Fascinating Characteristics and Applications of the Fibonacci Sequence

This thesis offers a brief background on the life of Fibonacci as well as his discovery of the famous Fibonacci sequence. Next, the limit of the ratio of consecutive Fibonacci terms is established and discussed. The Fibonacci sequence is then defined as a recursive function, a linear homogeneous recurrence relation with constant coefficients, and a generating function. Proofs for those particular properties are introduced and proven. Several theorems and identities from the field of number theory concerning the properties of the Fibonacci numbers are also introduced and proven. Finally, the famous Fibonacci puzzle is introduced and critiqued. These fascinating characteristics and applications demonstrate not only the universal nature of the Fibonacci sequence but also the aesthetic nature of God

In-Kind Transfers and Work Incentives.

Recent developments in rationing theory are used to examine the differences between the effects of in-kind and cash transfers on labor supply. It is not possible to tell a priori which type of transfer will cause the greater reduction in hours of work; the answer depends on the extent to which in-kind transfers distort consumption choices and on the relationship between the transferred commodities and leisure. Hicks-Allen complements can cause greater reductions in labor supply than equally generous cash transfers, while strong Hicks-Allen substitutes can induce increases in market work. Copyright 1988 by University of Chicago Press.