ECO102 Lecture Notes - Lecture 3: Definite Quadratic Form, Expenditure Function, Utility
Document Summary
Consumer theory comparative statics with two goods assuming strictly-quasiconcave utility function with |bh|>0 and interior solution. In matrix form, the above becomes and since. The determinant of the matrix of coefficients of the above system is equal to and since the bordered hessian of u and its determinant are respectively and it follows that. The effects of a change in the price of good 1 assuming all other money variables (m and p2) do not change can be found by setting dm = dp2 = 0 and applying cramer"s rule: that is, While the last derivative is unambiguously negative, the sign of the first two derivatives depends on the specifics of the utility function. (of course, it cannot be the case that both are positive). In matrix form, the above becomes which is the same as. The determinant of the matrix of coefficients of the above system is equal to.
