# me_4 - Chapter 5 INCOME AND SUBSTITUTION EFFECTS 1...

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1 Chapter 5 INCOME AND SUBSTITUTION EFFECTS

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2 Objectives How will changes in prices and income influence influence consumer’s optimal choices? We will look at partial derivatives
3 Demand Functions (review) We have already seen how to obtain consumer’s optimal choice Consumer’s optimal choice was computed Max consumer’s utility subject to the budget constraint After solving this problem, we obtained that optimal choices depend on prices of all goods and income. We usually call the formula for the optimal choice: the demand function For example, in the case of the Complements utility function , we obtained that the demand function (optimal choice) is: y x p p x 25 . 0 * + = I y x p p y + = 4 * I

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4 Demand Functions If we work with a generic utility function (we do not know its mathematical formula), then we express the demand function as: x * = x ( p x , p y , I ) y * = y ( p x , p y , I ) We will keep assuming that prices and income is exogenous, that is: the individual has no control over these parameters
5 Simple property of demand functions If we were to double all prices and income, the optimal quantities demanded will not change Notice that the budget constraint does not change (the slope does not change, the crossing with the axis do not change either) x i * = d i ( p x , p y , I ) = d i (2 p x ,2 p y ,2 I )

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6 Changes in Income • Since p x / p y does not change, the MRS will stay constant An increase in income will cause the budget constraint out in a parallel fashion (MRS stays constant)
7 What is a Normal Good? A good x i for which x i / I 0 over some range of income is a normal good in that range

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8 Normal goods If both x and y increase as income rises, x and y are normal goods Quantity of x Quantity of y C U 3 B U 2 A U 1 As income rises, the individual chooses to consume more x and y
9 What is an inferior Good? • A good x i for which x i / I < 0 over some range of income is an inferior good in that range

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10 Inferior good If x decreases as income rises, x is an inferior good Quantity of x Quantity of y C U 3 As income rises, the individual chooses to consume less x and more y B U 2 A U 1
11 Changes in a Good’s Price A change in the price of a good alters the slope of the budget constraint (p x /p y ) Consequently, it changes the MRS at the consumer’s utility-maximizing choices When a price changes, we can decompose consumer’s reaction in two effects: substitution effect income effect

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12 Substitution and Income effects Even if the individual remained on the same indifference curve when the price changes, his optimal choice will change because the MRS must equal the new price ratio the substitution effect The price change alters the individual’s real income and therefore he must move to a new indifference curve the income effect
13 Sign of substitution effect (SE) SE is always negative , that is, if price increases, the

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