Consumption, Saving, and Investment. Chapter 4. Copyright 2009 Pearson Education Canada

This Chapter In Chapter 3 we saw how the supply of goods is determined. In this chapter we will turn to factors that determine the demand for those goods and services. Output supply was determined by firms ND and HH s NS In the labour market, the equilibrium is reached through changes in w Output demand determined by firms investment and HH s consumption/savings decisions. In the goods market, the equilibrium is reached through changes in r Copyright 2009 Pearson Education Canada 4-2

This Chapter In particular, this chapter will focus on the goods market: The determinants of consumption and saving Borrowers vs. lenders (savers) Role of government in saving Investment Goods market equilibrium Copyright 2009 Pearson Education Canada 4-3

This Chapter Recall from the Expenditure Approach: Y = C + I + G + NX G is determined by non economic factors and by the political system (ignore it for now) Consider a closed economy (i.e. NX=0) Focus here is on C and I; Y = C + I Natural issue: what goods and services to consume today, and what to leave for tomorrow (savings)? Copyright 2009 Pearson Education Canada 4-4

Consumption and Saving Changes in consumers willingness to spend have major implications for the behaviour of the economy. Consumption accounts for about 60% of total spending. The decision to consume and to save are closely linked Define: aggregate desired consumption (C d ) as the aggregate quantity of goods and services that household want to consume, given income and other factors. Copyright 2009 Pearson Education Canada 4-5

Consumption and Saving (continued) Desired national saving (S d ) is the level of national saving that occurs when aggregate consumption is at its desired d level. Note: superscript d = desired C: consumption goods produced, i.e. ACTUAL amounts available C d : spending on consumption goods i.e. amounts that individuals want/desire C C d = undesired inventories of consumption goods Copyright 2009 Pearson Education Canada 4-6

Consumption and Saving (continued) With no international economic relationships, NX=0 but also NFP=0 When NFP=0, national a saving is: S=Y-C-G Then, desired national saving is: S d =Y-C d -G Copyright 2009 Pearson Education Canada 4-7

The Consumption and Saving Decision A lender earns (and a borrower pays) a real interest rate of r per year. 1 dollar worth of consumption today is equivalent to 1+r dollar s worth of consumption in the next time period. So, 1+r is the price of current consumption in terms of future consumption How do people decide when to consume? Copyright 2009 Pearson Education Canada 4-8

The Consumption and Saving Decision (continued) The consumption-smoothing motive is the desire to have a relatively even pattern of consumption over time. This seems to be consistent with observed behaviour. A good part of a one-time income bonus is likely to be saved, and the income earned on that saving likely to be spread over time. Copyright 2009 Pearson Education Canada 4-9

Changes in Current Income Marginal propensity to consume (MPC) is the fraction of additional current income that is consumed in the current period. MPC is a number between 0 and 1 When Y rises by 1: C d rises by less than 1; S d rises by the fraction of 1 not spent on consumption. Copyright 2009 Pearson Education Canada 4-10

A Formal Model of Consumption and Saving This part of the lecture follows closely Appendix 4.A (on the course website). Start by considering the choice of a single individual (micro foundations) in a simple economy: Two periods (the present and future) Individual id seeks to maximize i utility by choosing between present and future consumption. Copyright 2009 Pearson Education Canada 4-11

A Formal Model of Consumption and Saving To analyze a model of consumption and saving, we need to know two things: What people can afford to consume How people rank the different options they are facing. We need to consider the budget constraint. We need to consider preferences (utility) over consumption today and tomorrow. Copyright 2009 Pearson Education Canada 4-12

A Formal Model of Consumption and Saving Start by defining i the following: y = current real income y f = future real income a = real wealth at the beginning of the current period c = current real consumption c f = future real consumption r = real interest rate (for both borrowing and lending) We would like to obtain a budget constraint: for any level of current consumption (c), how much future consumption (c f ) can I afford based on my current and future income and initial wealth Copyright 2009 Pearson Education Canada 4-13

A Digression: The Concept of Present Value We can represent the budget constraint using the concept of present value which measures the value of payments to be made in the future in terms of today s dollars Suppose I ll have a future income (Y f ) of $13 200 (one year from now) but I would like to to spend it all now. I can get a bank loan but how much can I borrow given that Y f? Copyright 2009 Pearson Education Canada 4-15

A Digression: The Concept of Present Value (continued) The loan (L) at 10% current interest rate satisfies: L(1+0.10) 10) = $13 200 L = $13 200/1.1 = $12 000 If I was a saver and wanted to have $13 200 in the future, I would need to invest only $12 000 today to achieve that goal. Economically, at an interest rate of 10%, having $13 200 one year from now is equivalent to having $12 000 today. Copyright 2009 Pearson Education Canada 4-16

