Theory of Demand. ECON 212 Lecture 7. Tianyi Wang. Winter Queen s Univerisity. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
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1 Theory of Demand ECON 212 Lecture 7 Tianyi Wang Queen s Univerisity Winter 2013 Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
2 Intro Note: Quiz 1 can be picked up at Distribution Center. Second Quiz covers: Preferences, Budget and Optimal Choices. Core of theory of demand: how does demand change in different enviroments. Can have many directions. We will look at: effect of changes in price, and effect of changes in income. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
3 Effect of Changes in Price What happens to optimal choices when price changes. Derive demand function from consumer s optimal choices. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
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11 Demand Function Note, demand curve derived from definition: letting Px changes while holding others constant. See class notes for examples. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
12 Demand Function (Cont d) Demand curve is also a "willingness to pay curve" MRS says willness to substitute. MRS = Py Px, or willing to sacrifice Px Py unites of y. To translate into value, Py Px Py = Px. Willing to pay Px for additional unit of x. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
13 Effect of Changes in Income Income Consumption Curve (ICC): traces out optimal bundles on X-Y space as income changes. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
14 Effect of Changes in Income Income Consumption Curve (ICC): traces out optimal bundles on X-Y space as income changes. Engel curve (EC): depicts optimal choices on I-X space. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
15 Effect of Changes in Income Income Consumption Curve (ICC): traces out optimal bundles on X-Y space as income changes. Engel curve (EC): depicts optimal choices on I-X space. Normal good V.S. Inferior good. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
16 Effect of Changes in Income Income Consumption Curve (ICC): traces out optimal bundles on X-Y space as income changes. Engel curve (EC): depicts optimal choices on I-X space. Normal good V.S. Inferior good. Normal: positive slope for both ICC and EC Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
17 Effect of Changes in Income Income Consumption Curve (ICC): traces out optimal bundles on X-Y space as income changes. Engel curve (EC): depicts optimal choices on I-X space. Normal good V.S. Inferior good. Normal: positive slope for both ICC and EC Inferior: negative slope for both ICC and EC Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
18 Effect of Changes in Income Income Consumption Curve (ICC): traces out optimal bundles on X-Y space as income changes. Engel curve (EC): depicts optimal choices on I-X space. Normal good V.S. Inferior good. Normal: positive slope for both ICC and EC Inferior: negative slope for both ICC and EC With Quasilinear utility function, both are vertical line. (Math and intuition?) Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
19 Market Demand Horizontal summation of individual demand. See class notes for examples. Usually assume identical individuals. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
20 Income and Substitution Effect Does price increase always decreases demand (Giffen good)? Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
21 Income and Substitution Effect Does price increase always decreases demand (Giffen good)? Decrease (increase) in price can have ambiguous effect. relatively cheaper, buy more. richer, buy less (inferior good). Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
22 Income and Substitution Effect Does price increase always decreases demand (Giffen good)? Decrease (increase) in price can have ambiguous effect. relatively cheaper, buy more. richer, buy less (inferior good). These ambiguities include: the effect of wage rates on labor supply. the effect of interest rates on savings. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
23 Income and Substitution Effect Does price increase always decreases demand (Giffen good)? Decrease (increase) in price can have ambiguous effect. relatively cheaper, buy more. richer, buy less (inferior good). These ambiguities include: the effect of wage rates on labor supply. the effect of interest rates on savings. Price changes involve two seperate effects: Substitution effect: good 1 becomes cheaper, more attractive than good 2 (opp. cost changes) Income effect: b/c good 1 is cheaper, can buy more of it with a given amount of income. Purchasing power increased. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
24 Substitution Effect How to seperate? Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
25 Substitution Effect How to seperate? 1 keep relative price changes, take away (grant) money to keep sth. fixed. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
26 Substitution Effect How to seperate? 1 keep relative price changes, take away (grant) money to keep sth. fixed. 2 reimburse and hold the relative prices. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
