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ange in autonomous spending must be multiplied to give the change in output, equal to 1 divided by (1 – the marginal propensity to spend). multiplier \| The amount by which a change in autonomous spending must be multiplied to give the change in output, equal to 1 divided by (1 – the marginal propensity to spend). natio...
f production that has been corrected for any changes in overall prices. real gross domestic product [real GDP] \| A measure of production that has been corrected for any changes in overall prices. 5 https://socialsci.libretexts.org/@go/page/71917 real gross domestic product [real GDP] \| A measure of production that has ...
ase in inventories that comes about because firms have sold less than they anticipated. velocity of money \| Nominal GDP divided by the money supply. velocity of money \| Nominal GDP divided by the money supply. wealth effect \| The effect on consumption of a change in wealth. wealth effect \| The effect on consumption of ...
. . . . . . . . . . . . . . . . . 423 19 Eﬀects of Shocks in the Neoclassical Model 426 19.1 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426 14 19.2 The Eﬀects of Changes in Exogenous Variables on the Endogenous Variables . 428 19.2.1 Productivity Shock: Increase in At: ....
f Liquidity Transformation and Bank Runs 759 33.1 Model Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 759 33.2 Enter a Bank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 761 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ...
times quantities: GDPt = p1,ty1,t + p2,ty2,t + ⋅ ⋅ ⋅ + pn,tyn,t = pi,tyi,t n ∑ i=1 As deﬁned, GDP is a measure of total production in a given period (say a year). It must also be equal to total income in a given period. The intuition for this is that the sale price of a good must be distributed as income to the diﬀere...
caveat of GDP calculation below, in principle real prices are denominated in units of goods, whereas nominal prices are denominated in units of money. Money is anything which serves as a unit of account. As we’ll see later in the book, money solves a bartering problem and hence makes exchange much more eﬃcient. To mak...
of inﬂation – inﬂation was quite high and volatile in the 1970s but has been fairly low and stable since then. 32 7.58.08.59.09.510.05055606570758085909500051015Real GDPTrendLog real GDP and its trend-.20-.15-.10-.05.00.05.105055606570758085909500051015Detrended real GDP Figure 1.4: GDP Deﬂator Turning our focus back t...
f labor input in an economy. Because of diﬀerences and time trends in population, we typically divide this by L to express this as total hours worked per capita (implicitly per unit of time, i.e. a year or a quarter). This measure represents movements in two margins – average hours per worker and number of workers per ...
by households and the government are the same as in (a). Calculate the components of GDP. 2. Suppose the unemployment rate is 6%, the total working-age population is 120 million, and the number of unemployed is 3.5 million. Determine: (a) The participation rate. (b) The size of the labor force. (c) The number of employ...
ntation of reality will not have the ability to explain every aspect of that reality. In the same way, a simpliﬁed version of the economy will not be able to account for all the data that an economy generates. A model that can be useful to study how unemployed workers and ﬁrms ﬁnd each other will not necessarily be abl...
generations of economists recognized this shortcoming and attempted to rectify it by providing microeconomic foundations for consumption-saving decisions (Ando and Modigliani 1963), portfolio choice (Tobin 1958), and investment (Robert E. Lucas 1971). While each of these theories improved the theoretical underpinnings ...
urate to say that all economics is microeconomics. When you want to know how labor supply responds to an increase in the income tax rate, you analyze the question with indiﬀerence curves and budget constraints rather than developing some sort of alternative economic theory. Similarly, macroeconomics is simply microecon...
r than the growth rate in output per capita. 60 Figure 4.2: Capital per worker in the US 1950-2011. The fact that capital and output grow at similar rates leads to the third of Kaldor’s facts. 3. The capital to output ratio is roughly constant over long periods of time. If capital and output grew at identical rates fro...
re are growth miracles and growth disasters. Over the last four decades, some countries have become spectacularly wealthy. The people of Botswana, for instance, subsisted on less than two dollars a day in 1970, but their income increased nearly 20 fold over the last forty years. 68 Table 4.2: Growth Miracles and Growth...
th A. F (⋅) is a function which relates capital and labor into output. The bigger is A, the more Yt you get for given amounts of Kt and Nt – i.e. you are more eﬃcient at turning inputs into output. The function F (⋅) is assumed to have the following properties: FK > 0 and FN > 0 (i.e. the marginal products, or ﬁrst par...
