The budget constraint can be described as the following equation: m = p1 x1 + p2 x2
m = income p1 = price of good x1 p2 = price of good x2 Solving the budget constraint: m p1 m p2
= intersect on the x1 -axis = intersect on the x2 axis p1 p2
Slope of the budget line = -
Some key points to remember: The a¤ordable bundle of goods lie on or below the budget line, while the una¤ordable bundle of goods lie above it
The budget line is a straight line connecting two points on the two axes, but at times there can be a kink in the budget line (food stamps). 1
If income changes but prices remain constant, the whole budget line either shifts up or down. If prices change but income remains constant, the slope of the budget line changes. The change in the slope causes the buget line to pivot either to the right or to the left.
Solve the following example:
Q : Supposing you have an income of $50. x1 costs $5 and x2 costs $10. a) Write down your budget constratint The budget constraint is as follows: 5x1 + 10x2 = 50
b) If you spent all your income on x1 , how much could you buy? 50 = 10 5
c) If you spent all your income on x2 ; how much could you buy? 50 =5 10
Some exercises to work on:
Q1 : Murphy was consuming 100 units of X and 50 units of Y. The price of X rose from 2 to 3. The price of Y remained at 4.
a) How much would Murphy’ income have to rise so that he can still exactly s a¤ord 100 units of X and 50 units of Y?
Q2 : Martha is preparing for exams in economics and sociology . She has time to read 40 pages of economics and 30 pages of sociology. In the same amount of time she could read 30 pages of economics and 60 pages of sociology.
a) Assuming that the number of pages per hour that she can read does not depend on how she allocates her time, how many pages of sociology could she read if she decided to spend all of her time on sociology and none on economics? b) How many pages of economics could she read if she decided to spend all of her time reading economics? (Hint: The prices here are relative in terms of pages read. Think about the cost of reading 10 pages of economics.)
A1 : $100 A2 : a) 150 pages, b) 50 pages
Some key points to remember:
An individual will always choose the more preferred option from the set of all available options: / Strict preference vs Indi¤erence A B vs A B
Two bundles of goods are identically preferred if they lie on the same indi¤erence curve.
An indi¤erence curve shows all the consumption bundles which yield the same utility.
An individual strictly prefers a bundle of good above the indi¤erence curves to those on or below it.
Marginal Rate of Substitution: The rate at which one good is given up for another x2 x1
MRS= Slope of the indi¤erence curve =
In general, M RS is larger at the upper portion of the indi¤erence curve than it is at it’ lower portion. s
For example, to gain one unit of good x1 we have to forgo greater amounts of good x2 when the quantities of x2 an individual possesses is su¢ ciently larger than the quantities of x1 :
The MRS decreases when the consumer receives more of x1 . This can be seen by the change in slope of the indi¤erence curve.
A utility function u(x) represents a consumer’ preferences, such as s x0 % x" () U (x0 ) % U (x") Various types of utility functions: Perfect Substitution: V (x1 ; x2 ) = ax1 + bx2 Example: Coke and Pepsi. Perfect complements: V (x1 ; x2 ) = minfax1 ; bx2 g Example: Left-foot shoe and right-foot shoe. Cobb-Douglas: V (x1 ; x2 ) = xa xb ; a; b > 0 1 2
Marginal Utility: The rate of change of utility as the quantity of good changes. @U @xi
M Ui =
The general equation for a utility function is: U (x1 ; x2 ) = k
Treating k as a constant, let us totally di¤erentiate...