Lecture 4: Concepts and Mathematic Methods for Economics

SECTION 1) MRS and Price Ratio

Example: Suppose MRS=4 and the price ratio=2 what does this tell us about how the consumer could optimize preference? What rule does this reveal?

• The consumer is willing to give up 4 units of y for 1 unit of x. The market allows for 2 units of y to be given up for one unit of x. The consumer is willing to trade off more units of good y for good x than what the market requires, therefore the consumer should increase consumption of good x.

• Rule revealed: when MRS > price ratio then consume more of good x.

Example: Suppose MRS=1 and price ratio =2 what does this tell us about how the consumer should optimize preference? What rule does this reveal?

• The consumer is willing to give up one unit of y for one unit of x. The market requires that 2 units of y be given up for one unit of x. Since the consumer values good x less than the market does, they should consume less og good x.

• Rule: When MRS < price ration then consume less of x.

SECTION 2] OPTIMUM BASICS

What is the optimum formula

slope of indifference curve (MRS) = slope of budget constraint (price ratio)

MRS= mux/muy = Px/Py

• This is only true at the optimum, whereas MRS= mux/muy is true everywhere.

MRS= mux/muy = Px/Py can be rearranged as mux/Px= muy/ Py what does this remind you of?

• The equal marginal principle!

• Note: the optimum point satisfies the equal marginal principle and thus is the point where utility is maximized.

Graphing Optimums example: Consumer has an income of 500 dollars to spend on gas and all other goods. the price of gas was initially $2 but increases to 2.5. What happens to the quantity of gas? What happens to expenditures on gas?

What happens if mux/muy never equals Px/Py

Corner solutions!

SECTION 3) OPTIMUM MATHMATICALY

Where is the optimum of any function f(x)

• Either at a minimum or a maximum.

• where f’(x)= 0

• Individual economic decisions typically involve maxima (utility/profit) and minima (cost/ependiture), and constrains (income)

The derivative and studying marginal relationships

Derivative Review. What does a derivative < > = 0 mean in the function profit (pie)=f(quantity) where would this be on a graph

Second Derrivative Review: what does a positive, negative and zero second derrivative tell you about the same function above?

How do you optimize a single variable funciton?

optimizing a 2 variable function