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Lecture

# Classroom Lecture Notes - Kings

6 Pages
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School
Western University
Department
Economics
Course
Economics 2150A/B
Professor
Hugh Cassidy
Semester
Fall

Description
Chapter 5.1 Optimal Choice and Demand We have solved for optimum given exogenous variables. (Px, Py, I) Demand: how does the optimal (demanded) quantity of a good change as some exogenous variables change? Price Consumption Curve: Set of optimal bundles as price of good changes, holding other exogenous variables constant. U = xy I =12, Py=1 hold these fixed. Px1 = 4 Px2 = 3, Px3 =2 MRS = 1/1 x y/x = Px/Py = Px/1  y = PxX Y = 4x, 12 = 4x + y  12 = 4x + 4x12 = 8x  x = 3/2, y = 4x = 6 (3/2, 6) Y = 3x, 12 = 3x + 3x = 6x  x = 2, y = 6 (2,6) Y = 2x, 12 = 2x + 2x = 4x  x = 3, y = 6 (3,6) Straight Line across 6 is the Price Consumption curve, Y – int = 12, X –int = 3, 4, and 6. Straight lines to them all. Look in textbook Demand Curve: optimal quantity of a good as a function of its price, holding all other variables constant, bowed towards the origin. Income Consumption Curve: A set of optimal bundles as the income changes, holding all other exogenous variables constant. Look in textbook for example Engel Curve: Optimal quantity of a good as a function of income, holding all other exogenous variables constant. Look in textbook for example Normal Good: A good whose optimal quantity increases as income increases Inferior Good: A good whose optimal quantity decreases as income increases Giffen Good: A good whose optimal quantity increases as price increases Solving for Engel/Demand curve - Same procedure as solving for the optimum, but without substituting for exogenous variables c d 1) Cobb -Douglas. U = X Y , MRS = c/d x y/x  Set MRS = Px/Py c/d x y/x x = Px/Py y = d/c x XPx/Py Sub into equation below I = PxX + PyY I = PxX + Py(d/c x XPx/Py) I = PxX + (d/c x XPx) I = XPx( 1 + d/c) = XPx(c+d/c) X = (c/c+d) I / Px Y = (d/c+d) I / Py Example 2 U = x y c = 2 d= 1 Demand for X = (2/2+1) I / Px Y = ( 1/1+2) I / Py X = (2/3) I / Px Demand curve for X at I = 12 X = 2/3 (12) / Px X = 8 / Px Px = 8/x, now you can graph it Engel Curve for X at Px = 1 X = 2/3 I/ Px X = 2/3 I / 1 X = 2/3 I I = 3/2 X, now you can graph it. If I changes to 24. New demand curve X = 2/3 24 / Px = 16/Px. The demand curve shifts up. Perfect Compliments U = min{ax, by} Optimality condition: ax = by Y = a/b x X Budget Constraint I = PxX + PyY I = PxX + Py(a/b x X) I = X(Px + a
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