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# Chapter 3 -consumption and investment for BBA

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### Chapter 3 -consumption and investment for BBA

1. 1. Chapter 3 Consumption and Investment
2. 2. Consumption (C) and investment (I)  Since we are more concerned with two sector model in our course, we will discuss about consumption and investment.  In a two sector model, a simple but an imaginary assumption of no government and no foreign trade is made.  Here Yd =C+S or Yd =AD (aggregate demand)  This also implies that C+S=C+I
3. 3. Consumption  Introducing you with: (Think yourself in advance)  What is consumption?  What is consumption function?  What are the determinants of consumption?  What is MPC?  What is APC?
4. 4. Consumption “Consumption is the sole end and purpose of all production.” Adam Smith  Consumption is the act of spending income for buying goods and services to satisfy wants.  Determinants of consumption are disposable income (after tax income) of the consumers, their accumulated wealth or assets, their expected future income, the actual price level, the expected general price level, rate of interest, thriftiness, their age, sex and family size etc.
5. 5. Consumption function  A relation between consumption and its various determinants is called the consumption function. The consumption function taking all these determinants into account can be written as: C=f (Yd, W, Ye, P, Pe, r, s, DF…..)
6. 6. Keynesian Consumption function  Keynes, however, asserts that income alone is the most important determinant of consumption. Here, income refers to the disposable income. The Keynesian consumption function, thus, can be written as:  C=f (Yd), 1>f>0  Where, C=Consumption demand Yd = Disposable income= (Y-T) Y=Personal income T=Taxes (related to income)
7. 7. Keynesian Consumption function  The assumption of the Keynesian consumption function is that consumption depends on income, other things being equal. The higher the income, higher is the consumption, ceteris paribus.  Keynes‟ psychological law of consumption (The concept of the marginal propensity to consume).  Keynes argue that when the income increases, consumption also increases but not to the same extent as the increase in income.
8. 8. Keynesian Psychological Law “ The fundamental psychological law, upon which we are entitled to depend with great confidence both a priori from of our knowledge of human nature and from the detailed facts of experience is that men are disposed of, as a rule and on the average, to increase their consumption as their income increases, but not by as much as the increase in their income.”  The idea is that when the income increases, consumption also increases but less than proportionately. Alternatively, marginal propensity to consume (MPC) is positive but less than unity (0<MPC<1).
9. 9. Marginal Propensity to Consume  Keynesian Psychological Law is also called the MPC.  Given the consumption function: C= f (Yd), the MPC is the ratio between change in consumption expenditure and the change in income level.  MPC=∆C = Change in consumption ∆Yd Change in disposable income  i.e. 0< =∆C <1 ∆Yd
10. 10. Marginal Propensity to Consume  Suppose, initial income level is Rs. 1000 and consumption demand is Rs. 800. When income level increases to Rs. 1500, and consumption demand to Rs. 1200, MPC will be:  =∆C/ ∆Yd =400/500=0.80  This implies that when income increases by Rs. 100, consumption demand increases by Rs 80. And the difference Rs. 20 is the saving.  This means Yd = C+S  i.e. Disposable income=Consumption+Saving
11. 11. Consumption function  Short run Keynesian consumption function is often written as: C=Ca+bYd  Ca is autonomous consumption function. This implies that Ca is not related to income level (Yd) since a minimum level of consumption is required just for survival even if there is no income.  And “b” is MPC.
12. 12. Average Propensity to Consume  The fraction of total disposable income spent on consumption demand is called the average propensity to consume (APC).  APC= Consumption demand = C Disposable income Yd  APC implies the average spending tendency of the community or the people of a country.  Given the consumption function, C=Ca+bYd  APC=C/Yd=Ca+bYd/Yd  Or, APC = C + b Yd
13. 13. Calculating APC and MPC Yd C APC MPC S=Yd-C 0 100 200 300 400 500 600 100 175 250 325 400 475 550 - 1.75 1.25 1.08 1 0.95 0.92 - 0.75 0.75 0.75 0.75 0.75 0.75 -100 -75 -50 -25 0 25 50
14. 14. Main observations  When disposable income increases, consumption also increases but not proportionately.  When disposable income increases, APC declines.  When disposable income increases, MPC remains constant and APC>MPC.  At low level of income, there is dissaving and at higher level of income there is saving.  At particular level of income (i.e. at Rs. 400, C=Yd ), saving is just zero. This point is called the break even point.
