9. Real business cycles in a two period economy

Transcription

1 9. Real business cycles in a two period economy Index: 9. Real business cycles in a two period economy Introduction The Representative Agent Two Period Production Economy The representative firm problem The household problem The government budget constraint Aggregate demand (AD) The aggregate demand curve Shifts in aggregate demand Aggregate supply (AS) Labour market equilibrium Partial equilibrium: Shifts in labour supply and demand The aggregate supply Shifts in aggregate supply The natural interest rate Adjustment to economic shocks What happens when future productivity increases? What happens when current productivity increases? What happens when government consumption increases temporarily? The Heterogeneous Agent Two Period Production Economy (HATPPE) 9 Further reading...9 Review questions and exercises...0 5/08/08,

2 9. Introduction In previous handouts, we addressed the cases of (a) a static economy with endogenous labour, and (b) a two period economy with endogenous savings. In this note, we put the two pieces together, to discuss a more general case in which agents face simultaneously the choice between consumption and leisure and the choice between consumption and savings. This setup is more realistic, but also more complex. Because of this, and to keep the model tractable, we make a set of simplifying assumptions. In particular, we consider a model without capital and where the utility function is additively separable. Even though, we are able to sketch out some key propositions of the business cycle model. This note is organized as follows. In Section, we present the main model and the implied optimality conditions. In Section 3 we describe the aggregate demand, as a relationship between spending and the real interest rate. In Section 4 we describe the aggregate supply, as a positive relation between output and the real interest rate. In Section 5 we solve for the closed economy equilibrium, to find out the endogenous interest rate. In Section 6 we use the model to analyse the impact of shifts in productivity and in government spending. In Section 7, we examine how the model conclusions change when we replace the assumption of a representative consumer by the assumption that a given fraction of households is constrained on borrowing. 9. The Representative Agent Two Period Production Economy Consider a two-period economy with a large number of equal firms and households. This economy may be labelled as the Representative Agent Two-Period Economy (RATPPE). In this economy, the government buys from firms the amount of output it desires, and finances these purchases with a lump-sum tax T on households. Each consumer is endowed with a given amount of time, h. Firms hire labour from households, paying a wage rate w, and produce a final good that can be used for private consumption or for government spending. The production function is linear in labour and there is no capital. 9.. The representative firm problem 5/08/08,

3 Production takes place using a Ricardian production function: Q z N t=, () t t t Where z is a productivity term, N is labour input, and t is a time suffix. Firms hire working time from households at the wage rate w and sell output (numeraire). The representative firm profits in period t are: Q w N. () t t t t Firms take the wage rate as given and choose N so as maximize profits, (). This leads to the following demands for labour in period and in period : w z (3) w z (4) These conditions, together with () imply that profits are zero: 0 (5) 9.. The household problem Households are endowed with h units of time. Time can be split into working hours, N, and leisure, l: h N t l t (6) The preferences of the representative consumer are assumed additively separable : U lnc (7) lnc lnl lnl This is the simplest possible formulation of the utility function to make the point. It is assumed that all goods are weighted equally in the utility function. In Exercise 3, you will workout a slightly more general case. 5/08/08, 3

4 Where c t denotes for private consumption in moment t, and l t for leisure in moment t. Households maximize their life-time utility function subject to an inter-temporal budget constraint of the form: C wl hw T C wl hw T (8) r r The right hand side of (8) is the representative agent life-time wealth: hw T hw T (9) r The first order conditions of the household maximization problem imply: C (0) l w C () l w C r () C l w w r. (3) The first two equations state that the marginal rate of substitution between consumption and leisure each period shall be equal to the real wage in that period. Condition () states that the marginal rate of substitution between future consumption and present consumption shall be equal to the real interest rate. Condition (3) shows that the consumer can substitute inter-temporally not only current consumption for future consumption but also current leisure for future leisure: an 5/08/08, 4

