Microennomics Expert
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micro3.pptx0
Individual Demand
The material for the next two lectures very abstract, but it is important to learn how consumers make purchasing decisions in some detail.
- Gain a deeper understanding of what lies behind demand curves.
- The utility maximizing model is crucial in understanding the remainder of Micro.
1
Individual Demand (Illustration)
Effect of Price Changes
Reduction in the price of food
(income & the price of C fixed)
=> Consumers choose different market baskets.
(a) The baskets that maximize utility for various prices of food (point A, $2; B, $1; D, $0.50) trace out the price-consumption curve.
(b) The demand curve - relates the price of food to the quantity demanded.
(Points E, G, and H correspond to points A, B, and D, respectively).
2
Individual Demand
Notes about this demand curve:
a) It slopes down. We got a downward sloping demand curve because of the way we drew the consumer’s preferences. Elaborate more later.
b) As we move along the demand curve, the level of utility changes.
- Utility rises as P fall.
- Consumer is happier if his purchasing power increases.
c) At each point on the demand curve:
MRS = PF/PC (utility maximization condition).
=> As PF falls while PC is held constant, MRS must be falling.
- As the consumer acquires more food, the amount of clothing he is willing to give up to get more food is decreasing.
3
Individual Demand (Numerical Example)
An individual consumes two goods, X and Y with a utility function given by the expression:
U(X,Y) = X0.5 Y0.5
Denote the price of X and Y by PX and PY respectively and the individual income by I.
Find the Individual demand curves for X and Y.
4
Individual Demand (Numerical Example)
Do as before but instead of actual prices and income, substitute for by notations:
5
Individual Demand (Numerical Example)
Additional Step:
6
Individual Demand (Illustration)
Income Changes
If income increases (prices fixed):
Budget line shifts outside
=> consumers alter their choice of market baskets.
(a) The baskets that maximize consumer satisfaction for various incomes (point A, $10; B, $20; D, $30)
(b) => Demand curves shift outside (Points E, G, and H correspond to points A, B, and D, respectively.)
7
Individual Demand
Normal versus Inferior Goods
An Inferior Good
If income increases
=> Less consumption of one of the two goods.
Figure: Hamburger,
A normal good between A and B,
Inferior good between B and C.
8
Individual Demand
Engel Curves
Engel curves:
Quantity of a good consumed as a function of to income.
(a) Food is a normal good
- The Engel curve is upward sloping.
(b) Hamburger:
Normal good for income less than $20.
Inferior good for income greater than $20.
- The Engel curve is upward then downward sloping .
● Engel curve Curve relating the quantity of a good consumed to income.
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Individual Demand
Engel Curves for U.S. Consumers
Health care and entertainment are normal goods.
Rental housing is an inferior good for incomes above $35,000.
10
Individual Demand
Substitutes and Complements
From Lecture-2:
Two goods are substitutes: An increase in the price of one leads to an increase in the quantity demanded of the other.
Two goods are complements: An increase in the price of one good leads to a decrease in the quantity demanded of the other.
Two goods are independent: A change in the price of one good has no effect on the quantity demanded of the other.
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Income & Substitution Effects
The question of Interest:
- When the price of X changes, consumer changes the consumption due to two things, the relative price of X has changed, his purchasing power has changed.
Example: A fall in the price of a good has two effects:
Consumers will tend to buy more of the good that has become cheaper and less of those goods that are now relatively more expensive.
Because one of the goods is now cheaper, consumers enjoy an increase in real purchasing power.
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Income & Substitution Effects (Illustration)
Income and Substitution Effects: Normal Good
A decrease in the price of food has (income effect + substitution effect)
Initially at A, on budget line RS.
- Price of food falls,
=> consumption increases by F1F2.
The substitution effect F1E (A to D)
- Changes the relative prices of food and clothing but keeps real income (satisfaction) constant.
- The income effect EF2 (D to B) keeps relative prices constant but increases purchasing power.
=> Food is a normal good because the income effect EF2 is positive.
13
Income & Substitution Effects
Substitution effect (SE) Change in consumption of a good associated with a change in its price, with the level of utility held constant.
- For the most part we work with to goods that are substitute so the SE is negative.
Income effect (IE) Change in consumption of a good resulting from an increase in purchasing power, with relative prices held constant.
- Depends whether the good is normal or inferior.
- For normal good the IE is positive.
- For inferior good the IE is negative.
Total Effect (F1F2) = Substitution Effect (F1E) + Income Effect (EF2)
The total effect of a change in price is given theoretically by the sum of the substitution effect and the income effect:
14
Income & Substitution Effects
Income and Substitution Effects: Inferior Good
Initially at A on budget line RS.
Price of food declines:
=> moves to B.
=> Food demand:
- SE: F1E (from A to D),
- IE: EF2 (from D to B).
Food is an inferior good because the income effect is negative.
But SE > IE,
Decrease in the price of food
Increase in the quantity of food demanded.
15
Income & Substitution Effects
Upward-Sloping Demand Curve: The Giffen Good
If food is an inferior,
If IE> SE, the demand curve will be upward-sloping.
Initially at point A. Price of food falls, moves to B and consumes less food.
IE: (EF2) > SE (F1E),
The decrease in the price of food leads to a lower quantity of food demanded.
Giffen good Good whose demand curve slopes upward because the (negative) income effect is larger than the substitution effect.
16
Income & Substitution Effects Numerical Example
Back to the original example:
U(X,Y) = X0.5 Y0.5
a) Calculate the optimal basket when Px = 4 and Py = 1, and income is $120.
b) Calculate the income and substitution effects of a decrease in the price of food to $10.
17
Income & Substitution Effects (Numerical)
The initial bundle is:
If the Price changes to 10 the demand for X will be:
Therefore the total effect of the rise in the price is the reduction in the demand from 15 to 6.
18
Income & Substitution Effects (Numerical)
The SE is the movement along the same indifference curve but with the new prices.
=> The SE should satisfy the new MRS = Px/Py and should yield the same utility (30):
Therefore the reduction in the demand from 15 to 9.487 is the SE whereas the rest is the IE:
TE = 15-6 = SE ( = 15-9.487) + IE( = 9.487-6)
19
Income and Substitution Effects Example
Effect of a Gasoline Tax with a Rebate
A gasoline tax is imposed when the consumer is initially buying 1200 gallons of gasoline (Point C).
Budget line shifts from AB to AD
Preferences maximized at E
Consumption of 900 gallons.
However, when the proceeds of the tax are rebated to the consumer, his consumption increases somewhat, to 913.5 gallons at H.
=> Despite the rebate program, the consumer’s gasoline consumption has fallen, as has his level of satisfaction.
20
Tutorial Question
Quasi-linear Utility Function. A consumer has the following utility function: U(x, y) = y + x1/2. Let px and py be the corresponding prices and I her income.
a) Write down the corresponding Lagrangian function and find the first order conditions (FOCs).
b) Use these FOCs to find the expression for the marginal rate of substitution (MRS) and graph it.
c) Find the demand functions for x and y.
d) Let px = py = 1 and I = 1/9. find the optimal consumption levels for x and y?
e) How does your answer to the previous part change if I = 1 and still px = py = 1 ?
f) For px = py = 1 , draw the income consumption curve and the Engel curve for good x.
g) Is x a normal or an inferior good? In terms of share of income spent on x, what happens to it as I increases?
h) Is y a normal or an inferior good? Justify your answer?
i) If px rises to 2, what find the substitution and the Income effects on x.
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