03 consumer choice Flashcards
(20 cards)
The Problem of the Consumer - Topics Today
-Budget Constraint
-The decision of the consumer as a mathematical maximization
problem
-How to analyze the consumer problem?
(algebraically ,graphically)
-Cobb-Douglas Preferences and their properties
What is the consumer’s problem?
it describes the decision-making process of
individuals, where they select the optimal bundle of goods from their
budget set that aligns with their preferences.
if preference is represented by a utility function u(x1,x2,…,xn), then bundles with higher utility are preferred.
What is the budget constraint?
p1 . x1 + p2 . x2 ≤ m
p1 . x1 + p2 . x2 ≤ m
if m=100, p1=2, p2=5, is the bundle (20, 10) in the budget set?
90 ≤ 100, so yes
The set of bundles that satisfy the budget constraint is called..
the budget set
The consumer problem consists of..
choosing from the budget set the
bundle (x1 ,x2 ,…,xn ) that maximizes the utility u(x1,x2,…,xn).
The optimal bundle must lie on the..
budget line because
with monotonic preferences, any bundle below the line leaves unused income that could be spent to achieve a higher utility
How Can the Consumer Problem Be Solved?
a general solution strategy:
1- Find all bundles that satisfy MU1(x1,x2) / MU2(x1,x2)= p1/ p2
and p1x1 + p2x2 = m, and could therefore be interior maxima.
2- Consider all possible boundary solutions.
3- Compare utility among all solution candidates and determine the
optimum.
The optimal bundle..
- must lie on the budget line!
The indi!erence curve through the optimal bundle..
cannot intersect the budget line!
The slope of the budget line is given by
the MRS
What defines the slope of the budget line?
The budget line was defined by the equation:
p1x1 + p2x2 = m.
Solving for x2, we get
x2 = m/p2 - p1/p2 . x1
The slope of the budget line is p1/p2
x1 = x1(p1, p2, m)
x2 = x2(p1, p2, m)
these two functions are called the consumer’s demand for good 1 and
good 2.
How do we find the SOLUTION to the consumer problem?
1- calculate the MRS (marginal rate of substitution)
2- The tangency condition MRS=
α/1-α . x2/x1 = p1/p2 together with the budget condition p1x1 + p2x2 = m yields a candidate solution for the consumer
problem
The solution to the consumer problem is given by
(x1, x2) = (αm/p1 , (1-α)m/p2)
How does a consumer with Cobb-Douglas preferences spends their budget on goods?
A consumer with Cobb-Douglas preferences always spends the same
proportion of their budget on each good!
This property of Cobb-Douglas preferences is very specific but makes it
easy to empirically determine the unknown parameter alpha!
What happens if price p1 increases to .. ?
The demand function does not change when the price changes.
Optimal Bundle and MRS?
For the optimal bundle, MRS must equal the price ratio p1/p2
Concepts you should know and understand:
-Consumer’s problem
-Cobb-Douglas preferences
Methods you should be able to apply:
-Solve the consumer’s problem analytically.
-Analyze the consumer’s problem graphically.
What you should be able to explain:
-How the modeling approach can be used in practice to model simple consumer decisions.
