; while spending the least that it can. We have shown that the government’s consideration of optimal depends on the properties of the production function, which may change depending on g the state of the solar industry. 6.0. Conclusion
Intuitively, this limits the firm’s growth rate such that it can at most double its capacity in one year. As shown below, the firm will choose not to grow for all values of g up to .951, after which it will always choose the maximum growth rate of 1. This is the smallest g at which the firm will be able to profit; in our further analysis, we will call this point the optimal g. The result indicates that perhaps our assumption of α = 1 is unrealistic; this defines a production function with constant returns to scale. Instead, we want to understand the relationship between n and g under a production function with decreasing returns to scale. Thus, we take the perspective of the government and search for the optimal g for each level of α. The graph below describes the relationship between optimal g and α; the dotted exponential trend line has an R2 of almost exactly 1, indicating a nearly perfect fit. Intuitively, higher levels of α have higher returns to scale of the production function. In our model, our constraints define that the production function must have decreasing returns to scale. This means that as α approaches 1, doubling capacity will nearly, but not quite, double generation. As α decreases, the production function has lower returns to scale. From the government’s perspective, it is optimal to provide subsidy at the optimal g; in other words, the government wants to stimulate solar capacity growth while spending the least that it can. We have shown that the government’s consideration of optimal g depends on the properties of the production function, which may change depending on the state of the solar industry. 6.0. Conclusion
Team07-TheFutureofSolarEnergyintheUScopy.docx