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. What you don’t remember!!! 1.Set up Langrangian 2.L= U(x 1,x 2 )+ λ(m-p 1 x 1 - p 2 x 2 ) 3.Take derivatives w.r.t. x 1, x 2, and λ. 4.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.

Cobb Douglas Let us solve for Cobb Douglas x 1 2 x 2 1 using the MRS method. Let us solve for Cobb Douglas x 1 2 x 2 3 using the substitution method. 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.