27 Substitution Effect How to seperate? 1 keep relative price changes, take away (grant) money to keep sth. fixed. 2 reimburse and hold the relative prices. Hicks Decomposition: fix (initial) utility level. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
28 Substitution Effect How to seperate? 1 keep relative price changes, take away (grant) money to keep sth. fixed. 2 reimburse and hold the relative prices. Hicks Decomposition: fix (initial) utility level. Slutsky Decomposition: fix purchasing power (not income). Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
29 Substitution Effect How to seperate? 1 keep relative price changes, take away (grant) money to keep sth. fixed. 2 reimburse and hold the relative prices. Hicks Decomposition: fix (initial) utility level. Slutsky Decomposition: fix purchasing power (not income). We will use Hicks below (clean intuition). how much consumer would require in payment to accept a change. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
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35 Point A is original optimizing bundle. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
36 Point A is original optimizing bundle. Decrease in price of X rotate budget line outward, and new optimal bundle is C. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
37 Point A is original optimizing bundle. Decrease in price of X rotate budget line outward, and new optimal bundle is C. Point B is the optimal bundle, that if we reduce the income just enough so that the consumer could just obtain the original utility level, at different relative prices. this is the sub. effect. Note the hypothetic budget at B is smaller than that at A (why?). We seperate sub. effect out by taking away implicit income changes. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
38 Point A is original optimizing bundle. Decrease in price of X rotate budget line outward, and new optimal bundle is C. Point B is the optimal bundle, that if we reduce the income just enough so that the consumer could just obtain the original utility level, at different relative prices. this is the sub. effect. Note the hypothetic budget at B is smaller than that at A (why?). We seperate sub. effect out by taking away implicit income changes. Point C is the optimal bundle, that if we hold the new relative prices and add back the income that we took away. this is the inc. effect. shift the hypothetic BC back to get implied changes in consumption. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
39 Point A is original optimizing bundle. Decrease in price of X rotate budget line outward, and new optimal bundle is C. Point B is the optimal bundle, that if we reduce the income just enough so that the consumer could just obtain the original utility level, at different relative prices. this is the sub. effect. Note the hypothetic budget at B is smaller than that at A (why?). We seperate sub. effect out by taking away implicit income changes. Point C is the optimal bundle, that if we hold the new relative prices and add back the income that we took away. this is the inc. effect. shift the hypothetic BC back to get implied changes in consumption. See class note for examples. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
40 Hicks substitution effect also know as Compensated Demand Curve. consumers are compensated just enough to obtain the original utiliy. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
41 Hicks substitution effect also know as Compensated Demand Curve. consumers are compensated just enough to obtain the original utiliy. Note sign of substitution effect must be negative Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
42 Hicks substitution effect also know as Compensated Demand Curve. consumers are compensated just enough to obtain the original utiliy. Note sign of substitution effect must be negative Sign of income effect can be positive or negative (normal v.s. inferior) Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
43 Hicks substitution effect also know as Compensated Demand Curve. consumers are compensated just enough to obtain the original utiliy. Note sign of substitution effect must be negative Sign of income effect can be positive or negative (normal v.s. inferior) Therefore Giffen good must be inferior good. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
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45 Slustsky defines substitution effect by keeping purchasing power constant. both original BC and hypothetical BC go through A. Note incomes are different. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
46 Application: Consumption and Leisure Choice In practice, instead of taking income as given, consumer earn it by supplying labour. Assume: Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
47 Application: Consumption and Leisure Choice In practice, instead of taking income as given, consumer earn it by supplying labour. Assume: Consumer s endowment of time T = 24 hours, Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
48 Application: Consumption and Leisure Choice In practice, instead of taking income as given, consumer earn it by supplying labour. Assume: Consumer s endowment of time T = 24 hours, Time can be used in labour (L) and leisure (R). Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