15. 15. Graphical presentation 45 line (Y=C+S) Disposable income (Yd ) C,S C Ca=100 400 600200 E C=Y=400S=-50 S=50
16. 16. Short run and long run consumption Disposable income (Yd ) C,S CSR Consumption in the short run C=Ca+bYd Ca CLR: Consumption in the long run C=bYd
17. 17. Short run and long run consumption  The short run consumption is non- proportional in the sense that consumption is partly autonomous and partly induced that is related to the current disposable income.  The long run consumption fully depends on income. The long run autonomous consumption is zero and according to Keynes, in the long run, we all die if fail to generate our own income.
18. 18. Saving Function  The part of the disposable income not spent on consumption is called saving. In this case, saving is the difference between disposable income and consumption.  It is based on the premise that Yd=C+S  Then S=Yd-C  S=Yd- (Ca+bYd)  Or, S= -Ca+(1-b)Yd Where, -Ca=Autonomous saving that is negative or that is dissaving. A person must borrow in order to survive.  1-b is marginal propensity to save as we know b is marginal propensity to consume.
19. 19. Saving Function  From the macroeconomic perspective, aggregate saving is that part of real output that is produced but not sold to consumers. Thus, aggregate saving is the sum total of the private saving, and government saving.  Gross National Saving=Govt. saving+ private saving  Personal saving is the difference between personal disposable income and the personal consumption expenditure.  Private saving is the sum of personal saving and gross business saving. Gross business saving is the profits minus dividends paid to individuals plus depreciation.  Government saving is the difference between government revenues and government expenditures.
20. 20. Again to remind: types of saving private saving = (Y – T) – C public saving = T – G national saving, S = private saving + public saving = (Y –T ) – C + T – G = Y – C – G
21. 21. Marginal Propensity to save  MPS is the change in saving as a result of an additional unit of disposable income.  MPS =∆S = Change in saving ∆Yd Change in disposable income  Since MPC+MPS=1, when MPC increases, MPS decreases. This relationship between MPC and MPS can also be shown graphically by plotting MPS on the vertical axis and MPC on the horizontal axis. First think and draw yourself.
22. 22. MPC+MPS=1 MPC MPS O b2 b1 S2 S1 B1+s1=1 B2+s2=1
23. 23. Average Propensity to save  APS is the ratio between total saving and total disposable income.  APS =S = Saving Yd Disposable income  APS increases when disposable income increases and vice versa.
24. 24. Graph for saving function S -Ca o S Yd E
25. 25. Determinants of consumption and Saving  Since consumption is the counterpart of saving, both are related to each other.  Factors affecting the consumption demand also affect saving.  Thus, determinants of consumption and saving are interrelated and presented in the next slide.
26. 26. Determinants of consumption and Saving 1. Change in disposable income affects consumption and saving.  Once the Yd changes, both consumption and saving change. A higher Yd increases both C and S.  However, it also depends on the preference of an individual.  Increase in Yd shifts the budget line rightward indicating that more consumption and more saving are possible.
27. 27. Determinants of consumption and Saving 2. Change in interest rate affects consumption and saving.  Real interest rate is the difference between nominal interest rate (i) and inflation rate (Π), i.e. r=i- Π.  There is a positive relationship between real interest rate, r and saving, S. When r increases S also increases since r is the reward for saving. However, increase in r reduces consumption. Even people who borrow and consume are discouraged to consume more.  When there is more saving and less consumption due to increase in r, it is called the substitution effect of increased real interest rate.
28. 28. Determinants of consumption and Saving 2. Change in interest rate affects consumption and saving.  But the increased interest rate will also raise the future income relative to the current income. In this case, consumption may increase with the expectation of higher future income. This effect of higher interest rate on consumption is called income effect. This leads towards less saving at higher interest rates.  However, the effect of higher interest rate on S and C depends on the relative strength of substitution effect and income effect.
29. 29. Determinants of consumption and Saving 2. Change in interest rate affects consumption and saving.  For low income group, substitution effect will outweigh the income effect- saving increases with higher rate of interest.  For high income group who tend to save relatively large parts of their income, the income effect may outweigh the substitution effect. At high interest rates saving declines.