5 increase in the interest rate increases the price of current leisure relative to the price of future leisure, and all else equal the consumer optimally decides to postpone leisure. This effect is labelled inter-temporal substitution of leisure. Inter-temporal substitution effects also arise from variations of real wage over time. For instance, when the current wage rate rises relative to the future wage rate, this means that current leisure becomes relatively more expensive, inducing the household to postpone leisure and work more today. Note that this intertemporal substitution effect refers to the price incentive only: as long as changes in wages come along with changes in life-time wealth, there will be income effects that may reinforce or offset the inter-temporal substitution effects. The demands for consumption and leisure in both periods are all implied by (0)-() together with (8): C wl C wl (4) r r 4 It is important to note that, whenever the price of one good declines (say w ), the quantity demanded of that good ( l ) increases, but the share of that good in total spending remains unchanged. This is a direct consequence of postulating a unit elasticity of substitution between each two goods in the utility function. If the elasticity of substitution between any two goods was different from one, a change in the price of any good would deliver uncertain results in the demands for the other goods The government budget constraint With this assumption, one can generate employment expansions during booms, and employment contractions during recessions, without departing from full employment. 5/08/08, 5

6 Assuming that lump-sum taxes are available, the government inter-temporal budget constraint is given by: G T G T (5) r r 9.3 Aggregate demand (AD) 9.3. The aggregate demand curve Since this economy is closed to capital flows and there is no investment, aggregate demand in this economy shall be equal to: Q d C G (5) Using (4), (9), (5) and (5), the demand for goods and services becomes: 4 Q d G or Q d z h 4 G z h G r G (6) This is the equation for aggregate demand - or the IS curve. It establishes a negative relationship between the demand for goods and services and the real interest rate: when the 5/08/08, 6

7 real interest rate increases, the current value of the household life-time wealth declines. Consequently, the consumer optimally decides to reduce its consumption expenditures 3. The negative relationship between the real interest rate and the level of aggregate demand in (6) is displayed in figure. Figure : The aggregate demand 9.3. Shifts in aggregate demand From equation (6), it is easy to see how the aggregate demand shifts in response to changes in the exogenous parameters. Consider first the effect of a temporary increase in productivity. In this case, the partial derivative is: 3 In a more general case accounting for investment decisions, there is an additional reason why the aggregate demand slopes down: when the real interest rate increases, the optimal capital stock decreases and hence the firm reduced its current investment spending. 5/08/08, 7

8 z Q d h 4 0 The reason is that the increase in productivity makes the household richer, and accordingly she decides to spend more in current consumption. Thus, everything else constant, the aggregate demand shifts to the right, as described in Figure. Note that the impact is only 4 to : since the consumer values four different goods in the same manner (current consumption, future consumption, current leisure and future leisure), the additional wealth brought about with the productivity shock is equally divided by these four goods. Also note that the increase in productivity comes along with an increase in income, and only half of this increase is spend this year: the other half is spend in future consumption and future leisure. Hence, the household savings increases. Having analysed this case, one shall remember a limitation of the exercise: we are assuming two periods only. Thus, the wealth effect implied by the productivity shift is split into two periods only. Obviously, if we allowed the household to live more periods, the impact of a temporary productivity shock on current consumption and leisure would be much smaller and close to negligible. Consider now the effect of a future increase in productivity When agents anticipate a higher productivity in the future, the effect on aggregate demand will be: z Q d h 4 r 0 In this case, the household starts spending before the productivity change actually takes place. Thus, there will be a fall in private savings today. Now, we consider the two shocks together: as we already know, a permanent increase in productivity has a much stronger impact on aggregate demand than when shocks are temporary: z Q d dz dz h r 4 r 0 5/08/08, 8

9 In this case, because the shock is of permanent nature, there is no need to smooth it. Hence, the effect on savings will be negligible. Note that the multiplier is close to ½, because the increase in wealth also gives rise to more leisure, today and in the future. An increase in government spending is like a negative productivity shock: when the household anticipates an increase in government spending in period, she will reduce consumption because its life-time wealth declines: G Q d 4 r 0 Finally, when current government expenditures increase, there are two effects: on one hand, consumer spending declines by one fourth. On the other hand, the government spending adds to aggregate demand on a one-to-one basis. The net effect is: G Q d In sum, aggregate demand expands whenever productivity increases more if the effect is permanent when current government expenditure increases and when future government expenditure decline. 9.4 Aggregate supply (AS) To find out the aggregate supply function, remember that the production function is linear in labour (eq. ). Employment, in turn, is determined by the demand for labour and the supply of labour Labour market equilibrium The demand for labour, given by equation (3), is represented by the horizontal line in Figure. It is a horizontal curve, because we are assuming constant returns on labour. The supply of labour is determined by the resource constraint, (6), and the demand for leisure implied by (9) and (4). This gives: 5/08/08, 9