49 Application: Consumption and Leisure Choice In practice, instead of taking income as given, consumer earn it by supplying labour. Assume: Consumer s endowment of time T = 24 hours, Time can be used in labour (L) and leisure (R). earn wage (w) on each working hour. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
50 Application: Consumption and Leisure Choice In practice, instead of taking income as given, consumer earn it by supplying labour. Assume: Consumer s endowment of time T = 24 hours, Time can be used in labour (L) and leisure (R). earn wage (w) on each working hour. Consumer values consumption (C) and leisure (R), max U(C, R). Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
51 Application: Consumption and Leisure Choice In practice, instead of taking income as given, consumer earn it by supplying labour. Assume: Consumer s endowment of time T = 24 hours, Time can be used in labour (L) and leisure (R). earn wage (w) on each working hour. Consumer values consumption (C) and leisure (R), max U(C, R). Need to use wages to buy consumption good, Price = 1. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
52 Application: Consumption and Leisure Choice In practice, instead of taking income as given, consumer earn it by supplying labour. Assume: Consumer s endowment of time T = 24 hours, Time can be used in labour (L) and leisure (R). earn wage (w) on each working hour. Consumer values consumption (C) and leisure (R), max U(C, R). Need to use wages to buy consumption good, Price = 1. Formulate consumer s problem, see class notes for example. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
53 Backward bending labour supply We can find demand for leisure from optimal choices, by varying wage rate (see graph below). Since: supply of labour + demand for leisure = 24 hours. L = T R. (See graph below). Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
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63 Substitution effect makes an hour of leisure more expensive. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
64 Substitution effect makes an hour of leisure more expensive. Income effect increases your overall endowment. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
65 Substitution effect makes an hour of leisure more expensive. Income effect increases your overall endowment. Sub. effect if negative. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
66 Substitution effect makes an hour of leisure more expensive. Income effect increases your overall endowment. Sub. effect if negative. If leisure is normal good, consume more when income raises. Income effect is positive. Inc. effect counteracts sub. effect. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
67 Substitution effect makes an hour of leisure more expensive. Income effect increases your overall endowment. Sub. effect if negative. If leisure is normal good, consume more when income raises. Income effect is positive. Inc. effect counteracts sub. effect. Labour supply curve bends baceward. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
68 Compensating Variation and Equivalent Variation Two ways to measure consumer welfare. Price changes result in welfare change. Rather than describe welfare in utility terms, we would like to describe it in terms of dollars. Suppose price of X increases, (utility level drops): Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
69 Compensating Variation and Equivalent Variation Two ways to measure consumer welfare. Price changes result in welfare change. Rather than describe welfare in utility terms, we would like to describe it in terms of dollars. Suppose price of X increases, (utility level drops): 1 Ask how much money to compensate a consumer, at the new price, such that she obtains her initial utility level. This is Compensating Variation. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
70 Compensating Variation and Equivalent Variation Two ways to measure consumer welfare. Price changes result in welfare change. Rather than describe welfare in utility terms, we would like to describe it in terms of dollars. Suppose price of X increases, (utility level drops): 1 Ask how much money to compensate a consumer, at the new price, such that she obtains her initial utility level. This is Compensating Variation. 2 Ask how much money to take away from a consumer, at the initial price, such that the effect is equivalent to the price change. This is Equivalent Variation. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
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78 Note: these are pure income effects. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
79 Note: these are pure income effects. Note: Change in consumer surplus includes both inc. effect and sub. effect. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
80 Note: these are pure income effects. Note: Change in consumer surplus includes both inc. effect and sub. effect. Which measure is higher depends on income elasticity. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
81 Note: these are pure income effects. Note: Change in consumer surplus includes both inc. effect and sub. effect. Which measure is higher depends on income elasticity. However as the budget share of most goods are small, they are virtually identical. Tianyi Wang (Queen s Univerisity) Lecture 7 Winter / 46
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