ts of 3The reason that (5.10) is not listed here is because it is redundant given that both (5.12) and (5.14) must hold. 78 wt and Rt are units of fruit. So, the household “wakes up” in period t with a stock of capital (say 10 trees) and an endowment of time (say 24 hours). It leases its trees to a ﬁrm for Rt fruits pe...
initial kt from the curve. Since the curve lies above the 45 degree line in this region, we see that kt+1 > kt. To then think about how the capital stock will evolve in future periods, we can functionally iterate the graph forward another period. Use the 45 degree to reﬂect the new value of kt+1 down onto the horizonta...
ncrease as capital accumulates and transitions to the new steady state. wt will not react in period t, but will follow a similar dynamic path as the other variables thereafter. This happens because of our underlying assumption that FN K > 0 – so having more capital raises the marginal product of labor, and hence the wa...
s to maximize c∗, it must be the case that dc∗ ds be the case if: = 0. Since dk∗ ds > 0, this can only Af ′(k∗) = δ. (5.59) Figure 5.13 below graphically gives a sense of why (5.50) must hold. It plots yt = Af (kt), it = sAf (kt), and δkt against kt. For a given kt, the vertical distance between yt and it is ct, consu...
one twist. The twist is that there is a government. Each period, the government consumes a fraction of output, sG. Hence, the aggregate resource constraint is: Yt = Ct + It + Gt. Where Gt = sGYt. Deﬁne private output as Y p = Yt − Gt. Suppose that t investment is a constant fraction, s, of private output (consumption ...
household continues to supply 1 unit of labor inelastically each period. We will also allow Zt to change over time. In particular, assume: Zt = (1 + z)Zt−1, z ≥ 0. (6.8) Here, z ≥ 0 is the growth rate of Zt across periods. As with labor input, normalize the period 0 level to Z0 = 1 and iterate backwards, meaning we can...
initially sits in a steady state associated with s0. Then, in period t, the saving rate increases to s1 > s0 and is expected to remain forever at the higher rate. Qualitatively, this has exactly the same eﬀects as it does in the basic model. This can be seen in Figure 6.2: Figure 6.2: Increase in s The steady state ca...
) − (1 − δ) ≈ z + n + δ (since zn ≈ 0). This implies that in steady state: ̂it = (z + n + δ)̂kt. (6.66) (6.66) is “break-even” investment per eﬃciency unit of labor – i.e. the amount of investment per eﬃciency unit of labor necessary to keep the capital stock per eﬃciency unit of labor from declining. What is slightly ...
d N are governed by Equations (6.7) and (6.9). Create columns in your Excel sheet to measure the levels of N and Z in periods 1 through 100. (e) Use these levels of Z and N , and the series for ̂k you created above, to create a series of the capital stock per work, i.e. kt = ̂ktZt. Take the natural log of the resulting...
Figure 7.4, we observe a much stronger negative relationship between the initial level of real GDP and subsequent growth. The correlation between initial GDP and cumulative growth over the ensuing 60 years comes out to be -0.71, which is substantially stronger than when focusing on all countries. What are we to conclu...
h we believe the Solow model, this leaves diﬀerences in productivity – i.e. diﬀerent levels of A across countries – as the best hope to account for large diﬀerences in standards of living across countries. In a sense, this result is similar to our conclusion in Chapters 5 and 6 that productivity must be the primary dri...
un diﬀerences in income across countries. However, if the production function is mis-speciﬁed by omitting intangible forms of capital like human capital, the combined values of the capital shares may be much bigger which would allow for saving rates to play a bigger role in cross country income determination. • If diﬀe...
ty ﬂows are discounted relative to current utility ﬂows by 0 < β < 1, where β is called a discount factor and measures a household’s degree of impatience. Formally, lifetime utility is: U = u(cy,t) + βu(co,t+1) (8.3) A young household’s objective is to pick st to maximize (8.3) subject to the two ﬂow budget constraints...
t = Af (kt) − Aktf ′(kt) ct = cy,t + co,t 1 + n cy,t = wt − kt+1(1 + n) (8.35) (8.36) (8.37) (8.38) (8.39) (8.40) (8.41) (8.42) (8.43) (8.35)-(8.43) are the same as (8.19)-(8.27), except they are written in per worker terms and Nt and has been eliminated using (8.28). The key endogenous variable in (8.35)-(8.43) is kt+...
he growth rate per generation, not per year. If the population grows at 1 percent per year, then over thirty years it ought to grow at (1 + n)30 ≈ 35. Taking these subtle issues into account, the steady state and dynamics of the OLG and Solow models do not look as diﬀerent as one might conclude in the paragraph above. ...
