Two major points to discuss today: 1. Equilibrium v. identity 2. Solving the index number problem

1. Two major points to discuss today:1. Equilibrium v. identity2. Solving the index number problem

2. I. The Basic Classical Model • Aggregate supply: • Endogenous variables: W, P, Y. This defines the AS curve in figure 1. • However, we are one variable short for total equilibrium. • Note on AS: It is vertical because have perfectly flexible wages and prices. AS curve

3. Aggregate demand The standard way of closing the classical model is through deriving an aggregate demand curve. The simplest approach is to rely upon the quantity theory of prices and money. This holds that money supply is exogenous and money demand is proportional to money output:  (3) M = Ms (supply of money exogenous) (4) Md= kPY (demand for money) which gives the AD function: • Y = Ms /kP Note: The quantity theory is not essential here. We need aggregate demand as a function of fiscal, monetary, and other variables. (5) is just a simple and convenient example.

4. This is the classical AS-AD relationship. Notes: 1. Output is always at potential output. 2. No effect of M (or more generally AD) on output; AD only affects prices (“Money is neutral.”)

5. II. Supply and Demand for Loanable Funds Mankiw (chap 3) shows an alternative derivation of the classical model using the loanable funds. This approach examines the sources and uses of saving and investment. Do for simplest system: Basics: (1) Y = C + I (expenditure identity) (2) S = Y - C (definition of private saving) (3) I = I(r) (investment equation) These imply :  (4) S= I(r)  In this alternative approach, make sure you understand the difference between the savings-investment identity and the savings-investment equilibrium.

6. III. Equilibrium of saving and investment S(r) r Note: For now, assume that saving is interest-inelastic You should understand the effect of: • Shift in investment curve. • Increase in planned S. B r* I(r)

7. IV. Example of disequilibrium for S and I S(r) r In savings example, assume we have a “corn economy.” Corn can either be eaten or planted. People eat a certain amount of corn (C), and that leaves the rest (S) available for farmers to plant (I). If there is excess demand for I = AC, then the rate must rise to equilibrate S and I. This means that planned I at the original interest rate (r0) was excessive. Note that equilibrating mechanism will differ in different markets – Keynesian mechanism is quantity rather than price. B r* C r0 A I(r)

8. Let’s go back and ask:“Just what is this ‘Y’?”“Just how do we measure GDP and real GDP?”

9. How to measure output growth? • Now take the following numerical example. • Suppose good 1 is computers and good 2 is shoes. • How would we measure total output and prices?

10. The growth picture for index numbers:the real numbers! Source: Bureau of Economics Analysis

11. Some answers • We want to construct a measure of real output, Q = f(q1,…, qn ;p1,…, pn) • How do we aggregate the qi to get total real, GDP(Q)? • Old fashioned fixed weights: Calculate output using the prices of a given year, and then add up different sectors. • New fangled chain weights: Use new “superlative” techniques

12. Old fashioned price and output indexes Laspeyres (1871): weights with prices of base year Lt = ∑ wi,base year (Δq/q)i,t Paasche (1874): use current (latest) prices as weights Πt = ∑ wi,t (Δq/q)i,t

13. Start with Laspeyres and Paasche HUGE difference! What to do?

14. Solution Brilliant idea: Ask how utility of output differs across different bundles. Let U(q1, q2) be the utility function. Assume have {qt} = {qt1, qt2}. Then growth is: g({qt}/{qt-1}) = U(qt)/U(qt-1). For example, assume “Cobb-Douglas” utility function, Q = U = (q1)λ (q2)1- λ Also, define the (logarithmic) growth rate of xt as g(xt) = ln(xt/xt-1). Then Qt / Qt-1 =[(qt1)λ (qt2)1- λ]/[(qt-11)λ (qt-12)1- λ] g(Qt) = ln(Qt/Qt-1) = λ ln(qt1/qt-11) + (1-λ) ln(qt2/qt-12) g(Qt) = λg(qt1) + (1-λ) g(qt2) The class of 2nd order approximations is called “superlative.” This is a superlative index called the Törnqvist index. 14

15. What do we find?1. L > Util > P [that is, Laspeyres overstates growth and Paasche understates relative to true.

16. Currently used “superlative” indexes Fisher* Ideal (1922): geometric mean of L and P: Ft = (Lt × Πt )½ Törnqvist (1936): average geometric growth rate: (ΔQ/Q)t = ∑ si,T (Δq/q)i,t, where si,T =average nominal share of industry in 2 periods (*Irving Fisher (YC 1888), America’s greatest macroeconomist)

17. Now we construct new indexes as above: Fisher and Törnqvist Superlatives (here Fisher and Törnqvist) are exactly correct. Usually very close to true.

18. Current approaches • Most national accounts used Laspeyres until recently • Why Laspeyres? Primarily because the data requirements are less stringent. • CPI uses Laspeyres index. • US moved to Fisher for national accounts in 1995 • BLS has constructed “chained CPI” using Törnqvist since 2002 • China still uses Laspeyres in its GDP. • Who knows whether Chinese data are accurate???

19. Who cares about GDP and CPI measurement?Some examples where makes a big difference • social security for grandma • taxes for you • estimated rate of productivity growth for budget • and, therefore, Congress’s spending inclinations • comparisons of military “power” • overestimates of Soviet GDP in 1980s led Reagan administration to large increase in military budget • projections of emissions in global warming models