30. 30. Determinants of consumption and Saving 3. Change in price level and price expectations affect consumption and saving:  The effect of price level change on C and S depends on what happens to the real disposable income when price level changes.  If current disposable income rises or falls proportionately with the price level, real income remains unchanged. In this case, the shares of consumption and saving remain unchanged.
31. 31. Determinants of consumption and Saving 3. Change in price level and price expectations affect consumption and saving:  Real income= nominal income/price level  For example, real income at present is current income/price level i.e. 2000/5=400  After price level and Yd change say by 20 % i.e. 2400/6=400  In both cases S and C remain unchanged since there is no change in real income.
32. 32. Determinants of consumption and Saving 3. Change in price level and price expectations affect consumption and saving:  However, this may not be valid in the case of money illusion, a situation in which a person cares more about the nominal income than the real income. If a person increases his saving because of the money illusion than the real consumption will decline.  In the absence of money illusion, when real disposable income decreases because of the increase in price level, there will be an absolute decrease in real consumption expenditure.
33. 33. Determinants of consumption and Saving 3. Change in price level and price expectations affect consumption and saving:  Given the disposable income, expectation of a higher price level in the future may cause increase in consumption expenditure thereby reducing the saving. Because higher price in the future period will reduce the value of saving in real term (value of money declines due to price rise).  If the expected price level declines, people postpone consumption expenditure and increase saving with the hope that they can take advantage of higher purchasing power of money they deposited.
34. 34. Determinants of consumption and Saving 4. Pattern of income distribution:  According to N. Kaldor, people with low income level have higher MPC and hence lower MPS. On the contrary, people with higher income level have lower MPC and higher MPS.  This implies that MPS is higher for high income group and lower for low income group. In other words, low income group consumes whatever they earned while high income group saves more when income increases.
35. 35. Determinants of consumption and Saving 4. Pattern of income distribution:  However, still there are debates. A number of hypothesis in discussion are : Absolute income hypothesis (J. M. Keynes) Relative income hypothesis (James Duesenberry) Permanent Income hypothesis (M. Friedman) Life-cycle hypothesis (F. Modigliani)  These are discussed in advanced level.
36. 36. Determinants of consumption and Saving 5. Real assets, financial assets and outstanding debt affects consumption and saving:  Ceteris paribus, accumulation of wealth in terms of real (houses, other consumer durables) and financial (stocks, bonds, and other forms of deposit) assets leads to increase consumption expenditure. Given the size of real and financial assets, consumption expenditure depends on the rate of interest (as a return fro such assets) and the price level.  Any outstanding debt compels an individual to reduce consumption expenditure thereby saving more. In the case of no outstanding debt, this may be opposite.
37. 37. Determinants of consumption and Saving 6. Thriftiness, old age security and social safety net also affect consumption and saving:  Attitudes toward thrift (desire to save more) also influences the allocation of disposable income between consumption and saving. If people are thriftier, they keep aside increasing fraction of their disposable income for future consumption by reducing current consumption.  In a society with sufficient provision of old-age security and social safety net, people will save less and consume more. Converse will hold in the absence of such program in the society.
38. 38. Determinants of consumption and Saving 7. Growth rate of population and its age distribution affects the consumption-saving pattern: • Population growth rate and its age distribution affects the consumption-saving pattern accordingly. If population growth rate is quite high and exceeds that of economic growth rate, disposable income per capita declines. This reduction in income reduces per capita consumption expenditure and so does saving. • Another factor is the age structure. Big families spend proportionately more from income than small families. Young families busily acquire durables, while established families tend to replace only worn out durables. Thus, societies full of young or large families
39. 39. Determinants of consumption and Saving 8. Availability of credit and the state of financial institutions also affects consumption-saving pattern. • Consumption expenditure for durable goods may increase if credits are easily available. If getting credit is relatively difficult, expenditures on consumer durables decline. • Saving habit of people also depends on the institutional arrangement. For working people, the provision of provident fund, life insurance and arrangements of financial institutions also help to save more for future use.
40. 40. Aggregate expenditure  The desired expenditures, made up of desired consumption, desired investment, desired government purchases, and desired net exports account for total desired expenditure.  The result is total desired expenditure on domestically produced goods, and services called desired aggregate expenditure, or more simply aggregate expenditure (AE):  AE=C+I+G+NX
41. 41. Aggregate expenditure  Desired expenditure need not equal actual expenditure, either in total or in any individual category.  National income accounts measure actual expenditures in each of the four expenditure categories. National income theory deals with desired expenditures in each of these four categories.