) = −1.99.2 ) + β ln(c∗ 0 Figure 8.4 plots the dynamic trajectories of capital per worker (upper left), consumption (both aggregate consumption and consumption of each generation, upper right), and utility (lower left). For the utility graph, we show lifetime utility for young agents – i.e. U = u(cy,t) + βu(co,t+1) – ...
ZtNt ̂cy,t = ̂wt − Kt+1 Zt+1Nt+1 Zt+1Nt+1 ZtNt Which can be written: Which is just: (8.101) (8.102) (8.103) ̂cy,t = ̂wt − (1 + z)(1 + n)̂kt+1 (8.104) of course reduces to (8.43) when z = 0. All told, the equilibrium conditions of the (8.104) model re-written in stationary form are given below: ̂wt ̂st = β 1 + β ̂st (1 ...
ving could be positive, zero, or negative (i.e. borrowing). If the household takes a stock of St into period t + 1, it gets (1 + rt)St units of additional income (or, in the case of borrowing, has to give up (1 + rt)St units of income). rt is the real interest rate. Everything here is “real” and is denominated in units...
the household faces. The household acts as a price-taker and takes rt as given. To solve a constrained optimization problem, solve the constraint for one of the two choice variables (it does not matter which one). Solving for Ct+1, we get: Ct+1 = (1 + rt)(Yt − Ct) + Yt+1. (9.18) Now, plug (9.18) into the lifetime utili...
onsumption will be relatively small, while the marginal utility of period t + 1 consumption will be large. Hence, the ratio will be relatively small, and the indiﬀerence curve will be relatively ﬂat. Figure 9.3 plots some hypothetical indiﬀerence curves having this feature. Note that there is a diﬀerent indiﬀerence cur...
additional income, spending it all in the next period (so that Ct = 0.5 and Ct+1 = 1.5), then lifetime utility also increases to 1.9319. If, instead, the household increases consumption by 0.5 in both periods, saving 0.5 more in period t, then lifetime utility increases to 2. This is better than either of the outcomes...
n function. Suppose that the ﬂow utility function is the natural log, so u(Ct) = ln Ct. Then the Euler equation tells us that Ct+1 = β(1 + rt)Ct. Take this expression for Ct+1 and plug it into the intertemporal budget constraint, which leaves just Ct on the left hand side. Simplifying, one gets: Ct = 1 1 + β [Yt + Yt+1...
income, which causes the budget line to shift outward, shown in blue. The household will choose a new consumption bundle, C1,t, C1,t+1, where both period t and period t + 1 consumption are higher. Graphically, the eﬀects here are similar to what happens when there is an exogenous increase in future income. The househol...
≤ 1, while the probability of getting low income is 1 − p. The expected value of Yt+1 is the probability-weighted average of possible realizations: > Y l E(Yt+1) = pY h t+1 + (1 − p)Y l t+1 (9.56) Here, E(⋅) is the expectation operator. If p = 1 or p = 0, then there is no uncertainty and we are back in the standard cas...
that β(1 + rt) = 1. This means that the Euler equation under uncertainty reduces to: u′(Ct) = E[u′(Ct+1)] (9.70) In other words, an optimizing household will choose a consumption bundle so as to equate the marginal utility of consumption today with the expected marginal utility of consumption in the future. If there w...
locate at the new kink point, which puts it on the orange indiﬀerence curve. In this new bundle, current consumption is unchanged, and future consumption increases by the amount of the (anticipated) change in future income. 221 𝐶𝐶𝑡𝑡+1 𝐶𝐶𝑡𝑡 𝐶𝐶0,𝑡𝑡=𝑌𝑌0,𝑡𝑡 𝐶𝐶1,𝑡𝑡+1=𝐶𝐶0,𝑡𝑡+1=𝑌𝑌0,𝑡𝑡+1 𝐶𝐶0,𝑑𝑑...
