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!

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(x 1 ,x 2 ) s.t. p 1* x 1 +p 2* x 2  m, and x 1 ,x 2  0 • We maximize utility subject to the budget constraint!

Rational Constrained Choice

• The most preferred affordable bundle is called the consumer’s ORDINARY DEMAND at the given prices and budget.

• Ordinary demands will be denoted by x 1 *(p 1 ,p 2 ,m) and x 2 *(p 1 ,p 2 ,m). This is the solution to the previous problem.

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.

1. Substitution. 2. MRS=Slope of Budget constraint.

3. Lagrangian.

Substitution method.

1. Solve b.c. for one var. p 1 x 1 * + p 2 x 2 * = m 2. Plug into utility u(p 1 x 1 * , m/p 2 - p 1 x 1 * /p 2 ) 3. Take the derivative with respect to x 1 * and set this equal to zero. 4. Use this and original b.c to solve for x 1 * and x 2 * .

MRS method.

• (x 1 *,x 2 *) satisfies two conditions: • (a) the budget is exhausted; p 1 x 1 * + p 2 x 2 * = m • (b) the slope of the budget constraint, -p 1 /p 2 , and the slope of the indifference curve containing (x 1 *,x 2 *) are equal at (x 1 *,x 2 *).

Lagrangian method.

• • • 1.

2.

3.

4.

What you don’t remember!!!

Set up Langrangian L= U(x 1 ,x 2 )+ λ(m-p 1 x 1 Take derivatives w.r.t. x - p 2 x 2 ) 1 , x 2 , and λ. 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

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Cobb Douglas

• Let us solve for Cobb Douglas x 1 2 the MRS method.

x 2 1 using • Let us solve for Cobb Douglas x 1 2 the substitution method.

x 2 3 using • Solve for Cobb Douglas x 1 a x 2 b at home!

• Which prices does x 1 depend upon? What does this mean?

Constrained Choice Problems

• If preferences are monotonic, then we can usually obtain the ordinary demands are obtained by solving those 3 methods.

• Problems (IMPORTANT!!) 1. Preferences are not convex.

2. Corner Solutions. (x 1 * = 0 or x 2 * = 0) 3. Kinky I.C’s such as

min{ax 1 ,x 2 }

• Let us try solve 2 (with perfect substitutes) and 3.