Three essays in microeconomics

Essay I. Based on some results of Chipman and Moore (1990, 1991), we show that most frequently used pre-1970 functional forms for utility or demand functions do fall into the Gorman family of preferences, especially their characterization of two special members--preferences generating demands homothetic to a fixed origin and parallel preferences, where welfare analyses never need to use the questionable, though conventional, Marshallian consumer surplus as an welfare change indicator if any of these functional forms is assumed in the applied work (except the Rotterdam system). We also look at the three most popular flexible forms developed after 1970--the translog, the AIDS and the generalized Leontief functions--and find out the types of Gorman family members and the price-income restrictions under which these members are representable by these three forms. Some extensions based on these flexible forms are made and some implications are also observed. Essay II. It is well known that a line integral is path independent if the domain where the line integral is conducted is a simply connected open set and the Jacobian matrix of the integrand at any point in the domain is symmetric. When a line integral is path dependent on a certain domain, our result can be used to obtain a subset (defined by the constancy of some homogeneous functions) of that domain where the line integral is path independent. This result is also applied to the Marshallian consumer surplus line integral where we show that it is always path independent on the price-income set that maintains constant marginal utility of income. This result, however, does not resolve all the issues around the use of the Marshallian consumer surplus as a welfare change indicator. Essay III. We synthesize and extend Smith (1968), Lusky (1975, 1976) and others\u27 results allowing common property resources, waste discharge, clean-up and recycling activities as well as ordinary private commodities and economic activities to be included within a dynamic model. We compare the social optimum with the competitive result to show that environmental management through either (1) a direct control on resources extraction and waste discharges, (2) a tax/subsidy scheme on extracting, discharging and recycling activities, or (3) a marketable permit system allowing reallocation of property rights through a free market mechanism from any arbitrarily set initial assignment of property rights will help attain the social optimum. While this result is well-known for externalities in a static framework, we derive it in a dynamic framework. We also show that, the pursuit of higher GNP is not a problem in a dynamic context; what constitutes a problem is a society without recognition of environmental constraints and without remedial environmental policies