ize optimal behavior. Instead, think about it a little bit without doing any math. What must be true about Ct and Ct+1 if a household with this utility function is behaving optimally? (b) The period t and t + 1 budget constraints are 9.4 and 9.5 respectively. Use the condition from (a) and the intertemporal budget cons...
he problem into an unconstrained one of choosing Ct and Ct+1: max Ct,Ct+1 U = ln Ct + β ln Ct+1 + . . . + β2 ln [(1 + r)2Yt + (1 + r)Yt+1 + Yt+2 − (1 + r)2Ct − (1 + r)Ct+1] The partial derivatives with respect to Ct and Ct+1 are: ∂U ∂Ct ∂U ∂Ct+1 = 1 Ct = β − β2(1 + r)2 1 Ct+2 − β2(1 + r) 1 Ct+2 1 Ct+1 (10.25) (10.26) I...
n this case, the household still desires a constant level of consumption across time. But the intertemoral budget constraint just works out to the sum of consumption being equal to the sum of income. Hence, the consumption function becomes:1 ¯C = 1 T + 1 [Yt + Yt+1 + Yt+2 + . . . Yt+T ] (10.48) 1One would be tempted to...
interpretation on this equation? 3. An old person and young person both win a lottery worth the same dollar value. According to the life cycle model, whose current consumption will increase by more? How do you know? 4. Describe why a permanent change in taxes has a larger eﬀect on consumption than a one-time change in...
tal (like in the Solow model), where it is possible to transfer resources across time through the accumulation of capital. Suppose that the ﬁrst period budget constraint holds with equality for all agents. Then, summing (11.2) across all L agents, we get: Ct(j) + L L ∑ ∑ j=1 j=1 j=1 Yt(j) as aggregate consumption and i...
g out to the right. There is no shift of the IS curve since a change in Yt does not aﬀect autonomous expenditure. These eﬀects are shown in Figure 11.6 below: 257 𝑌𝑌𝑡𝑡𝑑𝑑 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡𝑑𝑑=𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡𝑑𝑑=𝐶𝐶𝑡𝑡=𝐶𝐶𝑑𝑑(𝑌𝑌𝑡𝑡,𝑌𝑌𝑡𝑡+1,𝑟𝑟0,𝑡𝑡) 𝑌𝑌0,𝑡𝑡 𝑌𝑌0,𝑡𝑡𝑑𝑑 𝑟𝑟0,𝑡𝑡 𝐼𝐼𝐼𝐼 𝑌𝑌...
epends only on the aggregate endowment pattern. Now let’s change things up a bit. Continue to assume two types of agents with identical preferences. There are L1 and L2 of each type of agent, with L = L1 + L2 total agents. Let’s change the endowment patterns a little bit. In particular, suppose that type 1 agents have ...
llocations. Which household is borrowing in the ﬁrst period and which household is saving? What is the economic intuition for this? (e) Describe why borrowing and savings occur in this economy, but not the representative household economy. Why does household B have higher consumption in each period? (f) Assuming β = 0....
reasing in At, and increasing in the capital stock. (12.17) , Kt + , At + ) Next, let us focus on the ﬁrst order condition for the choice of Kt+1, (12.16). First, what is intuition for why this condition must hold? Suppose that the ﬁrm wants to do one additional unit of investment in period t. The marginal cost of doin...
t consumption and leisure are utility substitutes in the sense that uCL < 0. In other words, this means that, when leisure is high (so labor is low), the marginal utility of consumption is relatively low. Conversely, when leisure is low (so labor is high), the marginal utility of consumption is high. Put another way, l...
rule out the “corner” solutions in which the household would choose either no work or no leisure. As in the two period consumption model, getting on 286 𝐶𝐶𝑡𝑡 𝐿𝐿𝑡𝑡 1 𝐷𝐷𝑡𝑡 𝑤𝑤𝑡𝑡+𝐷𝐷𝑡𝑡 Feasible Infeasible the highest indiﬀerence curve possible subject to the budget line requires that the slope of = wt, w...
at the substitution eﬀect dominates, and that labor supply is therefore increasing in the real wage. Key Terms • Modigliani-Miller theorem • Dividends Questions for Review 1. State the ﬁve assumptions on the production function we use in this chapter. 292 2. What is the terminal condition for the ﬁrm? Explain the econo...
