Module 3 The Keynesian Model

1. Module 3 The Keynesian Model

2. Contents Background on the Model Real Vs. Nominal The Product Market & IS Equation Graphing the IS Curve from the IS Equation The Money Market & LM Equation Graphing the LM Curve from the LM Equation AD (IS-LM)/AS Workshop: A Place to Put the Model in Motion

3. Background on the Model ‘Keynesian’ means different things to different people. It’s useful to think of the basic textbook Keynesian model as an elaboration and extention of the Classical macro model. Its variable velocity of money and ‘sticky’ prices reflects Keynes’ belief that the Classical model’s shortcomings arose from its overly-strict assumptions of constant velocity and highly flexible wages and prices. Our 10 equation model of aggregate demand (AD) can be split into two parts: The IS model of the ‘product market’ (equations 1-6) and the LM model of the ‘money market’ (equations 7-10).

4. Real vs. Nominal Total spending on final goods and services at current prices is called nominal or money GDP and is denoted by y. It can change over time either because there is a change in the amount (real value) of goods and services (denoted Dy) or a change in the prices of those goods and services (denoted DP). Hence, Y= nominal GDP = P • y y = real GDP = Y/P This distinction between real and nominal can also be applied to other monetary values, like wages. Nominal (money) wages can be denoted by W and decomposed into a real value (w) and a price variable (P). Hence, W = nominal wage = P • w w = real wage = W/P This conversion from nominal to real units allows us to eliminate the problems created by having a measuring stick (dollar value) that essentially changes length over time, as the price level changes.

5. The Product Market & IS Equation To derive IS (which stands for Investment Savings) we use 6 equations defined in “real terms.” 1) y = c + i + x + g Equilibrium Condition 2) c = c0 + c1(y-t) Consumption Function 3) t = t0 + t1y Tax Function 4) i = i0 - i2r Net Real Investment Function 5) x = x0 - x1y - x2r Net Export Demand Function 6) g = g0 Government Demand (assumed to be preset at level g0.) The next few slides will break down each equation…

6. Government purchases of goods and services Total demand for domestic output Investment spending by businesses and households is composed of Net exports or net foreign demand Consumption spending by households Aggregate Demand Remember that these are all measured in real terms, i.e adjusted for inflation. y = c + i + x + g

7. consumption spending by households After-tax income Marginal propensity to consume depends on Autonomous consumption The Consumption Function c = c0 + c1(y-t)

8. The Marginal Propensity to Consume To understand the Marginal Propensity to Consume (MPC) consider a shopping scenario. A person who loves to shop probably has a large MPC, let’s say (.99). This means that for every extra dollar he or she earns after tax deductions, he or she spends $.99 of it. This coefficient c1 measure the sensitivity of the change in one variable (c) with respect to a change in the other variable (y-t). Hence, it is the first derivative of the consumption function with respect to a change in real after-tax income. c = c0 + c1(y-t)

9. Income tax rate is made up of Before tax income This year’s total tax revenues Level of non-income taxes (e.g. property taxes or sales tax) The Tax Function t = t0 + t1y If t1 is .2 or 20%, then an increase in income of $2000 will create $400 in additional tax revenue to the government and tax payments for us.

10. Investment Spending depends on Real interest rate Marginal propensity to invest Autonomous investment spending (can be positive or negative) Net Investment Spending i = i0 - i2r

11. Net Exports or net foreign demand Net exports’ sensitivity to real income depends on Net exports’ sensitivity to real interest rates Autonomous net exports Net Export Demand Function x = x0 - x1y - x2r Notice that x varies inversely with y & r, meaning that as y and r rise, the level of net exports fall.

12. Here is the rationale between r & x in x = x0 - x1y -x2r An increase in r reduces the demand for real money balances as households and firms substitute other assets for cash holdings. A higher real rate of interest in the U.S. (relative to other nations) attracts saving that would have gone to other other parts of the world. This saving comes in several forms (e.g. demand for stocks and bonds and other securities) but regardless of form, requires a a swap of foreign currency for $ in order to buy the U.S. securities. Therefore, an increase in the real interest rate, r via events in the foreign exchange market leads to a stronger dollar and thereby a reduction in net exports, x. In other words… r  D$ makes our goods more expensive to foreigners, and their goods cheaper for us  x

13. Government Demand g = g0 We take the level of government spending as given.

14. After combining all 6 equations of the ‘product market’ into 1, and solving for y in terms of r, we get the IS Equation! y = m(z0 + g0 - c1t0) - m(i2 + x2) r where z0 = c0 + i0 + x0 and m (the Multiplier) = 1/ 1-c1+c1t1+x1 Notice that the IS equation contains two unknown variables y and r. All the other terms (m,i2,x2,z0) are parameters which can be estimated statistically, or policy instruments (g0,t0,t1) which we take as given. The IS equation tells us the value of y for a given level of r, or conversely, tells us the value of r for a given level of y.