10 h h w T N S 3 T (7) 4 4 r w 4w r Given the government budget constraint, and the fact that period- wages are equal to productivity, the optimal supply of labour as a function of the wage rate is: h h z G N S 3 G (7a) 4 4 r w 4w r The equilibrium in the labour market is depicted in Figure. In Figure, the supply of labour is upward sloped. The reason is that an increase in current wages, by increasing the opportunity cost of leisure today, leads households to postpone leisure 4. Because the model assumes constant returns on labour, the wage rate is only determined by productivity. The labour supply then determines the equilibrium level of employment, given the values of the other parameters. The equilibrium level of employment in period is: 3h h z G N G (8) 4 4 r z 4z r Figure : The labour market equilibrium 4 You may verify that the wage rate enters twice in equation (7). For an increase in the wage rate to hw T r T. have a positive impact on labour supply, the following (reasonable) condition must holed: 5/08/08, 0

11 9.4. Partial equilibrium: Shifts in labour supply and demand To see how the labour market adjusts to different types of shocks, consider first an increase in productivity today. This case is described in Figure 3. On the firms side, the productivity increase implies an upward shift in the demand for labour, determining an increase in the real wage rate. On the households side, there is a move along the labour supply function: a higher wage rate today leads households to consume less leisure through the inter-temporal substitution effect, and hence to work more. All in all, the employment level increases and the real wage rate increases. Figure 3: Temporary productivity shock Now consider a rise in future productivity, z. This case is analysed in Figure 4. When future productivity increases, the demand for labour remains unchanged, but the labour supply shifts to the left due to a wealth effect: the household understands he got richer and 5/08/08,

12 increases spending in all goods, including in current leisure. As a result, the level of employment declines. Note that if the demand for labour was negatively slopped, this shock should come along with an increase in the wage rate today as well. Figure 4: Anticipated productivity shock Finally, consider what happens when government spending decreases, today or in the future. From (7) it is easy to see that the present value of government spending impacts negatively on the labour supply. The reason is that lower government expenditures come along with an increase in household wealth, inducing more consumption and leisure. Thus, a decrease in the government life-time spending has an impact similar to that of anticipated productivity shock, as described in Figure 4. Finally, consider a decrease in the interest rate. When the interest rate decreases, it pays for the household to spend more today. This is valid for all goods, including consumption and leisure. Thus, the labour supply curve shifts to the left, determining a lower level of employment. Since a lower level of employment comes along with a lower level of output, there is a positive relationship between the real interest rate and output that underlies the aggregate supply curve The aggregate supply Given the production function and the equilibrium level of employment, the output supply in this economy becomes: 5/08/08,

13 hz G Q S 3hz G (9) 4 r r The aggregate supply is described in Figure 5. It slopes positively because when the interest rate increases, households optimally decide to reduce current leisure, through intertemporal substitution. Thus, the labour supply expands, and so will do the employment level and output. Figure 5: Aggregate supply Shifts in aggregate supply From the discussion above, it should now be clear how the aggregate supply shifts in response to different types of shocks. In brief, consider first the case of a productivity increase today. In that case, we know from Figure 3 that the labour supply expands and the employment level increases. On the other hand, because current productivity increases, the two terms in () are on the rise. The joint effect is a shift in the aggregate supply to the right, as depicted in Figure 5. The remaining cases operate through the effect on labour supply only: because the labour supply expands when future productivity declines and when the present value of government spending increases, the same will happen to the output supply curve. 5/08/08, 3

14 9.5 The natural interest rate We now close our model, by setting the aggregate supply equal to aggregate demand. Because we are in a closed economy, the variable that adjusts to make these two equal is the real interest rate. The equilibrium in the model is described in Figure 6. Figure 6: The natural interest rate Solving together the aggregate demand (6) and the aggregate supply (9), we obtain the natural interest rate in this economy: hz G hz G r (0) Substituting this in (6) or in (9), is easy to see that the equilibrium (natural) level of output in this economy will be hz G Q () Using () and the similar condition to period in (0), we see that: Q G Q G r (0a) Note that this is no more than the Euler equation. 5/08/08, 4

15 9.6 Adjustment to economic shocks Putting the pieces together, we now analyse how the economy adjusts to different types of shocks What happens when future productivity increases? The case of an anticipated productivity shift is analysed in Figure 7. In this case, we know that the aggregate demand expands (individuals will feel richer and will spend more) and aggregate supply contracts (individuals will devote more time to leisure). Clearly, the effect on the real interest rate will be positive: because output in the future rises relative to output today, the real interest rate must rise. Figure 7: The effect of an anticipated productivity surge 5/08/08, 5

