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The Keynesian Cross Model, The Money Market, and IS/LM Planned expenditure and actual expenditure.

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Constructing the Keynesian Cross Actual expenditure is Y and planned expenditure is E = C + I + G. I, G, and T are assumed exogenous and fixed. Our consumption function is C = c(Y–T), where c is the marginal propensity to consume (mpc). Mapping out E = c(Y–T) + I + G gives us… Y E E=C+I+G Y=E £1£1 mpc Y* E* The slope of E is the mpc. In equilibrium planned expenditure equals total expenditure or Y=E.

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Constructing the Keynesian Cross Y E E=C+I+G Y=E Equilibrium is at the point where Y = C + I + G. mpc Y* E* Y2Y2 Y1Y1 Inventory accumulates. Inventory drops. £1£1 Because actual expenditure exceeds planned expenditure, inventory accumulates, stimulating a reduction in production. Similarly at Y 2, Y < E Because planned expenditure exceeds actual expenditure, inventory drops, stimulating an increase in production. If firms were producing at Y 1 then Y > E

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Government expenditure and tax multipliers An increase of G by ΔG causes an upward shift of planned expenditure by ΔG. Y E ΔGΔG Y=E Y1Y1 E1E1 E2E2 Notice that ΔY > ΔG. This is because although ΔG causes an initial change in Y of ΔG, the increased Y leads to an increase in consumption and triggers a multiplier effect. Now suppose a decrease of T by ΔT that causes an upward shift of planned expenditure by mpc*ΔT. Y2Y2 Notice again that ΔY > ΔT but that ΔY is less than in the case with ΔG. This is because ΔT causes no initial change in Y as ΔG did, the decrease in T simply leads to an increase in consumption and triggers the multiplier effect. Y3Y3 E3E3 mpc*ΔT

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Building the IS curve The IS curve maps the relationship between r and Y for the goods market. IS Y E Y2Y2 Y1Y1 r I I(r) ΔIΔI Y2Y2 Y1Y1 r2r2 r1r1 r2r2 r1r1 I(r 1 )I(r 2 ) E=Y E=C+I(r 1 )+G E=C+I(r 2 )+G Let the interest rate increase from r 1 to r 2 reduce planned investment from I(r 1 ) to I(r 2 ). This decrease in investment causes the planned expenditure function to shift down. So Y decreases from Y 1 to Y 2. Y r The IS curve maps out this relationship between the interest rate, r, and output (or income) Y.

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Shifting the IS curve While changing r allows us to map out the IS curve, changes in G, T, or mpc cause Y to change for any level of r. This causes a shift in the IS curve. IS Y E Y1Y1 Y2Y2 ΔGΔG Y1Y1 Y2Y2 r1r1 E=Y E=C+I+G 2 E=C+I+G 1 Suppose an increase in G causes planned expenditure to shift up by ΔG. Y r For any r the increase in G causes an increase in Y of ΔG times the government expenditure multiplier. Therefore, the IS curve shifts to the right by this amount. IS´

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A loanable funds market interpretation The IS curve maps the relationship between r and Y for the loanable funds market in equilibrium. IS r I I(r) Y2Y2 Y1Y1 r2r2 r1r1 r1r1 r2r2 S(Y 2 ) Y r S(Y 1 ) Suppose Y increases from Y 1 to Y 2. This raises savings from S(Y 1 ) to S(Y 2 ) resulting in a lower equilibrium interest rate. The IS curve maps out this relationship between the lower interest rate and increased income.

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A loanable funds market interpretation of fiscal policy While changing r allows us to map out the IS curve, changes in G, T, or mpc cause Y to change for any level of r. This causes a shift in the IS curve. IS r I I(r) Y1Y1 r2r2 r1r1 r1r1 S(G 1 ) Y r r2r2 S(G 2 ) IS´ Suppose again an increase in G. In the loanable funds market this results in a decrease in S and an increase in the interest rate. Therefore, for a given Y there is a higher level of r. So, the IS curve shifts up by this amount.

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Building the LM curve The LM curve maps the relationship between r and Y for the money market. LM r Real Money Balances L(r,Y 2 ) Y1Y1 r2r2 r1r1 r1r1 Given money supply and money demand suppose an increase in income raises money demand. Y r r2r2 (M/P) s L(r,Y 1 ) The LM curve maps out this relationship between r and Y. Y2Y2

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Shifting the LM curve While changing money demand allows us to map out the LM curve, changes in M or P cause r to change for any level of Y. This causes a shift in the LM curve. r Real Money Balances r2r2 r1r1 Given money supply and money demand suppose a decrease in the money stock shifts real money supply to the left resulting in a higher equilibrium interest rate. (M 1 /P) s L(r,Y) Now there is a higher real interest rate for the current level of output. (M 2 /P) s The LM curve shifts up so that at the same level of output the interest rate is higher. LM Y r2r2 r1r1 Y r LM´

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IS=LM: The Short Run Equilibrium Given our IS and LM equation we can now determine the short run equilibrium interest rate and output LM Y* r* Y r IS By mapping out the relationship between Y and r when the goods market (or loanable funds market) is in equilibrium we get the IS curve. By mapping out the relationship between Y and r when the money market is in equilibrium we get the LM curve. When we set IS=LM we can solve for the equilibrium levels of r and Y. This represents simultaneous equilibrium in the goods market (or loanable funds market) and the money market.

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Conclusion We constructed the IS curve from the goods market and from the loanable funds market. We discussed shifting factors for IS. We constructed the LM curve from the money market and discussed shifting factors for LM. Finally, we set IS=LM to achieve equilibrium in all markets giving us short run equilibrium r and Y.

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