Ct+1), so as to locate on the highest possible indiﬀerence curve which does not violate the budget constraint. This involves locating at a point where the indiﬀerence curve is just tangent to the budget line (i.e. where the Euler equation holds). This is qualitative identical to what was seen in Chapter 9. From the hou...
umption. This eﬀect is negative. Hence, autonomous expenditure declines, so the expenditure line shifts down. This results in an inward shift of the IS curve. This is shown in blue in Figure 13.3. 302 Figure 13.3: Increase in Gt+1 The inward shift of the IS curve, coupled with no shift of the Y s curve, means that the ...
udget constraint. (b) Use this to ﬁnd the Euler equation. Is the Euler equation at all aﬀected by the presence of taxes, Tt and Tt+1? 308 (c) Use the Euler equation and intertemporal budget constraint to derive an expression for the consumption function. The government faces two within period budget constraints: Gt + S...
a medium of exchange. In the example listed above, it would not be easy to cut a cow up into 10,000 pieces in order to purchase a can of beer. Fiat money lacks these potential problems associated with commodity-based money. That being said, ﬁat money is prone to problems. Fiat money only has value because a government ...
ter the budget constraints in exactly the same way. The only diﬀerence is that bonds pay interest, it, whereas the eﬀective interest rate on money is zero. In writing the second period constraint, we have gone ahead and imposed the terminal conditions that the household not die with any positive or negative savings (i....
ney and the interest rate is positive, the household would choose to hold no money (i.e. we would be at a corner solution). If it = 0, then bonds and money would be perfect substitutes, and the household would be indiﬀerent between saving through bonds or saving through money. Hence, for the more general case in which ...
1 + rt − it 1 + it Mt Pt (14.52) 327 Combining (14.52) with (14.51), we get: Ct + Ct+1 1 + rt = wtNt + Dt + wt+1Nt+1 + Dt+1 + DI t+1 1 + rt − (Gt + Gt+1 1 + rt ) (14.53) There are two things worth noting. First, the real balance term, Mt Pt , drops out. Second, taxes disappear, leaving only the present discounted value...
Eﬃciency The conditions of the equilibrium model of production which we have been developing through Part III, expressed as supply and demand decision rules, are repeated below for convenience: Ct = C d(Yt − Gt, Yt+1 − Gt+1, rt) Nt = N s(wt, θt) Nt = N d(wt, At, Kt) It = I d(rt, At+1, Kt) Yt = AtF (Kt, Nt) Yt = Ct + It...
me critiques of these conclusions in Chapter 22. 338 15.1.2 Planner Gets to Choose Mt Now, let us consider a version of the hypothetical social planner’s problem in which the planner gets to choose Mt, in addition to Ct, Ct+1, Nt, Nt+1, and Kt+1. We continue to consider Gt and Gt+1 as being exogenously ﬁxed. The revise...
ons with respect to the choices of Gt and Gt+1 are: ∂U ∂Gt = −uC(Ct, 1 − Nt) + h′(Gt) ∂U ∂Gt+1 = −βuC(Ct+1, 1 − Nt+1) + βh′(Gt+1) (15.41) (15.42) 342 Setting these equal to zero and simplifying yields: h′(Gt) = uC(Ct, 1 − Nt) h′(Gt+1) = uC(Ct+1, 1 − Nt+1) (15.43) (15.44) Expressions (15.43)-(15.44) say that, an optimum...
s P ′(Q) P . We assume that < −1 so that a one Q percent increase in price leads to a more than one percent decrease in quantity. Rewrite (16.2) as = 1 P ′(Q)Q + P (Q) = C ′(Q) ⇔ + 1] = C ′(Q) ⇔ P (Q) [ 1 P (Q) C ′(Q) P (Q) − C ′(Q) C ′(Q) ⇔ = = 1 + −1 1 + The term on the right-hand side is the “price markup”, i.e. the...
to the household are dj,t = pj,tyj,t − mctyj,t = yj,t(pj,t − mct) mct = yj,t = Yt (mct − 1 − mct − 1 ) which is also independent of j. This means that ∫ 1 derive an expression for marginal cost. 0 dj,tdj = dt ∫ 1 0 dj = Dt. Return to (16.6) to 1 1 = ∫ p1− j,t dj 1 0 = p1− t ∫ = ( mct − 1 0 dj 1− ) 355 Solving for mct g...
