Economics, Mathematical

The purpose of this study is to determine what factors could influence an economic agents' decision to travel or vacation in Florida. This study measures this decision by analyzing the state Division of Tourism estimates for visitors in light of changes in; national gross domestic product, non-aviation gasoline prices, average airfares, and exchange rates. This data was compiled on a quarterly basis form 1980 to 1993 and analyzed by employing Translog and Cobb-Douglas demand functional forms for use in regression analysis. Based upon the regression results, the Cobb-Douglas functional form best represents what has historically occurred in the real economic world and follows generally accepted micro-economic demand theory. The Cobb-Douglas techniques reveal that an economic agents' future income expectations, measured by GDP levels, has a significant influence on Florida visitor estimates and has a role in the decision to vacation in Florida.

This thesis explored the impact of inflation upon fiscal automatic
stabilizers during the 1973-75 recession. Our study confined itself to
the three main devices purported to stabilize the U.S. economy automatically:
(1) federal personal income tax liability, (2) corporate
profits tax liability, and (3) unemployment compensation benefits.
A recursive model, similar to that used by Dusenberry, Eckstein, and
Fromm to study fiscal automatic stabilizers in the 1957-58 recession,
was constructed. Our simulation results led us to conclude that there
was a substantial reduction in output and employment due to the impact
of inflation upon federal personal income tax liability in the 1973-75
recession. We reached a tentative conclusion that the effects of
inflation upon output and employment via corporate profits tax liability
were negligible. Finally, we concluded that the effects of inflation
upon output and employment via unemployment compensation benefits paid
were negligible in the recent stagflation.

This thesis focuses on factor analysis as a
technique. It thus includes a survey of the various
factor mode ls, their theory and mathematical development,
a survey of its previous use for empirical studies in
economics, and empirical tests of sensitivity of alternative factor techniques. From the results of the
sensitivity test it was concluded that different factor
techniques yield very similar results and that factor
techniques are of value for empirical studies in economics.

This study demonstrates the importance of dynamic economic analysis, the role
played by difference equations in such analysis and the properties of systems of
difference equations. This is accomplished by proving the significance of dynamics
in general and difference equations in particular using the Cobweb model and the
"correspondence principle". The properties of systems of linear, first order difference
equations are discussed in detail and it is shown that a system of any order
can be reduced to first order so that the discussion is completely general. The
properties included in this analysis ore the traverse, impact, delayed, cumulative
and long run multipliers, and stability of a linear system. A simple Keynesian
model of income determination is estimated and simulated by the computer to
facilitate observation of these properties.

We generalize the theory of stochastic impulse control of jump diffusions introduced by Oksendal and Sulem (2004) with milder assumptions. In particular, we assume that the original process is affected by the interventions. We also generalize the optimal central bank intervention problem including market reaction introduced by Moreno (2007), allowing the exchange rate dynamic to follow a jump diffusion process. We furthermore generalize the approximation theory of stochastic impulse control problems by a sequence of iterated optimal stopping problems which is also introduced in Oksendal and Sulem (2004). We develop new results which allow us to reduce a given impulse control problem to a sequence of iterated optimal stopping problems even though the original process is affected by interventions.

Entrepreneurship occupies a curious place in economic theory. On one hand, the importance of entrepreneurship is widely recognized, particularly as it pertains to economic growth. However, the entrepreneur lacks a broadly accepted economic theory, and suffers from a dearth of literature on the subject. We believe that this is due to economics' heavy reliance on linear mathematical theory. In this thesis, we use nonlinear mathematics to construct a model of the entrepreneur that captures the sudden destabilization of a steady state, the unpredictability of a creative action, the possibility of entrepreneurial failure, and sensitivity to small changes in environment.