Лекции_Микроэкономика

Reason: demand curve shows the relationship b/w price and quantity demanded holding other things fixed, including money income. But with fixed money income the value that an individual puts on an additional unit of a good may depend on the amount that he has already spent on previous units of the good. As a result price is not identical to consumer’s marginal valuation of the associated unit of output.

Other measures of consumer’s welfare

Compensating variation (CV) - the change in money income just necessary to offset the change in utility induced by the price change

CV is measured at the new prices

x2

II p2

CV / p2

I

p2

Equivalent variation (EV) - the change in money income that is equivalent in its effect on the individual’s utility to a change in the price of a commodity.

EV is measured at the initial prices

x2

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To measure CV we need a schedule that shows how the quantity demanded varies with price, assuming that as price changes the consumer’s money income is adjusted to keep him at initial level of utility. This is a compensated demand curve that reflects only Hicks SE.

Derivation of compensated demand curve.

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Compensated demand curve arises from the expenditure minimization problem

Note: compensated demand curve reflects only SE, while ordinary demand curve shows both SE and IE.

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A.Friedman ICEF-2012

Inverse compensated demand function also can be interpreted as marginal valuation: it gives marginal valuation for arbitrary preferences (not only quasi-linear one) as marginal valuation of each dollar is not affected by the price.

Thus Marshallian CS is only an approximation of the true CS measured as an area below the compensated demand curve.

Question. Why Marshallian CS is widely used?

x2

0 x1

If price of normal good goes up, then EV< CS <CV.

If price of normal good goes down, then EV> CS >CV.

For the case of neutral good EV= CS =CV as Marshallian and compensated demand curves coincide.

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1.11 Price indexes

Ideally changes in the cost of living would be measured by the change in money income that is necessary for the consumer to achieve the same level of utility in the given year as in the base year. (Index based on CV)

Then, if the consumer’s money income increases more (less) then this measure of the cost of living we can infer that he is better (worse) off.

As compensated demand is not observable this ideal measure of cost of living (ICLI) cannot be used.

Instead we use some approximations: Laspeyras price index (LPI) and Paashe price index (PPI).

LPI - the ratio of the sum of given year prices weighted by the base year quantities to the sum

Using base year quantities to weight the prices of goods in a different year, LPI does not allow for the fact that a consumer tends to substitute away from goods that become relatively expensive. It implies that an individual whose income is indexed in accordance with LPI can purchase base year bundle, i.e. he can never be worse off. Moreover he could be better off by substituting away from relatively expensive goods. Thus agent might be better off even if his income increases slightly less then LPI.

Conclusion: LPI overstates increases in the true cost of living.

x2

PPI - the ratio of the sum of given year prices weighted by the given year quantities to the

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PPI understates increases in the true cost of living.

PPI gives a minimum estimate of the increase in the TCL since it assumes (erroneously) that

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had the consumer received in the base year an amount of income equal to pi0 xit he would

i 1

choose given-year bundle. Instead the consumer would tend to buy relatively more of the commodities which in base year were cheaper than in given year. This implies that for an individual whose income is indexed in accordance with PPI current year bundle was affordable in the base year. Thus he is never better off. Moreover an agent could be worse off even if his income rises a bit more than PPI.

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What determines the magnitudes of the errors in the LPI and PPI?

The extent to which relative prices change,

The extent to which the consumer substitutes b/w the commodities when relative prices do change

Individual versus representative agents (average bundle) index

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2. INTERTEMPORAL CHOICE

2.1 Consumption choices over time.

Let us assume that there are two periods: current period ( t 0 ) and future period ( t 1). Individual gets income of Y0 in current period and Y1 in future period. This bundle

corresponds to his endowment point (the bundle of present and future consumption that can be consumed without market trade). Assume that individual can borrow and lend at the same market interest rate r .

agent wants to consume more than he earns, then he has to borrow c0 Y0 and in the future

he will repay the debt together with interest payments, thus his future consumption equals c1 Y1 c0 Y0 1 r Y1 Y0 c0 1 r . It means that irrespective of whether agent

borrows or lends, his budget constraint is

c1 Y1 Y0 c0 1 r .

If we open the brackets and put consumption in the LHS, then the budget constraint can be rewritten as

c0 1 r c1 Y0 1 r Y1 .

In the LHS we have the future value of the life-time consumption and in the RHSthe future value of the life-time income. By dividing both sides by 1 r the budget constraint can be stated in terms of present values

This budget constraint states that present value of lifetime consumption has to be equal to the present value of endowment.

Graphically this intertemporal budget constraint can be represented by a straight line that goes through endowment point and has a slope of 1 r .

c1

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Assume that agent derives utility from consumption in both periods, u c0 ,c1 . Let more

consumption in either period be preferred to less, so that utility increases as we move further from the origin. As usually we assume diminishing MRS. As a result we get the convex indifference curves.

The MRS between current and future consumption reveals the intensity of individual’s preferences for consumption in different periods of time. If we write down MRS01 1 , then is the rate of time preference.

A person is said to be impatient if when consumption levels are the same in both periods is positive, meaning that person is willing to forego more than $1 of future consumption to increase current consumption by $1. The value of at point with c0 c1 is called the rate of time preference proper.

A person is said to be patient if when consumption levels are the same in both periods is

negative, meaning that person is willing to forego less than $1 of future consumption to increase current consumption by $1.

Point of tangency of budget constraint with IC indicates the optimal consumption bundle. If c0 Y0 , then agent is called a net lender, if c0 Y0 , then agent is called a net borrower.

c1

1 r Y0 Y1

Net lender

c1

Y1

1 r

1 r Y1

Conclusion: if financial market are perfect (agents can lend and borrow at the same interest rate), then consumption decision is determined by the present value of life-time income, not the income in current or future period alone.

Comparative statics

In this model interest rate plays a role of price.

An increase in the interest rate brings two effects: substitution effect and wealth effect. Due to substitution effect current consumption falls as it becomes relatively more expensive. The sign of income effect depends on whether we deal with net lender or net borrower (as consumption stands for aggregate commodity it is treated as a normal good).

For net borrower an increase in the interest rate decreases wealth and results in a fall in current consumption. So for net borrower both effects move in the same direction and current consumption definitely falls.

An increase in the interest rate increases the wealth of net lender and under given prices results in an increase in current consumption. So for net lender current consumption falls and

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saving increases if substitution effect dominates and current consumption rises together with fall in saving when income effect dominates.

The same results we can get from the analysis of Slutsky equation. Income effect is proportional to the amount of saving, that is why it may become dominant if saving is large enough:

Conclusions. Individual demand for borrowing is downward sloping, so does the aggregate demand. Individual supply of lending could be backward bending (upward sloping under low saving).

Lending-borrowing equilibrium.

Note: below we assume that backward bending part of individual supply disappears due to aggregation curve

r

2.2 Production and consumption over time: saving and investment

Suppose that investment (productive) opportunities are available but consumer has no access to the financial market. Investment opportunities are described by the PPC.

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c1 ,Q1

Suppose that investment (productive) opportunities are available and in addition consumer can borrow and lend at the same market interest rate.

c1 ,Q1

c1

Q1

wealth is the intercept of budget line with the horizontal axes. The highest attainable budget line is tangent to the PPC. The corresponding highest level of wealth equals W0 . Then consumer chooses the best bundle under given level of wealth.

On aggregate lending=borrowing, which implies that aggregate saving equals aggregate investment.

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