Raval (2019) estimate an elasticity of substitution in the manufacturing sector of about 0.7. 361 Integrating over the constant gives 1 = ( − 1 1− mct) Mt This implies mct = − 1 In other words, as more ﬁrms come enter the market to compete for labor, marginal costs go up. The equilibrium wage is 1 M −1 t wt = − 1 1 AtM...
Up Rate1975198019851990199520002005201020152020Year00.511.522.5Growth Rate of Working Age Population • Holding the factors of production ﬁxed, economic welfare is increasing in the number of products. This can either be thought of as ﬁrms using a wider variety of intermediate inputs or households consuming a broader va...
ivided by the sum of the number of job postings and employment. If employment is low and the number of job postings are high, the vacancy rate is also high. Figure 17.5 shows that there is a negative relationship between the unemployment rate and the vacancy rate in the data. When the vacancy rate is high and the unemp...
obability mass while leaving the mean the same. The intuition here is that the individual can reject any wage oﬀer less than b in t + 1 so it does not matter how low w gets conditional on it being less than b. On the other hand, the individual beneﬁts from the “upside” of the risk since it potentially means a higher wa...
unemployment. Ht ≤ min [ut, Vt] 4. The matching function is increasing at a decreasing rate in vacancies and unemployment. ψtMu(ut, Vt) > 0, ψtMv(ut, Vt) > 0 ψtMuu(ut, Vt) < 0, ψtMvv(ut, Vt) < 0 5. The matching function has constant returns to scale in unemployment and vacancies. Hence, for λ > 0 ψtM (λut, λVt) = λψtM...
put from a match, zt, and the household’s outside option, b. As χ goes to zero, we get wt = zt. In this case, workers capture all the surplus of a match. In contrast, as χ → 1, the ﬁrm has all the bargaining power, so workers are paid the minimum required to get them to search, which equals their outside option of b. T...
gain, this is the key tradeoﬀ in the model. If a ﬁrm successfully matches with a job candidate, they produce zt units of output. As before, the cost to posting a vacancy is κ. Expected proﬁts for the ﬁrm are Πt = −κ + qi,t(yt − wi,t) (17.34) where qi,t is the probability the ﬁrm ﬁlls their vacancy. q and f are linked b...
two-period McCall model, what is the reservation wage in t + 1. Is this higher or lower than the reservation wage in t? How might this generalize to reservation wages over the life cycle? 4. Suppose you can search for a job in market A or market B. The average wage is equal across markets, but market B has greater wage...
l, the M P C would be 1 − s. The consumption function depends negatively on the real interest rate, i.e. ∂Cd < 0. ∂rt Why is this? The real interest rate is the real return on saving – if you forego one unit of consumption in period t, you get back 1 + rt units of consumption in period t + 1. The higher is rt, the more...
Agents will behave this way whether the government does in fact balance its budget or not. This greatly simpliﬁes the model, as we do not need to worry about Tt, Tt+1, or the amount of debt issued by the government. We can re-write the household’s consumption function, (18.1), by replacing the tax terms with government...
Taking the exogenous variables At, Kt, and θt as given, equations (18.11)-(18.12) both holding determines a value of Nt. Given a value of Nt, along with exogenous values of At and Kt, the value of Yt is determined from the production function, (18.15). We will deﬁne the Y s curve (or “output supply”) as the set of (rt,...