15. The Multiplier For our six equations, the expenditure multiplier is m = 1/ 1-c1+c1t1+x1. When y = m(z0 + g0 - c1t0) - m(i2 + x2) r Suppose spending increases by $1, you’d expect equilibrium output (y) to also rise by $1. $1 y = [m(z0 + g0 - c1t0) - m(i2 + x2) r] $1 But it doesn’t! The multiplier shows that the change in demand for output (y) will be larger than the initial change in spending. Here’s why: An increase in spending will increase income. This increase in income will increase spending some more. The increase in spending will increase income again. This increase in income will increase spending etc… So, the multiplier process helps explain fluctuations in the demand for output. For example if something in the economy decreases investment spending (found in z0 = c0 + i0 + x0) people whose incomes have decreased will spend less, thereby driving equilibrium demand down even further.

16. Graphing the IS Curve from the IS Equation r IS -Dy = -m(i2+x2)Dr +Dr When r = 0, we attain the value of the horizontal intercept m(z0 + g0 - c1t0) y y = m(z0 + g0 - c1t0) - m(i2 + x2) r The inverse relationship between r and y is built into the downward slope of the IS curve. As we move up and along the IS curve, y decreases while r increases. because the - m(i2+x2) r drops out. Also, note that when r increases, y decreases by the amount Dy=-m(i2+x2)Dr. Later, you can visit the AD (IS-LM)/ AS Workshop to practice shifting IS. Throughout the course, we will only alter terms found in the intercept (e.g. z0), not the slope of the IS curve (e.g.x2,i2)

17. The Money Market & LM Equation Now that we’ve derived the IS part of AD, it’s now time to complete the model of AD by adding a money market equilibrium schedule, the LM curve. We will use the following 4 equations to derive our LM equation, and curve. L/P = M/P Equilibrium L/P = j0 + j1y - j2r Money Demand M = M0 Money Supply P = P0 Fixed Price Level The next few slides will explain each equation.

18. Money Demand in real terms Money Supply in real terms equals Money Market Equilibrium L/P = M/P The next few slides will define the specifics of the money market equilibrium.

19. Real money demand The sensitivity of real money demand to the real interest rate is made up of The sensitivity of real money demand to the level of income Autonomous money demand Money Demand L/P = j0 + j1y- j2r The positive sign is an indicator that as income rises, real money demand also increases. The negative sign is an indicator that as r rises, real money demand will decrease. Remember that r is the opportunity cost of holding money…as r rises that means it’s more expensive.

20. Money Supply M = M0 We take the money supply as given at the level of M0.

21. Fixed Price Level P = P0 We assume that the price level is constant at the level P0.

22. After combine all 4 equations of the money market in to 1, and solve for y in terms of r, we get the LM Equation. Notice that LM contains two unknown variables, y and r. All the other terms in the equation are parameters (j0,j1,j2) that are estimated statistically or policy instruments (M0), except for the price level (P0) which is held constant. Like the IS equation, the LM equation tells us the value of y for a given level of r, and conversely, tells us the value of r for a given level of y.

23. Graphing the LM Curve from the LM Equation r LM(P0) +Dr +Dy y The LM Equation is a linear positive relationship between AD (y) and real interest rate (r). It shows all combinations of y and r such that money demand (L/P) equals money supply (M/P). Here is the rationale. Start with our money market equilibrium condition where money demand equals money supply. j0+j1 y-j2 r = M/P Now increase income (y) in the equation and the curve. As a result, money demand exceeds money supply (L/P > M/P). Like in any market, when demand exceeds supply, the price rises to clear the market. The “price” is this case is r, the opportunity cost of holding money. As the interest rate rises, people reduce their money holdings (according to the -j2 parameter) until money demand and money supply are equal.

