Economic Rationality • The principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those available to it. • The available.
Download ReportTranscript Economic Rationality • The principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those available to it. • The available.
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.