0.5. Suppose that Yt+1 = 15, Gt = 10, Gt+1 = 10, At+1 = 5, and Kt = 15. Suppose that rt = 0.1. Create an Excel ﬁle to numerically solve for Yt. (d) Suppose instead that rt = 0.15. Solve for Yt in your Excel ﬁle. (e) Create a range of values of rt, ranging from 0.01 to 0.2, with a gap of 0.001 between values. Solve for...
t+1 will rise, as we saw above when analyzing the eﬀects of an increase in current At. This will make the household want to consume more in the present as well. Both the increase in desired investment and consumption raise autonomous desired expenditure in period t. This shifts the expenditure line up (shown in blue be...
expenditure is additional income for a diﬀerent household. In “round 2,” with (1 − M P C)dGt extra in income, that household will increase its consumption by M P C(1 − M P C)dGt – i.e. it will consume MPC of the additional income. Hence, in “round 2,” there is an additional increase in expenditure of M P C(1 − M P C)d...
the real wage), and one in which labor supply is relatively inelastic (i.e. relatively insensitive to the real wage). Comment on how the magnitudes of the changes in Yt, rt, wt, and Nt depend on how sensitive labor supply is to the real wage. 2. Consider the basic Neoclassical model. Suppose that there is an increase i...
and in the Model Variable Corr w/ Yt in Data Corr conditional on At Corr conditional on θt Ct It Nt wt rt Pt 0.88 0.91 0.87 0.20 0.10 -0.46 + + + - + + + + - We see that consumption, investment, and labor hours are strongly positively correlated with output – these correlations are all above 0.85. This means that when...
ught to have: wt = (1 − α)AtK α t N −α t (20.4) (20.4) is nothing more than the condition wt = AtFN (Kt, Nt). One can multiply and divide the right hand side of (20.4) to get: Re-arranging terms in (20.5), one gets: wt = (1 − α) Yt Nt 1 − α = wtNt Yt (20.5) (20.6) (20.6) says that 1 − α ought to equal total payments to...
e functions deﬁned by money. Currency is one particular kind of asset. An “asset” is deﬁned as “property owned by a person or community, regarded as having value available to meet debts, commitments, or legacies” (this deﬁnition comes from a Google search of the word “asset”). Currency (a physical representation of mon...
ney multiplier then fell drastically post-2008 and has not recovered. The real world phenomenon driving this behavior is that commercial banks have been holding excess reserves – they have not been lending out the maximum amount of reserves. As noted above, the central bank can directly control the monetary base, M Bt....
of our theory, the velocity of money could not be constant for two reasons – changes in ψt and changes in it. Increases in it increase the velocity of money, while 471 1.41.51.61.71.81.92.02.12.22.3606570758085909500051015Velocity of Money increases in ψt reduce it. Figure 21.7 below plots the time series of the (annu...
wo years (eight quarters). To the extent to which money is nonneutral empirically, it is only so for a couple of years at most. After a period of several years, changes in the money supply do not seem to impact real variables, and monetary neutrality seems to be an empirically valid proposition. This fact forms the bas...
tion. For example, suppose a ﬁrm has ten tractors. One quarter, the ﬁrm operates each tractor for 18 hours a day. The next quarter, the ﬁrm operates the tractors only 9 hours a day. To an outside observer, the ﬁrm’s capital input will be the same in both quarters (ten tractors), but the eﬀective capital input is quite ...
his up later in the book in Part VI. 487 0123456789-.05-.04-.03-.02-.01.00.01.02.03.0455606570758085909500051015Baa Credit SpreadCyclical Real GDPBaa spreadCyclical Real GDPCorrelation = -0.38 22.1.8 An Absence of Heterogeneity The basic neoclassical model with which we have been working features a representative house...
on home production is the sum of desired expenditure by the household, C h t . There is an additional term, Xt, which stands for exports. Exports represent expenditure by the rest of the world on home-produced goods and services. Total desired expenditure on home-produced goods and services is the sum of these four com...
given by: Y d t = C d(Yt − Gt, Yt+1 − Gt+1, rt) + I d(rt, At+1, Kt) + Gt + N X d(rt − rF t , Qt) (23.35) This is simply the aggregate resource constraint, (23.27), without imposing the equality between income and expenditure, combined with the optimal demand functions for the diﬀerent components of aggregate expenditur...
ical model. We will do so graphically. We will start in the IS − Y s equilibrium and determine the eﬀects of a shock on rt and Yt, and from that we can infer the eﬀects on the expenditure components of output as well. We will then determine the eﬀect on the price level. Then we will determine the eﬀect on the real and ...