24. r LM(P0) +Dr +Dy=+j2/j1Dr y The positive relationship between r and y is built into the upward slope of the LM curve. As we move up and along the LM curve, we see that y and r both increase. When r increases, money demand will decrease as given by L/P= j0+j1y-j2r. Here L/P < M/P, so y will rise by the amount Dy=j2/j1Dr to equalize money demand with money supply (L/P=M/P). When r is zero, the second term on the right-hand side of the equation drops off, leaving the horizontal intercept to be Now let’s put IS and LM together in order to complete our model of aggregate demand.

25. IS r LM(P0) r0 y y0 The IS-LM Model of AD All the elements of our 10 equation model compiled in our IS & LM curves/solutions determine the level of aggregate demand in our economy.

26. LM(2P0) B B From IS-LM to AD You probably noticed from the IS and LM diagrams that r and y were on the two axes. Now we’re going to bring a third variable, the price level (P) into the analysis. We can accomplish this by linking both two-dimensional graphs. IS-LM Curves (in y & r) AD Curve (in y & P) IS r To derive AD, start at point A in the top graph. Now increase the price level from P0 to 2P0. This shows up in our LM equation as a  P. LM(P0) A This lowers the real value of the money supply, and y, shifting LM leftward to point B. y P Notice that r increased. From equations 4 & 5 (i= i0 - i2 r) (x = x0 - x1y - x2r) we know that both investment and net export spending will both decrease setting off a multiplier process since - Di and -Dx, cause a -Dy. The - Dy triggers -Dc as we move up the IS curve. A AD The +DP triggers a sequence of events that end with a -Dy, the inverse relationship that defines the downward slope of AD. y

27. Adding Aggregate Supply Now that we have a theory of AD, we must incorporate scarcity which can be done by adding a model of Aggregate Supply. Recall from the Classical Model the vertical AS* which assumed that changes in the price level left no lasting impact on y (because of the market clearing process). We’ll take this model and use it for consideration of the long-term. Here we’ll call it ASLR. But we need a theory for the short-run, defined as the interval of time during which markets are not fully cleared. ASLR P A simple, but useful first approach is to assume short-run price rigidity. As AD shifts to AD we slide in an east-west direction to point B on ASSR. Then, in the LR, we move from B to C (move up and along AD). C B P0 ASSR A AD AD y* y y* = f (n,k,inst)

28. AD(IS-LM)/AS Workshop A Place to Put the Model in Motion IS-LM

29. AD (IS-LM) /AS Mechanics 1) Most exam questions will revolve around the impact of either a Policy Change(g0, t0 or M0) or an Outside Event (c0, i0, x0 or j0or k, inst). 2) Read the question carefully to figure out which of these variables change, hence which of the underlying curves will shift. a) c0, i0, and x0 all shift IS & AD (via the z0 term). b) g0 and t0 also shift IS & AD (but in opposite directions). c) j0 shifts LM & AD (with +j0 shifting LM to the left). d) M0 also shifts LM & AD. e) k, inst shift AS* 3) Make the appropriate shifts in the diagram to either IS & AD, LM & AD, or AS*. 4) Now you can read the short and long run effects on y, r, and P directly from the diagram. 5) Once you determine how y, r, and P are affected, you can plug in those effects into equations 1-10 to determine how the rest of the economy is affected.

30. IS LM (P2) IS´ C B C P2 B LM AD´ Suppose there is a +Dx0. Look at the appropriate equation that captures the x0 term: Notice that z0 was increased, thus increasing the value of the horizontal intercept which translates into a rightward shift of the IS and AD curves. IS r LM(P0) In the short-run, we move along ASSR from point A to point B. A But as the output market clears, in the long-run, the price level will increase from P0 to P2. This +DP decreases the value of the LM equation’s horizontal intercept which translates into a leftward shift of the LM curve. y ASLR P ASSR P0 A AD y Finally, this leaves us at point C in both diagrams.