A Digression: Present Value and the Budget Constraint In our two period model, we can define the present value of lifetime resources (PVLR) as the present value of current income and expected future income plus initial wealth: PVLR = y + y f /(1+r) + a Next, divide both sides of the budget constraint by y( (1+r) and then add c to both sides: c + c f /(1+r) = y + y f /(1+r) + a PVLC = PVLR Copyright 2009 Pearson Education Canada 4-17

A Digression: Present Value and the Budget Constraint PVLC is the present value of lifetime consumption. The budget constraint shows that the PV of lifetime consumption equals the PV of lifetime resources. If we choose to consume all the resources today y( (set c f = 0), then we get: c = y + y f /(1+r) + a This is the horizontal intercept on the budget constraint graph. Copyright 2009 Pearson Education Canada 4-18

Consumer Preferences To graphically represent consumer preferences for current and future consumption, we introduce indifference curves which represent all combinations of current and future consumption that yield the same level of utility Indifference curves have three important properties: 1. Slope downward from left to right. 2. Further away from origin represents more utility. 3. Are bowed towards the origin because we assume consumption smoothing (a preference for smooth changes to consumption). Copyright 2009 Pearson Education Canada 4-19

The Optimal Level of Consumption We can combine the budget line and indifference curves and find the optimal level of current consumption and saving Graphically, the optimum level of c is the point where the budget line is tangent to an indifference curve (i.e. It just touches the highest indifference curve it can reach) Copyright 2009 Pearson Education Canada 4-21

Effect of a Change in Income or Wealth The effect will depend d on how the PVLR is changed when either y, y f or a is changed. All three changes move the PVLR line without changing its slope -(1+r). It is an income effect. An increase in y raises both c and current saving (y-c). An increase in y f or a raise c but lower current saving since current income (y) is not affected. The consumer moves from point D to point J (not H or K because of consumption smoothing). Copyright 2009 Pearson Education Canada 4-23

The Permanent Income Theory In terms of the model, a temporary change in income is represented by a change in y with y f held constant. A permanent change would assume both components (y and y f ) change. This would have a larger effect on PVLR and so on both c and c f since the increase in income lasts for a longer duration. The theory is known as the permanent income theory (Milton Friedman, 1950s) Copyright 2009 Pearson Education Canada 4-25

The Life-Cycle Model The two period model can be generalised to many periods which capture real world phenomena. Income tends to follow a pattern over the life of the economic agent, rising from early years and then peaking between ages 50 to 60. After retirement, income falls sharply. Consumption patterns tend to be smoother (which is consistent with consumption smoothing) than patterns of income over time. Saving as a result is first negative, then positive and then negative. The Life Cycle theory is attributable to Franco The Life-Cycle theory is attributable to Franco Modigliani. Copyright 2009 Pearson Education Canada 4-26

Excess Sensitivity and Borrowing Constraints Studies confirm that y, y f and a all affect consumption and that permanent income changes have larger effects on consumption than temporary changes. Other studies point out that consumption responds to current income more strongly than theory predicts: excess sensitivity Possible reasons: People are short sighted. Borrowing constraints may be binding Copyright 2009 Pearson Education Canada 4-28

The Real Interest Rate and the C-S Decision What happens to the budget line when the real interest rate changes? It rotates around a point (E in the figure) where there is neither borrowing or lending (c=y+a and c f =yy f ). Since such a point involves neither borrowing or lending; it remains on the budget line no matter what the interest rate. Since an increase in r causes the line to become steeper, it must rotate around E. Copyright 2009 Pearson Education Canada 4-29

The Substitution Effect Recall that an increase in r raises the price of c in terms of c f. Starting ti from a no-borrowing/lending point, the increase in r will cause consumers to lower c and increase s. This increase in saving reflects the substitution effect of the interest rate on saving The increase in saving is measured along the horizontal axis as a drop in c. Copyright 2009 Pearson Education Canada 4-31

The Substitution Effect and Income Effect Together Assume the consumer is initially a lender. We can use the graphical model to separate the two effects: (board) Let the budget constraint pivot around the initial position (D). The drop in c (equivalent to a rise in s) from going from D to P is the substitution effect. The income effect is measured by the movement from P to Q. Note that if the initial position was one of dissaving, saving would unambiguously rise. Copyright 2009 Pearson Education Canada 4-33

Changes in the Real Interest Rate For a lender an increase in r has two opposite effects: increase in current saving (substitution effect); decrease in current saving (income effect). From our little model saving seems to rise nonetheless. Copyright 2009 Pearson Education Canada 4-35