nge Rate 513 𝑀𝑀𝑡𝑡 𝑃𝑃𝑡𝑡 𝑀𝑀0,𝑡𝑡 𝑃𝑃0,𝑡𝑡 𝑃𝑃𝑡𝑡𝑀𝑀𝑑𝑑(𝑟𝑟0,𝑡𝑡+𝜋𝜋𝑡𝑡+1𝑒𝑒,𝑌𝑌0,𝑡𝑡) 𝑀𝑀𝑠𝑠 𝑃𝑃1,𝑡𝑡 𝑃𝑃𝑡𝑡𝑀𝑀𝑑𝑑(𝑟𝑟1,𝑡𝑡+𝜋𝜋𝑡𝑡+1𝑒𝑒,𝑌𝑌0,𝑡𝑡) 𝑟𝑟𝑡𝑡−𝑟𝑟𝑡𝑡𝐹𝐹 𝜖𝜖𝑡𝑡 𝜖𝜖𝑡𝑡=ℎ(𝑟𝑟𝑡𝑡−𝑟𝑟𝑡𝑡𝐹𝐹) 𝜖𝜖0,𝑡𝑡 𝑟𝑟0,𝑡𝑡−𝑟𝑟0,𝑡𝑡𝐹𝐹 𝑟𝑟1,𝑡𝑡−𝑟𝑟0,𝑡𝑡𝐹𝐹 𝜖𝜖1,𝑡�...
n model, if the economy ﬁnds itself with an equilibrium level of output that is higher (lower) than what would obtain in the neoclassical model, there is pressure on the price level to increase. This adjustment of the price level causes the AS curve to shift, and eventually ensures that the equilibrium of the New Keyne...
ow in Figure 24.5 for completeness. 526 𝑟𝑟𝑡𝑡 𝑟𝑟𝑡𝑡 𝑀𝑀𝑡𝑡 𝑌𝑌𝑡𝑡 𝑃𝑃0,𝑡𝑡𝑀𝑀𝑑𝑑(𝑟𝑟𝑡𝑡+𝜋𝜋0,𝑡𝑡+1𝑒𝑒,𝑌𝑌0,𝑡𝑡) 𝑀𝑀𝑠𝑠 𝑟𝑟0,𝑡𝑡 𝑌𝑌0,𝑡𝑡 𝑀𝑀0,𝑡𝑡 𝑟𝑟1,𝑡𝑡 𝐿𝐿𝑀𝑀(𝜋𝜋1,𝑡𝑡+1𝑒𝑒) 𝑃𝑃0,𝑡𝑡𝑀𝑀𝑑𝑑(𝑟𝑟𝑡𝑡+𝜋𝜋1,𝑡𝑡+1𝑒𝑒,𝑌𝑌0,𝑡𝑡) 𝐿𝐿𝑀𝑀(𝜋𝜋0,𝑡𝑡+1𝑒𝑒) Figure 24.5: The IS Cur...
ical model. The supply side of the neoclassical model is characterized by the following three equations: Nt = N s(wt, θt) Nt = N d(wt, At, Kt) 535 (25.1) (25.2) Yt = AtF (Kt, Nt) (25.3) (25.1) is the labor supply curve, (25.2) is the labor demand curve, and (25.3) is the production function. The AS curve is deﬁned as t...
e at Y f t , determined by the production function and labor demand and supply intersecting) and the extreme case where the AS curve is horizontal at ¯Pt. Intermediate values of γ give an upward-sloping, but non-vertical and non-horizontal, AS. Mathematically, Y f t can be found as the solution to the following system ...
is determined by the intersection of the AD and AS curves and the equilibrium quantity of labor input must be consistent with this, in the neoclassical model labor input is determined by the intersection of labor demand and 556 𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑁𝑁𝑡𝑡 𝑁𝑁𝑡𝑡 𝐴𝐴𝐴𝐴 �...
ward shift of the IS curve. For the purposes of understanding how consumption and investment react, it is important to know which exogenous variable is changing and in which direction. These eﬀects are shown graphically in Figure 26.7. The IS curve shifts to the right. This results in a rightward shift of the AD curve....
el ﬁxed). In thinking about monetary non-neutrality and the three diﬀerent models, there is a simple intuition. In the neoclassical model, the central bank cannot aﬀect Mt – any change in Mt is met by a proportional change Pt 576 𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑁𝑁𝑡𝑡 𝑁𝑁𝑡𝑡 𝐴𝐴𝐴𝐴 ...

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