31. LM(P2) y +, because y moved from y* to y´ IS IS´ r LM(P0) C P 0, because prices are sticky in the SR. +, because a +Dy leads to a rise in r as IS slides along the LM curve. B r A c +, because a +Dy increases the level of consumption (c=c0+c1(y-t)). y ASLR i – , since r increased, the level of investment decreased (i=i0-i2r). P C P2 x ?, +Dr and +Dy both decrease the net exports function (?x=x0-x1y-x2r), but since our initial step was a +Dx, we can’t tell from this information which will dominate. B ASSR P0 A AD´ AD y y´ y * b –, since y rose, tax revenues rise and decrease the deficit (b= g-t). Now it’s time to determine the effects on the variables in the economy. For the variables y, P, and r, you can read the effects right off the diagrams. The other variables c, i, x, and b require you to plug in the effects of y and r to determine what happens. Remember that SR is the movement from A to B. Short-run Impacts

32. For the variables y, P and r, you can read the effects right off the diagrams. y 0, because rising P shifts LM to left, returning y to y* as required by long-run AS*. IS´ p +, in order to eliminate the excess demand at P0. C r +, reflecting the leftward shift in LM due to +DP B c 0, since both y and t are back to their initial levels (c=c0+c1(y-t)). i – – , since r has risen even more due to the +DP (i=i0-i2r). x +, we know that Dy=Dg=Dc=0 and net investment falls, therefore net exports must rise. (y=c+i+x+g). C P2 B AD´ b 0, because neither FP nor the tax base change (b= g0-t0-t1y). y y´ The other variables c, i,x, and b require you to plug in the effects of y and r to determine what happens. Remember that LR is the movement from A to C. Long-run Impacts LM(P2) IS r LM(P0) A y ASLR P ASSR P0 A AD y *

33. LM IS r LM(P0) A B y ASLR P P2 ASSR P0 B LM LM A AD´ AD y Suppose there is a +DM0. Look at the appropriate equation that captures the M0 term: Notice that M0 was increased, thus increasing the value of the horizontal intercept which translates into a rightward shift of the LM and AD curves. (P2) In the short-run, we move along ASSR from point A to point B. = C But as the output market clears, in the long-run, the price level will increase from P0 to P2. This +DP decreases the value of the LM equation’s horizontal intercept which translates into a leftward shift of the LM curve. C Finally, this leaves us at point C in both diagrams.

34. y +, because y moved from y* to y´ P 0, because prices are sticky in the SR. –, because a +Dy leads to a decrease in r as LM slides along the IS curve. r c +, because a +Dy increases the level of consumption (c=c0+c1(y-t)). i + , since r increased, the level of investment decreased (i=i0-i2r). x ?, since there is a -Dr and +Dy, the net exports function (?x=x0-x1y-x2r) yields an inconclusive result. b –, since y rose, tax revenues rise and decrease the deficit (b= g-t). Now it’s time to determine the effects on the variables in the economy. For the variables y, P, and r, you can read the effects right off the diagrams. The other variables c, i, x, and b require you to plug in the effects of y and r to determine what happens. Remember that SR is the movement from A to B. Short-run Impacts

35. For the variables y, P and r, you can read the effects right off the diagrams. y 0, because rising P shifts LM to left, returning y to y* as required by long-run AS*. p +, in order to eliminate the excess demand at P0. r 0, reflecting the leftward shift in LM due to +DP, restoring r to its original level. c 0, since both y and t are back to their initial levels (c=c0+c1(y-t)). i 0, since y or r has not changed. x 0, since y or r has not changed. b 0, because neither FP nor the tax base change (b= g0-t0-t1y). The other variables c, i,x, and b require you to plug in the effects of y and r to determine what happens. Remember that LR is the movement from A to C. Long-run Impacts Notice that the only LR impact of an increase in the money supply was an increase in the price level.

36. Then... IS AD LM AS 1) y= c + i + x + g 2) c= c0 + c1(y-t) 3) t= t0 + t1 y 4) i= i0 - i2 r 5) x = x0 - x1y -x2 r 6) g = g0 7) L/P=M/P 8) L/P=j0+j1y-j2r 9) M=M0 10SR) P=P0 10LR) y*=F(n*,k0,i0nst) If... What happens if there is a +Dc0 ? What is the impact on y,P,r,c,i,x,b? Note: b is net real borrowing by the government (the deficit) defined as b=g-t.