16 In the labour market, there are two opposing effects: on one hand, the fact that future productivity increases makes individuals richer and hence they will consume more leisure today: in figure 7 this is represented by a shift in the labour supply curve to the left, that underlies the contraction of the aggregate supply curve. Then, there is a general equilibrium effect through the change in the real interest rate: as the real interest rate increases to the new natural level, current leisure more expensive, inducing households to work more (the labour supply curve moves to the right again). In the particular model we are using, these two effects exactly cancel each other What happens when current productivity increases? The effect of a temporary productivity shift is examined in Figure 8. In this case, there is a strong effect on aggregate supply, because workers are more productive. On the other hand, there are wealth effects that give rise to more consumption and leisure today. Note however that these effects are of lower magnitude: the increase in the household life-time wealth impacts of current consumption on a :4 basis, only (and the impact would be even lower, in a model with many periods). Since the effect on aggregate supply dominates the expansion in the aggregate demand, the real interest rate declines unambiguously. In the labour market, there are three different effects: on one hand, the higher demand for labour pressures the real wage up, inducing a higher work effort (movement along the initial labour supply). On the other hand, two other effects imply a shift of the labour supply to the left: first, the increase in the household lifetime wealth induces a higher demand for leisure; second, the fall in the real interest rate induces households to consume more leisure 5/08/08, 6

17 today through the inter-temporal substitution effect. On balance, the increase in real wage and the shift in the labour supply curve exactly cancel out, so employment does not change at all 5. Figure 8: The effect of a temporary productivity shift What happens when government consumption increases temporarily? Now, consider what happens when there is a temporary increase in government spending. 5 Note that this prediction of the model is inconsistent with the real world fact that employment is procyclical. 5/08/08, 7

18 First, let s consider the impact on households choices. Because a higher government spending implies an increase in life-time taxation, the household will get poorer. Thus, through a wealth effect, the household will reduce leisure, expanding the labour supply. By the same token, private consumption will increase, expanding the aggregate demand. These effects are however of second order. In a more realistic setup with many periods, the implied shifts in the AD and in the AS curve should be close to negligible. In contrast, the impact of government expenditures on aggregate demand is of first order and dominates the wealth effects. Hence, the overall effect shall be a slight expansion of aggregate supply and a large expansion of aggregate demand, causing the interest rate to increase. The increase in the interest rate amounts to the required to keep the household in shape with the Euler equation after the partial crowding out of private consumption by government consumption. Note that the prediction of the model that private consumption declines when government expenditures and output increase does not square well with the real world facts: the empirical evidence reveals that private consumption is pro-cyclical. Figure 9: The effect of a temporary increase in government spending 5/08/08, 8

19 In the labour market, there are two reinforcing effects: First, that fact that the increase in government expenditures comes along with a lower life-time wealth, the household reduces its current leisure and works more. Thus, the labour supply shifts to the right through a wealth effect. Second, the increase in the real interest rate turns current leisure more expensive relative to future leisure. Thus, through an inter-temporal substitution effect, the household will be induced to work more today, resulting in a further expansion of the labour supply to the right. On balance, the labour supply will increase unambiguously. As for the wage rate, it remains constant in our model because we are assuming constant returns: in a more general model with diminishing returns on labour, the real wage rate should decline. 9.7 The Heterogeneous Agent Two Period Production Economy (HATPPE) Further reading Williamson, Macroeconomics, Chs 0, 3. 5/08/08, 9