Changes in the Real Interest Rate (continued) For a borrower when r increases the substitution and income effects both result in increased s. The empirical evidence is that an increase in r reduces c and increases s, but the effect is not very strong. Copyright 2009 Pearson Education Canada 4-36

Taxes and the Real Return to Saving Interest earning (and other returns on savings) are often taxed The real return earned by savers is actually less than the difference between i and π e The expected after-tax tax real interest rate ( ra t) is the after-tax nominal interest rate minus the expected inflation rate. r a t = (1 t)i π e Copyright 2009 Pearson Education Canada 4-37

Taxes and the Real Return to Saving (continued) By reducing the tax rate on interest the government can increase the real rate of return for savers and (possibly) increase the rate of saving in the economy. This is one motivation behind RRSPs (Registered Retirement Savings Plans) Copyright 2009 Pearson Education Canada 4-38

Fiscal Policy Let s make an assumption that the economy s aggregate output is given, it is not affected by the changes in fiscal policy. In general, fiscal policy affects C d by affecting households current and expected future incomes The government fiscal policy has two major components: government purchases and taxes. Copyright 2009 Pearson Education Canada 4-39

Government Purchases Government purchases increase temporarily: Indirect effects: C d falls, because higher h taxes burden (and lower income) is expected, but by less than the rise in taxes (MPC). Therefore, S d increases. Direct effect: S d falls, because G increases: S d = Y C d G Total effect is a reduction in S d (the direct effect of the rise in G outweighs the indirect effect), and a fall in C d Copyright 2009 Pearson Education Canada 4-40

Taxes A government tax cut (lump sum, so each taxpayer gets the same amount) without a reduction in current government spending should: Increase income and, therefore, C d increases by a fraction of the tax cut. But expectations of higher taxes in the future (lower future after-tax tax income) would cause people to consume less today, offsetting the positive effect of the increased current income. A current tax cut could either raise/lower C d Copyright 2009 Pearson Education Canada 4-41

Taxes (continued) According to the Ricardian equivalence proposition the positive and the negative effects of the tax cut without reduction of the current spending should exactly cancel. If there s no change in G, tax cuts don t t affect C d and therefore don t affect S d Will not hold if: People aren t that t forward-looking People are credit constrained (so spend it) People don t understand how today s T, G affect tomorrow s T Copyright 2009 Pearson Education Canada 4-42

Ricardian Equivalence in it s Strict Form In the model of consumer behaviour, Ricardian equivalence would suggest that a change in current taxes does not affect the PVLR and thus shouldn t affect C d or S d (board) If the government cuts taxes today then y rises, which should raise c, all else being equal. Assuming unchanged spending, the government must borrow the difference. But taxpayers are ultimately responsible for the government s debt, so y f will be lower. Under certain conditions one offsets the other. Copyright 2009 Pearson Education Canada 4-43

Investment Now consider a second major component of spending: investment spending Like C-S decisions, there is a tradeoff between the present and future. e.g. A firm commits its current resources to increasing its capacity to produce and earn profits in the future. Copyright 2009 Pearson Education Canada 4-44

Investment (continued) Investment spending fluctuates sharply over the business cycle and typically contributes half of the total decline in spending. Investment plays a crucial role in determining the long-run productive capacity of the economy. Copyright 2009 Pearson Education Canada 4-45

The Desired Capital Stock Desired capital stock is the amount of capital that allows a firm to earn the largest expected profit. Recall, MPK is the increase in output from adding a unit of capital (other factors held constant). Since lags occur in obtaining capital, we can define MPK f as the expected future MPK (i.e. Benefit from increasing investment today by one unit of capital) Copyright 2009 Pearson Education Canada 4-46

The User Cost of Capital Compare the expected future benefit to the expected cost User cost of capital is the expected real cost of using a unit of capital for a specified period of time. uc = rp + dp = (r + K uc is the user cost of capital r is the expected real rate of interest K d)p d is the rate at which capital depreciates p K is the real price of capital goods Copyright 2009 Pearson Education Canada 4-47 K

Determining the Desired Capital Stock The desired capital stock is the capital stock at which MPK f = uc. This is where expected profit is maximized. If MPK f > uc, add K; If MPK f < uc, sell K. The MPK f curve (slopes down) falls as K rises (diminishing i i marginal productivity) it The uc curve does not depend in the amount capital and is a horizontal line Copyright 2009 Pearson Education Canada 4-48

Changes in the Desired Capital Stock Any factor that shifts the MFK f curve or changes uc, changes K If r falls (other factors held constant), t), the uc line falls (shifts downward), then MFK f >uc, and K rises. The same is true when d or pk fall (other factors held constant). Copyright 2009 Pearson Education Canada 4-50

