MAT133Y1 Lecture Notes - Lecture 15: Economic Surplus, Integral, Equilibrium Point

• School: UTSG
• Department: Mathematics
• Course: MAT133Y1
• Professor: Paul Kergin

Document Summary

Mat133y1y - lecture 15 -chapter 14. 10, 15. 1, 15. 2: Suppose a demand function p = f(q) and supply function p = g(q) (this p is the unit price at which all producers will produce q units total). When p0 and q0 intersect, that is the equilibrium point. Producer surplus is 0 q0 f(q) - p0 dq. q0 p0 - g(q) dq. Integration by parts is a reverse (integration) version of the product rule. Formula: u dv - uv - u du. Let u= lnx, dv=dx, so, du = dx/x, v=x which is found by integrating dv = dx any constant of integration will do. Lnx dx = xlnx - x dx/x = xlnx - dx. A check: d/dx [(xlnx)-x) = (x)(1/x) + lnx -1 = lnx. Summary of all non-approximate methods for finding indefinite integrals:\ Partial fractions is a method for integrating any rational function f(x) / g(x).