  The paper presents instructive interdisciplinary applications of constrained
mechanics calculus in economics on a level appropriate for the undergraduate
physics education. The aim of the paper is: 1. to meet the demand for
illustrative examples suitable for presenting the background of the highly
expanding research field of econophysics even on the undergraduate level and 2.
to enable the students to understand deeper the principles and methods
routinely used in mechanics by looking at the well known methodology from the
different perspective of economics. Two constrained dynamic economic problems
are presented using the economic terminology in an intuitive way. First, the
Phillips model of business cycle is presented as a system of forced
oscillations and the general problem of two interacting economies is solved by
the nonholonomic dynamics approach. Second, the Cass-Koopmans-Ramsey model of
economical growth is solved as a variational problem with a velocity dependent
constraint using the vakonomic approach. The specifics of the solution
interpretation in economics compared to mechanics is discussed in detail, a
discussion of the nonholonomic and vakonomic approaches to constrained problems
in mechanics and economics is provided and an economic interpretation of the
Lagrange multipliers (possibly surprising for the students of physics) is
carefully explained. The paper can be used by the undergraduate students of
physics interested in interdisciplinary physics applications to get in touch
with current scientific approach to economics based on a physical background or
by university teachers as an attractive supplement to the classical mechanics
lessons.