20 Review questions and exercises. Explain why aggregate supply is a positive function of the real interest rate.. Explain how an anticipated productivity slowdown shifts the aggregate demand and the aggregate supply. What will happen to the interest rate? What would happen if prices were sticky and the real interest rate could not adjust? 3. Consider the following utility function for the representative agent: U lnc lnl lnc lnl. Find out the optimal demands for current consumption and leisure as a function of life-time wealth,. 4. (Aggregate demand) Consider a two-period economy with a large number of firms and households. Each household is endowed with h=4 units of time, that can be sold to firms at the wage rate w. The preferences of the representative consumer are given by U lnc lnc lnl lnl. In this economy, the production function each period is given by qt zt Nt, with t=,. There is also a government, which spends G t each period and levies a lump sum tax Tt on consumers. a) (Firms problem) From the firm optimization problem, find out the expressions of the labour demand. b) (Household problem) From the household optimization problem, find out the expression for optimal consumption in period. c) (Aggregate demand) Find out the expression for aggregate demand in this economy, as a function of the exogenous parameters. Then, consider the following parameterization of the model: Z Z 0, G T 40, G 0. Find out the expression of aggregate demand and represent it in a graph. In particular, find out what the level of aggregate demand when: (c) +r=.; (c) +r=; (c3) +r=.5. Explain the intuition. d) (temporary fiscal expansion) Departing from c), suppose the government decides to increase the current expenditure and taxes to G T 80. Describe, quantifying, what will happen to aggregate demand. At a constant interest rate (say, +r=.) what will happen to private consumption? e) (announced fiscal expansion) Departing from c), suppose instead that the government decided to increase the future expenditure and taxes to G T 48. Describe, quantifying, what will happen to aggregate demand. At a constant interest rate (say, +r=.) what will happen to private consumption? f) (Fiscal cut) Departing from c), suppose instead that the government decided to cut the current taxes to zero: T 0, keeping its spending unchanged.. 5/08/08, 0

21 Describe, quantifying, what will happen to aggregate demand. At a constant interest rate (say, +r=.) what will happen to private consumption? g) (Temporary productivity change) Departing from c), suppose that current productivity decreased to Z 8. Describe, quantifying, what will happen to aggregate demand. At a constant interest rate (say, +r=.) what will happen to private consumption? h) (Anticipated productivity shift) Departing from c), suppose that future productivity increased to Z 3. Describe, quantifying, what will happen to aggregate demand. At a constant interest rate (say, +r=.) what will happen to private consumption? i) (Permanent productivity shift) Departing from c), suppose that both private and future productivity increased to Z Z. Describe, quantifying, what will happen to aggregate demand. At a constant interest rate (say, +r=.) what will happen to private consumption? j) Discussion): suppose that, instead of living two periods, households leaved 50 periods. Explain how this would alter the impact of temporary (one-period) changes of exogenous variables. 5. (Aggregate Supply) Consider a two-period economy with a large number of firms and households. Each household is endowed with h=4 units of time, that can be sold to firms at the wage rate w. The preferences of the representative consumer are given by U lnc lnc lnl lnl. In this economy, the production function each period is given by qt zt Nt, with t=,. There is also a government, which spends G t each period and levies a lump sum tax Tt on consumers. a) (labour supply) From the households optimization problems, find out the expression of the optimal supply of labour as function of the exogenous variables. b) (aggregate supply) Using the labour market equilibrium condition and the production function, find out the expression of aggregate supply as a function of the interest rate. c) Consider the following parameterization of the model: Z Z 0, G T 40, G 0. Find out the expression of aggregate demand and represent it in a graph. In particular, find out what the level of aggregate supply when: (c) +r=.; (c) +r=; (c3) +r=.5. Explain the intuition. d) (temporary fiscal expansion) Departing from c), suppose the government decides to increase the current expenditure and taxes to G T 80. Describe, quantifying, what will happen to aggregate supply. At a constant interest rate (say, +r=.) what will happen to labour supply and demand? e) (announced fiscal expansion) Departing from c), suppose instead that the government decided to increase the future expenditure and taxes to G T 48. 5/08/08,

22 Describe, quantifying, what will happen to aggregate supply. At a constant interest rate (say, +r=.) what will happen to labour supply and demand? f) (Fiscal cut) Departing from c), suppose instead that the government decided to cut the current taxes to zero: T 0, keeping its spending unchanged.. Describe, quantifying, what will happen to aggregate supply. At a constant interest rate (say, +r=.) what will happen to labour supply and demand? g) (Temporary productivity change) Departing from c), suppose that current productivity decreased to Z 8. Describe, quantifying, what will happen to aggregate supply. At a constant interest rate (say, +r=.) what will happen to labour supply and demand? h) (Anticipated productivity shift) Departing from c), suppose that future productivity increased to Z 3. Describe, quantifying, what will happen to aggregate supply. At a constant interest rate (say, +r=.) what will happen to labour supply and demand? i) (Permanent productivity shift) Departing from c), suppose that both private and future productivity increased to Z Z. Describe, quantifying, what will happen to aggregate supply. At a constant interest rate (say, +r=.) what will happen to labour supply and demand? j) (Discussion): suppose that, instead of living two periods, households leaved 50 periods. Explain how this would alter the impact of temporary (one-period) changes of exogenous variables. 6. (Real Business Cycle Model) Consider a two-period economy with a large number of firms and households. Each household is endowed with h=4 units of time, that can be sold to firms at the wage rate w. The preferences of the representative consumer are given by U lnc lnc lnl lnl. In this economy, the production function each period is given by qt zt Nt, with t=,. There is also a government, which spends G t each period and levies a lump sum tax Tt on consumers. a) (Aggregate demand) Find out the expression of aggregate demand as a function of the exogenous parameters. b) (Aggregate supply) Find out the expression of aggregate supply as a function of the exogenous parameters. c) Consider the following parameterization of the model: Z Z 0, G G 0. Find out the equilibrium real interest rate. Then, find out how much is the employment level and private consumption. Represent the equilibrium graphically. d) (Anticipated productivity shift) Departing from c), examine the implications of a future productivity shift to Z. 5. Find out the new equilibrium real interest rate and quantify the effects on output, private consumption and employment. 5/08/08,

