Choice Ch 5: ChoiceCh 6: Demand (sec. 2,5,6,8 & appendix)Ch 15: Market Demand (sec. 1& 2)2Rational ChoiceThe principal behavioral postulate is that a decisionmaker chooses its most preferred alternative from those available to it.In terms of our model, this means choosing a bundle from the highest indifference curve that can be reached without exceeding the budget set.3Rational Constrained Choicex1x2Affordablebundles4Rational Constrained ChoiceAffordablebundlesx1x2More preferredbundles5Rational Constrained Choicex1x2x1*x2*(x1*,x2*) is the mostpreferred affordablebundle.6Rational Constrained ChoiceThe most preferred affordable bundle is called the consumer‟s ORDINARY DEMAND at the given prices and budget.Ordinary demands will be denoted byx1*(p1,p2,m) and x2*(p1,p2,m).
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7Choice with monotonic preferencesSupposed preferences are monotonic, i.e. more is better;Then the consumer will always choose a bundle that exhausts the budget.The chosen bundle is “interior” if it contains strictly positive quantities of both goods.8Rational Constrained ChoiceWhen preferences are monotonic, indifference curves are smoothly convex and the chosen bundle is interior, (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*).9Choice: The canonical casex1x2x1*x2*(x1*,x2*) is interior .(a) (x1*,x2*) exhausts thebudget; p1x1* + p2x2* = m.(b) The slope of the indiff.curve at (x1*,x2*) equalsthe slope of the budgetconstraint.10Solving for the optimum bundleIf the budget is exhausted, then the optimum bundle must satisfy the budget constraint with equality:p1x1* + p2x2* = mIf the optimum bundle is interior, then it must be a point at which the slope of the budget line equals the slope of the indifference curve, i.e.:- p1/p2= MRSWe can use these two equations to solve for the two variables x1*and x2*.11Computing Ordinary Demands -a Cobb-Douglas Example.Suppose that the consumer has Cobb-Douglas preferences.ThenU xxx xa b(,)1212MUUxaxxab11112MUUxbx xa b2212112Computing Ordinary Demands -a Cobb-Douglas Example.So the MRS isAt (x1*,x2*), MRS = -p1/p2soMRSdxdxUxUxaxxbx xaxbxaba b 211211212121//. axbxppxbpapx21122121****.(A)