# Lecture 0 - Math review

version from 2016-09-07 18:02

## Section

what branch of science is economics?social science
what is the language of all sciences?math
what is the goal of optimization?to maximize profits
Give 2 examples of marginal analysis.MC(marginal cost) & MB(marginal benefits)
what the first "first derivatives" of math functions?marginal analysis
what is marginal analysis?an important decision-making tool in the business world that allows business owners to measure the additional benefits of one production activity versus its costs.
Look @ slides #8-9
Draw a graph of firm with the objective to maximize profits & label it's equation (slide 8)
Now using the derivate of the slope, find q that will maximize the profits between TC & TR and label the slope of each.
what is the slope of TR?MR & first derivative
What is the slope of TC?MC & first derivative
what does TR stand for?total revenue
what does TC stand for?total cost
what does MC stand for?marginal cost
what does MR stand formarginal revenue
what is the equation of MR? How do you get there?Tr/q=deltatr/deltaq=dtr/dq
what is the equation of MC? How do you get there?tc/q=deltatc/deltaq=dtc/dq
what does delta equal? what does d mean w/ /respect to q?d ; small changes in q
what is the most common type of differentiation used?power rule
Look @ slide 12 to understand how to find these marginals.
If TR=500q - 5q^2, what is MR?500 - 10q
if TC=300+7.5q^2, what is MC?15q
if MC=54q+7, what is TC?27q^2 + 7q
if ln(y)=a+bln(x), what is dy/dx equal to?b x (y/x)
what are ln and exp known as?functional operations
if y=ln(x), what does x equal?e^y
what do the marginals (MR & MC) depend upon?explicit form of your equations