37. LM(P2) 1) +Dc0 causes the IS curve to shift right to IS' due to the z0 in the IS equation (increasing the value of the horizontal intercept). IS' LM(P0) IS C · · B A · P2 C · A B · · LM AD' r IS 2) This leads to a rightward shift in AD to AD’. Short Run: Move from A to B. y Long Run: Market clears at P0 to P2 from B to C. P ASLR 3) +DP causes LM(P0) to shift leftward to LM(P2) due to the lowering of the real value of the money supply (decreasing the value of the horizontal intercept.) P0 ASSR AD y IS-LM

38. Now, try to determine the short and long run impacts for yourself.

39. Short Run: Long Run: 0 + ++ + -- - 0 y + P 0 r + c + i - x - b -

40. What is the impact of a +Dg on the macroeconomy? It has three options for financing government spending: (+Dg= +Dt0) Taxes: coercion now (“theft” if we did it) (+Dg= +Db) Borrowing (bonds: coercion later) (+Dg= +DM0) Printing money (“counterfeiting” if we did it) “It depends” on 1) Initial position y=y* or y<y* 2) Short-run or Long-run 3) How the government finances its spending

41. Tax-Financed Increase in Government Spending (+Dg0=+Dt0) U.S. Tax $$ 1040

42. IS' LM(P2) IS'' LM(P0) m0+Dg0 E · · B m0-c1+Dt0 E · P2 A B · · AD'' Tax-Financed Increase in Government Spending (+Dg0=+Dt0) r IS Result: A small rightward shift in both IS (IS to IS'') and AD (AD to AD'') and a movement along ASSR to point B. A · Given our IS equation: y=m(z0+g0-c1t0)-m(i2+x2)r +Dg shifts IS to IS'. y But, +Dt shifts IS back to the left (to IS''). Note: the shift leftward from IS' to IS'' is less than the original rightward shift because the tax multiplier (-c1t0) is less than the expenditure multiplier (m). P ASLR As the market clears, the rising price level contracts LM and the economy moves to point E. ASSR P0 AD y

43. The bearer of the United States Treasury bond is hereby promised the repayment of the principle value plus the interest which it incurs through the terms stated thereof. The United States will justly repay its bearers in its entirety and will not default under any circumstances. Signature of the President ___________________ Bond-Financed Increase in Government Spending (+Dg0=+Db) US. Treasury Bond

44. LM(P2) IS' LM(P0) E · · B E · P2 A B · · AD'' Bond-Financed Increase in Government Spending (+Dg0=+Db) r IS A · Given our IS equation: y=m(z0+g0-c1t0)-m(i2+x2)r +Dg shifts IS to IS'. Note: +Db is not part of our 10 equation AD/AS model, and therefore it doesn’t impact AD (IS-LM) or AS. y P ASLR In the short run, the +Dg causes a rightward shift in both IS (IS to IS'') and AD (AD to AD'') and a movement along ASSR to point B. ASSR P0 As the market clears, the rising price level contracts LM and the economy moves to point E in the long run. AD y

45. Money-Financed Increase in Government Spending (+Dg0 =+DM0)

46. IS' LM(P2) Given our LM equation: LM(P0)' LM(P0) · P2 B C B A C E E · · · · · · AD'' AD'' Money-Financed Increase in Government Spending (+Dg0=+DM0) r IS A · The +DM0 causes a rightward shift in both LM (LM(P0) to LM(P0)') an AD (AD to AD''') and a movement along ASSR to point C. Given our IS equation: y=m(z0+g0-c1t0)-m(i2+x2)r +Dg shifts IS to IS'. P y ASLR The +Dg causes a rightward shift in both IS (IS to IS'') and AD (AD to AD'') and a movement along ASSR to point B. As the market clears, the rising price level contracts LM(P0)' to LM(P2) and the economy moves to point E in the long run. ASSR P0 AD y

47. Financing Gov't Spending LM LM IS LM LM LM LM LM IS r r r IS IS IS IS IS y y y AS* AS* AS* P P P P2 P2 P2 P0 ASSR ASSR ASSR AD AD AD AD AD AD AD y y y +Dg=+Dt +Dg=+Db +Dg=+DM SR:strongest impact on y with Dr indeterminately small (without additional info). LR: strongest impact on P; Dr same as for deficit-financing; Dy=0. SR: relatively small +Dy and +Dr; DP=0. LR: relatively small impact on P, r; Dy=0. SR:stronger impact on y and r; DP=0. LR:stronger impact on r,P; Dy=0.