Changes in the Desired Capital Stock (continued) When technology improves (other factors held constant) the MFK f curve shifts upward, then MFK f >uc, and K rises. Copyright 2009 Pearson Education Canada 4-52

Taxes and the Desired Capital Stock Let s incorporate taxes into the investment decision The after-tax MPK f is (1-τ)MPK f. MPK f = uc (r + d)p = 1 τ 1 τ k uc/(1-τ) is tax-adjusted user cost of capital. Copyright 2009 Pearson Education Canada 4-54

Taxes and the Desired Capital Stock (continued) An increase in the tax rate τ raises the tax-adjusted user cost and so reduces the desired stock of capital. The effective tax rate is a single measure of the tax burden on capital. This is the tax rate or a firm s revenue that has the same effect on the desired stock of capital as would actual provisions i of the tax code. Copyright 2009 Pearson Education Canada 4-55

From the Desired Capital Stock to Investment In general, K changes over time through two opposing channels: Gross investment is the total purchase or construction of new capital goods. Depreciation is the capital wearing out. K increases or decreases over the year depending on which is greater. Copyright 2009 Pearson Education Canada 4-56

Investment (continued) Net investment t is the difference between gross investment and depreciation. K t+ 1 K t = I t dk t I K K + t = t+ 1 t dk t I t is gross investment during year t. K t and K t+1 is capital stock at the beginning of year t and t+1. dk t is the amount of depreciation during year t This says that gross investment is equal to changes in the capital stock plus depreciation. Copyright 2009 Pearson Education Canada 4-57

Investment (continued) The firm s gross investment during the year has two parts: The desired ed net increase in capital stock over the year (K*-K t ), (K* is the desired capital stock) Depends on factors like taxes, interest rates, and MPK f The investment needed to replace worn-out out or depreciated capital (dk t ). * I = K K + t dk Typically there are lags in achieving K*. These concepts also apply to investment in inventories and housing t Copyright 2009 Pearson Education Canada 4-59 t

Goods Market Equilibrium Just as prices (w) adjusted d to clear L market, now r (real interest rate) adjusts to clear goods market, i.e. to equate quantities of goods demanded and supplied. Prices coordinate decisions i of: HH s demand for C d and S d, and firm s demand for I d In equilibrium, firm s desired production equals the economy s desired purchases Copyright 2009 Pearson Education Canada 4-60

Goods Market Equilibrium (continued) The goods market equilibrium condition is when the aggregate quantity of goods supplied equals the aggregate quantity of goods demanded: d d Y = C + I + G We can also write this condition to emphasize the S-I relationship by subtracting C d + G from both sides: I d = Y C d G S d = I d Copyright 2009 Pearson Education Canada 4-61

The Saving-Investment Diagram The saving curve, S, is upward sloping (empirically supported). A higher real interest rate raises desired national savings. Drawn for given levels of Y, Y f, wealth, G, T The investment curve, I, is downward sloping. A higher interest rate increases the user cost of capital and, thus, reduces investment. Drawn for given levels l of the effective tax rate and MPK f Copyright 2009 Pearson Education Canada 4-62

The Saving-Investment Diagram (continued) Adjustments of the real interest rate, in response to excess supply or demand for saving, bring the goods market into equilibrium. If r too low, S d < I d, return to savings bid up by firms, r increases until the equilibrium is reached If r too high, S d > I d, return to savings falls, r decreases until the equilibrium is reached Copyright 2009 Pearson Education Canada 4-63

The Saving-Investment Diagram (Continued) Goods market equilibrium can also be expressed as Y (supply of goods) equal to C d + I d + G (demand d for goods): C d depends on r because a higher r raises S d. I d depends on r because a higher r raises uc, which lowers I d. In the same way, adjustments of r eliminate excess supply or demand for saving. Copyright 2009 Pearson Education Canada 4-65

Shifts of the Saving Curve The saving curve shifters are all factors, excluding the real interest rate, which affect national saving. E.g. The crowding out of investment by government purchases: increase in G causes a decrease S d; S d curve shifts to the left; the equilibrium i r goes up; I d falls because of higher uc. This occurs because the government is using more real resources which h otherwise would have gone into private investment. Copyright 2009 Pearson Education Canada 4-66

Shifts of the Investment Curve The investment curve shifters are all the factors which affect investment, excluding the real interest rate (it determines the movement along the curve). Copyright 2009 Pearson Education Canada 4-68

Shifts of the Investment Curve Example: An innovation or economic reform raises MPK f. The increase in I d shifts the investment curve to the right. r rises to a new equilibrium level. S increases. Copyright 2009 Pearson Education Canada 4-69