42. 42. Equilibrium National Income  …is that level of national income where desired aggregate expenditure equals actual national income. Desiredexpenditure Actual National income 45 line or actual expenditure AE or Desired expenditure line E
43. 43. Determination of equilibrium income and output Y=AD, AD=C+I+G+NX AD=Y E1 E AD Y AE1 AE2 Planned spending precisely matches production in the points E, and E1.
44. 44. Determination of equilibrium income and output  In the previous graph:  Increase in AE has shifted the equilibrium income upward.  Given the intercept, a steeper aggregate demand function-as would be implied by a higher marginal propensity to consume-implies a higher level of equilibrium income.  Similarly, for a given MPC, a higher level of autonomous spending-a larger intercept- implies a higher level of equilibrium income.
45. 45. The Multiplier Model • A question arises, by how much does a Rs 1 increase in autonomous spending (aggregate expenditure) raise the equilibrium level of income? In other words, we want to know the magnitude of change in equilibrium GDP as a result of the change in aggregate expenditure. • A simple answer may be, since in equilibrium, income equals aggregate demand, it would seem that a \$1 increase in autonomous demand or spending should raise equilibrium income by Rs 1. But this is wrong. • Suppose first that output increased by Rs 1 to match the increased level of autonomous spending. This increase in output and income would in turn give rise to further induced spending as consumption rises because the level of income has risen.
46. 46. The Multiplier Model • How much does a Rs 1 initial increase in income would be spent on consumption? Out of this, a fraction „b‟ is consumed. Assume that production increases further to meet this induced expenditure, i.e. output and income increases by 1+b. • This will again create an excess demand because the expansion in production and income by 1+b will give rise to further induced spending. This process goes on like this and is explained by the multiplier model. • Multiplier analysis is an important tool of income expansion, and business cycle analysis.
47. 47. The Multiplier Model • The multiplier is the ratio of the change in GDP to the change in expenditure. • It is also defined as the ratio of the final change in income to the initial change in autonomous expenditure i.e. ∆Ā. ∆Ā stands for any increase in autonomous expenditure, this could be an increase in investment or in the autonomous component of the consumption. • Thus a multiplier can be written as K= ∆Y/ ∆Ā, where K is multiplier, ∆Y is change in GDP, and ∆Ā is change in autonomous expenditure. • The dynamic multiplier process is shown in the following table.
48. 48. The Dynamic Multiplier process Round Increase in demand this round Increase in production in this round Total increase in income (all rounds) 1 2 3 4 …. ∆Ā b∆Ā b2∆Ā b3∆Ā ….. ∆Ā b∆Ā b2∆Ā b3∆Ā ….. ∆Ā (1+b) ∆Ā (1+b+b2) ∆Ā (1+b+b2+b3)∆Ā 1 ∆Ā (1-b)
49. 49. The Multiplier  The equation ∆AD= (1+b+b2+b3 ) ∆Ā, following the rule of geometric series, simplifies to:  1 *∆Ā, (1-b) .  The idea is that cumulative change in aggregate spending is equal to a multiple of the increase in autonomous spending. The multiple 1/(1-b) is called the multiplier.  The multiplier is the amount by which equilibrium output changes when autonomous aggregate demand increases by 1 unit.
50. 50. The Multiplier  You should note that, 1-b is Marginal Propensity to Save (MPS), thus multiplier in other words is the reciprocal of MPS. That is, K=1/(1-b).  It should also be understood that the multiplier effect occurs when one person‟s spending becomes someone else‟s income, and some of the second person‟s income is subsequently spent, becoming the income of a third person, and so on.  Discuss an example, where MPC is o.5 and autonomous expenditure is Rs. 10,000, what is the final income?
51. 51. The Effect of Multiplier C+I+I' O C C Y C+I C Y2Y1 0.5 45º E1 E2 Y1 increased to Y2 because of the multiplier effect and a new equilibrium is attained.
