On a welfare economics problem involving public interest goods

Official URL: https://risc01.sabanciuniv.edu/record=b3150193_(Table of contents)

Governments worldwide devise policies to assist the public in adapting to a new technology or good that is known to be beneficial to society or the environment. A well-known example of such a good is electric vehicles. The government uses subsidy policies aimed at both customers and manufacturers to incentivize the consumption and production of such so-called public-interest goods. This thesis studies how the government aims to increase social welfare and can set its subsidy policy to consumers and manufacturers to promote a specific public-interest good. Part of the government’s subsidy policy is to increase the supply of such a good by giving subsidies to the manufacturer, and another part is to give rebates or tax reductions to the consumers to increase the demand. In this thesis, we analyze this problem in both centralized and decentralized economies. In a centralized economy, the government, next to determining its own subsidy policy, has complete control over the market’s supply side and dictates the manufacturer the price and production quantity of the public interest good. This problem can be formulated as a nonlinear optimization problem consisting of the decision variables production quantity and price demanded by the manufacturer, subsidy for each produced product, and rebate to be offered to each buying customer. In a decentralized economy, the government has only control over its subsidy policy and cannot dictate to the manufacturer the supply and price of the product. As such, the government only knows that for any announced subsidy policy, the manufacturer taking into account this subsidy policy iv will determine the price and production to increase its profit. In this thesis, this problem is formulated as a so-called bilevel optimization problem with the same decision variables as used before. Such a formulation is called a Stackelberg game, where the manufacturer is the follower and decides over price and quantity, and the government is the leader and decides over rebate and subsidy. To keep the analysis tractable we only consider in this thesis the deterministic demand case where the demand is given by some demand function. The more complicated case of random demand is not considered in this thesis. The purpose of this research is to provide, under the most general conditions on the demand side, an almost analytical solution to the above problem in both a centralized and decentralized economy. In our first formulation of the problem in both a centralized and decentralized economy, the objective consists of adding the consumer surplus and profit of the manufacturer and externality effects for the economy and subtracting the total expenditures of the government spend on its subsidy policy. In our second formulation, we consider in both economy settings the objective from which we delete from the previous one the expenditures of the government but now include these expenditures as a budget restriction. In the first formulation, we analyze the problem only assuming that the demand function is continuous. In the second formulation, including the budget constraint, we analyze this problem for a very general class of demand functions covering a subset of the class of log-concave demand functions. Finally, these results are refined for some well-known demand functions like to power demand function, the linear demand function, the log-linear demand function, and the logit demand function.