23 e) (Temporary productivity change) Departing from c), examine the implications of a productivity shift to Z. 5. Find out the new equilibrium real interest rate and quantify the effects on output, private consumption and employment. f) (permanent productivity change) Departing from c), examine the implications of a permanent productivity change to Z Z. 5. Find out the new equilibrium real interest rate and quantify the effects on output, private consumption and employment. g) (temporary fiscal expansion) Departing from c), examine the implications of an increase in current expenditure and taxes to G T 40. Find out the new equilibrium real interest rate and quantify the effects on output, private consumption and employment. h) (announced fiscal expansion) Departing from c), examine the implications of an increase in future expenditure and taxes to G T 40. Find out the new equilibrium real interest rate and quantify the effects on output, private consumption and employment. i) (Tax cut) Departing from c), suppose the government decided to cut the current taxes to zero: T 0, keeping spending unchanged.. Find out the new equilibrium real interest rate and quantify the effects on output, private consumption and employment. 7. (Heterogeneous agents) Consider a two-period economy with a large number of firms and households. Each household is endowed with h=4 units of time, that can be sold to firms at the wage rate w. In this economy, 50% of the households are Ricardian (have access to financial markets), while the other 50% are Hand-tomouth (they cannot borrow or lend). Ricardian households maximize U R lnc lnc lnl lnl subject to a conventional inter-temporal budget constrain. Hand-to-mouth households solve the one-period problem, maximizing U HTM lnc lnl subject to a static budget constraint. Further assume that: the production function is Q 0N in both periods; government expenditures are zero in both periods; taxes, R T, HTM T, R T, HTM T (transfers, if negative) may apply. a) (Ricardian household) Find out the expressions for optimal consumption and optimal demand for labour of the Ricardian household. b) (Hand-to-mouth) Find out the expressions for optimal consumption and optimal demand for labour of the Hand-to-Mouth household. c) (Government budget constraint): write down the expression of the government inter-temporal budget constrain. d) (Aggregate demand): Find out the expression of aggregate demand as a function of the fiscal parameters and of the interest rate. e) (Aggregate supply): Find out the expression of aggregate supply as a function of the fiscal parameters and of the interest rate. 5/08/08, 3

24 R R HTM HTM f) (Baseline): assume that T T T T 0. Find out the equilibrium levels of output, interest rate and employment in each group [A: r=0; Q=0; N=]. g) (Tax cut): assume now that the government sets a uniform tax in the first period T R T HTM 30, which proceeds are to be returned uniformly to households next period ( T R T HTM 0 ). Find out the impact of such policy on: aggregate supply; aggregate demand; interest rate; output; employment and consumption of each group. Explain what will happen in the debt markets. [A: r=0.8; Q=0, R HTM N 0.5, N 3. 5 ]. h) (Income transfer today) Departing from g), examine the implications of a redistributive policy, from HTM to Ricardian consumers, fully financed within the HTM R period, that is T 60 T. Find out the impact of this policy on: aggregate supply; aggregate demand; interest rate; output; employment and consumption by R HTM each group. [A: r=0.8; Q=0, N 9, N 5 ]. i) (Income transfer tomorrow) Departing from g), examine the implications of a redistributive policy in the future, from HTM to Ricardian consumers, fully HTM R financed within that period, that is: T 60 T. Find out the impact of this policy on: aggregate supply; aggregate demand; interest rate; output; employment and consumption by each group. 5/08/08, 4