52. 52. The Multiplier  The basic assumption of the above mentioned multiplier principle for a two sector economy are:  there is no change in the marginal propensity of consume during the adjustment process which remains more or less constant,  there is no induced investment (i.e. accelerator is not operating),  the new higher level of investment is maintained long enough for the completion of the adjustment process,  the output of consumer goods is responsive to effective demand for these goods,  there is complete absence of government activity like taxation or expenditure,  there is no time lag between the receipt of income and its expenditure, and  there is a closed economy.
53. 53. Leakages and Injections in Multiplier Leakages:  Households receive income in terms of factor payments. The HHs income is divided into four components: consumption demand (C), Taxes to the government (T), import expenditure (M), and saving.  The total households income that is not used for consumption demand is called the leakages or withdrawals.  Here leakages = net saving+ net taxes +import expenditure  Saving is the difference between Yd and consumption. Generally, this is deposited at banks. Net saving is the difference between savings deposited at banks and any borrowing made there from.  Net taxes is the difference between government tax revenue and any transfer payments made by the government.  Expenditure on imported goods is another form of leakages from the circular flow of income.
54. 54. Leakages and Injections in Multiplier Types of economic model Leakages (Withdrawals) Two sector Three sector Four Sector S, (Net savings) S+T (Net savings, Net taxes) S+T+M (Net savings, Net taxes, Imports) In addition, leakages can also result in from debt conciliation, price inflation, hoarding, and purchase of stocks and securities.
55. 55. Leakages and Injections in Multiplier Injections:  Injections are the sources of demand for goods and services other than consumer demand.  In two sector model, the sources of AD are C and I. In three sector model, the sources of AD are C+I+G. And in open economy, the components of AD are C+I+G+X.
56. 56. Leakages and Injections in Multiplier Types of Economic models Injections Two sector Three sector Four sector Investment (I) Investment, government spending (I+G) Investment, government spending, Exports (I+G+X)
57. 57. Investment  Investment is the spending devoted to increasing or maintaining the stock of capital. Investment demand can be disaggregated into: business fixed investment, residential investment, and inventory investment.  Investment is a flow variable and its counterpart stock variable is capital.  Capital  Produced, durable, used for further production  Examples: tangibles (structures, equipment), intangibles (software, patents)  Capital stock will increase if there is positive net investment and vice versa.
58. 58. Investment  Capital stock increases if gross investment>depreciation  Capital stock deceases if gross investment< depreciation. Basic role of investment in macro  Important for short run because it is a volatile part of aggregate demand  Recall decline of I in Great Depression  Important for long run because key determinant of growth of potential output and major way that governments affect economic growth.
59. 59. Investment  Why does investment occur?  When there is a discrepancy between desired stock of capital (K*) and actual stock of capital (K).  Desired stock of capital refers to the expected capital stock by the business community in order to conduct their business. Actual capital stock implies the existing stock of capital at any point in time.  Investment occurs in order to bridge the gap between the desired stock of capital and the actual stock of capital.
60. 60. Investment Determinants of investment demand  Expectations: desired investment is primarily driven by expectations of future profit and sales. Investment takes place when expected return exceeds the expected cost of capital. Expectations depend on several factors: 1. Degree of confidence in the future course of economic events: Business cycle expectations are important in this regard. 2. Government spending and tax policies: Favorable expenditure and tax policy having lower rates and wider base helps to increase the incentive to invest. 3. Behavior of input and output prices: Increase in input prices without any rise on output prices may lower the expectations. Increasing prices of output relative to the input prices increase expectations. For example, if wage rate is increasing without increase in the labor productivity.
61. 61. Investment Determinants of investment demand Interest rates:  An increase in the real interest rate raises the cost of capital and discourages investment demand. However, a decline in the real interest rate reduces the cost of capital and stimulates the investment demand. This implies that there exists an inverse relationship between interest rate and the investment demand. This is what suggested by the classical view of the investment demand curve (function).  The Keynesian view, however, is different. According to Keynes, role of expectations is important. Even if there is no change in interest rate, investment demand can stimulate if there are high expectations about the business. And even at a lower level of interest rate if expectations worsen, investment demand curve may shift to the left.
62. 62. Investment Determinants of investment demand Change in the output level:  During recovery, investment rises very rapidly. When economic growth rate slows down, investment demand falls dramatically. The idea is that there is a positive relationship between investment demand and the change in output level (national income).  This relationship is also explained by the accelerator theory.
