Economic Rationality

1
Economic Rationality

• The principal behavioral postulate is that a
  decisionmaker chooses its most preferred
  alternative from those available to it.
• The available choices constitute the choice set.
• How is the most preferred bundle in the choice
  set located?
• This combines utility and budget sets!

2
Choice!

• Draw the budget set. Draw the indifference
  curves. Best choice is at the highest
  indifference curve that is still in the budget
  set.
• This is equivalent to solve the problem
• Max x1,x2 U(x1,x2)
• s.t. p1x1p2 x2?m, and x1,x2?0
• We maximize utility subject to the budget
  constraint!

3
Rational Constrained Choice

• The most preferred affordable bundle is called
  the consumers ORDINARY DEMAND at the given
  prices and budget.
• Ordinary demands will be denoted byx1(p1,p2,m)
  and x2(p1,p2,m). This is the solution to the
  previous problem.

4
To solve the consumer problem

• Check to see what type of preferences. Smooth
  preferences such as Cobb-Douglas can be solved in
  one of 3 ways.
• Substitution.
• MRSSlope of Budget constraint.
• Lagrangian.

5
Substitution method.

1. Solve b.c. for one var. p1x1 p2x2 m
2. Plug into utility u(p1x1 , m/p2 - p1x1 /p2 )
3. Take the derivative with respect to x1 and set
   this equal to zero.
4. Use this and original b.c to solve for x1 and
   x2 .

6
MRS method.

• (x1,x2) satisfies two conditions
• (a) the budget is exhausted p1x1
  p2x2 m
• (b) the slope of the budget constraint, -p1/p2,
  and the slope of the indifference curve
  containing (x1,x2) are equal at (x1,x2).

7
Lagrangian method.

• What you dont remember!!!
• Set up Langrangian
• L U(x1,x2) ?(m-p1x1 - p2x2)
• Take derivatives w.r.t. x1 , x2 , and ?.
• Set them equal to zero and solve.
• See me after class or look at the book for an
  example.
• Note All methods basically are the same.

8
Cobb Douglas

• Let us solve for Cobb Douglas x12 x21 using the
  MRS method.
• Let us solve for Cobb Douglas x12 x23 using the
  substitution method.
• Solve for Cobb Douglas x1a x2b at home!
• Which prices does x1 depend upon? What does this
  mean?

9
Constrained Choice Problems

• If preferences are monotonic, then we can usually
  obtain the ordinary demands are obtained by
  solving those 3 methods.
• Problems (IMPORTANT!!)
• Preferences are not convex.
• Corner Solutions. (x1 0 or x2 0)
• Kinky I.Cs such as minax1,x2
• Let us try solve 2 (with perfect substitutes) and
  3.