63. 63. Investment Determinants of investment demand Level of income (output):  Profit is the pivot around which investment revolves. And profit depends upon the level of income. Therefore, it is argued that, investment could be the function of income:  I=I (Y)  1>I(Y)>0, when income level increases, investment also increases but less than the increase in income level.
64. 64. Investment Determinants of investment demand Marginal Efficiency of Capital (MEC):  According to Keynes, MEC is the major determinant of investment. Keynes says, “MEC as being equal to that rate of discount which would make the present value of the series of annuities given by the returns expected from the capital asset during its life just equal to its supply price.”  The idea is MEC is that rate of discount which would make the present value of the expected net returns from the capital goods just equal to its supply price (considering the supply price as constant over the years).
65. 65. Investment Determinants of investment demand Marginal Efficiency of Capital (MEC):  MEC of capital is also called the Internal Rate of Return.  Cost=R1/(1+r)+R2/ (1+r)2+Rn/(1+r)n  Where, Cost is the supply price of investment, R1 is the expected return from investment in year 1 and so on, r is the MEC, and n is the number of periods.  If we sum the right side of the equation, we will get the present value (PV) of all future returns.  If cost<PV of future returns, investment is made.  If cost>PV of future returns, investment is not made.  If MEC is higher than market rate of interest, investment is profitable. If MEC is lower than market rate of interest, investment is unprofitable.
66. 66. Investment MEC schedule: Investment project MEC Supply price (Cost) Cumulative supply price A B C D 15% 12% 10% 9% 1000 1200 900 400 1000 2200 3100 3500
67. 67. Investment  MEC schedule:  If the market rate of interest is 10%, projects A,B, and C could be undertaken depending upon the availability of the fund. Project D can not be undertaken since its MEC is less than the market rate of interest.  This is also shown in the graph in the next slide.
68. 68. Investment  Investment Demand Curve: MEC MEC MEC=r Investment 15% 1000 3100 10%
69. 69. Investment Investment function: The aggregate investment function can be expressed as: I= I (Y, r). This implies that I changes either due to the change in Y or due to the change in r.  The classical case: Investment is the function of the interest rate. I=I (r). When r increases, I declines and vice versa.  The Keynesian case: Investment demand is better explained by the expected reruns from the investment projects under consideration. As already discussed in the MEC section, investment decision is based on: the expected flow of income from the investment projects, the purchase price of the capital good, and the market rate of interest.
70. 70. Investment - Accelerator Theory Accelerator theory: Oldest and simplest theory, states that investment is a function of change in output. Investment demand is proportional to the change in output. The term accelerator refers that a relatively modest rise in national income can cause much larger increase in investment demand. - Here, the idea is there is a target capital-output ratio, K* = v Y. Where, K* is desired capital stock, v is capital output ratio and Y is output.
71. 71. Investment - Accelerator Theory - I* = ΔK* + δK = v Δ Y + δK. - Where, I* is desired investment, K is capital stock, ΔY is the acceleration of production, and δ = depreciation rate. - The actual investment might differ from the desired, but this is a simple and useful model. It shows why there is a close relationship between investment and output change. - This model is little used now because it assumes a fixed v. Modern I theory assumes v depends upon financial conditions.
72. 72. Investment - Accelerator Theory • Denoting current change in output by ∆Yt, and change in output in the past year by ∆Yt-1 the accelerator theory asserts that: • Investment will increase when the growth of national income/output is rising. If ∆Yt> ∆Yt-1 , investment increases. • Investment will be constant even if national income is growing, when the increase in income this year is the same as last year, i.e. ∆Yt= ∆Yt-1, investment remains the same. • If the growth rate of income/output is slowing down, investment will fall even if national income is still growing, i.e. if ∆Yt< ∆Yt-1 , investment declines.
73. 73. Investment - Summary of investment theory 1. The major components of investment are residential, business plant and equipment, software, and inventories. 2. These are among the most volatile components of output in the short run. 3. In equilibrium, demand for capital determined where the rental cost of capital equals the marginal productivity of capital.
74. 74. Investment - Summary of investment theory 4. The major theories are the accelerator theory, the neoclassical theory, and the Q theory. We have not discussed the latter two. These apply differently in different sectors. 5. Economic policy affects investment through both monetary and fiscal policy: • monetary policy through r • fiscal policy through things like depreciation policy and investment tax credits.
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