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sion. Relative to the neoclassical model, in the New Keynesian model output “under-reacts” to supply shocks and “over-reacts” to demand shocks. Put a little diﬀerently, nominal rigidity makes demand shocks have bigger eﬀects on output and supply shocks smaller eﬀects compared to a world with no price stickiness. This p...
the neoclassical equilibrium in the short run, ¯Pt will adjust, the AS will shift, and by the third year the equilibrium of the economy will coincide with the hypothetical neoclassical equilibrium. In other words, deviations from the neoclassical equilibrium are only temporary 589 phenomena which arise because of impe...
𝑌𝑌𝑡𝑡=𝑌𝑌𝑡𝑡 𝑟𝑟𝑡𝑡 𝐴𝐴𝐴𝐴 𝐴𝐴𝐴𝐴′ 𝑁𝑁1,𝑡𝑡𝑠𝑠𝑠𝑠 𝐼𝐼𝐴𝐴′ 0 subscript: original 1 subscript: post-shock sr or mr superscript: short run or medium run Original Post-shock Post-shock, post price adjustment Original, hypothetical flexible price Post-shock, flexible price 𝑁𝑁𝑑𝑑(𝑤𝑤𝑡𝑡,𝐴𝐴𝑡𝑡,𝐾𝐾𝑡�...
t > ¯P sr t = Y sr 605 Figure 27.11: Partial Sticky Price: Increase in Mt, Short Run to Medium Run Figure 27.12 plots the dynamic paths of diﬀerent variables throughout period t, which we again divide into three segments – years 1 and 2 are the short run, while by year 3 it is the medium run. 0 subscripts denote value...
𝑌𝑌1,𝑡𝑡𝑚𝑚𝑠𝑠 𝑃𝑃1,𝑡𝑡𝑚𝑚𝑠𝑠 𝑟𝑟1,𝑡𝑡𝑚𝑚𝑠𝑠 𝑃𝑃1,𝑡𝑡𝑠𝑠𝑠𝑠 𝑟𝑟1,𝑡𝑡𝑠𝑠𝑠𝑠 𝑌𝑌1,𝑡𝑡𝑠𝑠𝑠𝑠 Table 27.2: Qualitative Eﬀects of Exogenous Shocks on Endogenous Variables in the Partial Sticky Price Model, Transition from Short Run to Medium Run Variable Yt Nt wt rt it Pt Exogenous Shock ↑ IS curve -...
ay that there would be no eﬀect of the increase in Mt on Yt. In eﬀect, an anticipated increase in Mt would cause the AD curve to shift right and but the AS curve to simultaneously shift up in such a way as to leave output unaﬀected. In terms of (27.2), a fully anticipated monetary expansion would be met with a coincide...
price level and output as the economy transitions to the medium run? 2. Critically evaluate the following claim. “In the New Keynesian model, a central bank can increase output by increasing the money supply. Therefore, the central bank should increase the money supply by ever larger amounts each period. This will gen...
uctivity, manifested in an increase in At. This is shown in Figure 28.3. The blue lines and 1 subscripts show what would happen in the short run absent any policy change. The AS curve would shift right, by a horizontal amount equal to the shift of the hypothetical vertical neoclassical AS curve, ASf (the shift of which...
=𝑃𝑃�0,𝑡𝑡 𝐴𝐴𝐼𝐼′ 𝑌𝑌1,𝑡𝑡=𝑌𝑌1,𝑡𝑡𝑓𝑓 𝑟𝑟1,𝑡𝑡 policy is relatively easy since ﬂuctuations in the price level (or inﬂation rates) are much easier to observe at high frequencies and in real time. Does the Divine Coincidence always hold in the New Keynesian model? Unfortunately, the answer turns out to be no...
justing Mt in response to diﬀerent shocks, it is not very transparent how this is done and a central bank behaving in this way has a lot of discretion. For these reasons, many economists now think about monetary policy in the form of explicit rules relating target values of economic variables to a central bank’s policy...
LM curve, which is upwardsloping in a graph with rt on the vertical axis and Yt on the horizontal axis. Along with this, we plot a dashed line corresponding to the implied lower bound on the real interest rate of −πe t+1 (where again we take expected inﬂation to be exogenous.) 650 Figure 29.1: The LM Curve and the ZLB...
expand. 658 Figure 29.7: Sticky Price Model: Positive Supply Shock with Binding ZLB The exercises demonstrated graphically in Figures 29.6 and 29.7 reveal an important point. The ZLB accentuates the diﬀerences between the New Keynesian and neoclassical models. Output responds even more to IS shocks, and even less to su...
LB no longer binds. This is depicted in Figure 29.11. Figure 29.11: Fiscal Expansion to Exit the ZLB The other option available for escaping the ZLB relies on the manipulation of expected inﬂation. In particular, the lower bound on the real interest rate is the negative of the rate of expected inﬂation. If policymakers...
Great Depression) output is low. Given this, would a supply shock as the reason for a binding ZLB make empirical sense? Exercises 1. Suppose that you have a sticky price New Keynesian model in which the ZLB is binding. Consider an exogenous reduction in At+1. Show how this aﬀects the equilibrium values of the endogenou...
economy model is ﬂatter than in the closed economy model, output increases by more (and the real interest rate falls by less) when the economy is open than when it 678 𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑁𝑁𝑡𝑡 𝑁𝑁𝑡𝑡 𝐴𝐴𝐴𝐴 𝐼𝐼𝐴𝐴𝑜𝑜𝑜𝑜 𝑟𝑟0,𝑡𝑡 𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡 𝑁𝑁𝑠𝑠(𝑤�...
would ordinarily cause the IS curve to shift horizontally to the right. Because the IS curve is horizontal in the small open economy model, there ends up being no horizontal shift in the IS curve, and therefore no eﬀect on output, the real wage, or labor input. In other words, graphically there is no eﬀect on the equi...
e. ﬂoating exchange rates), and the equilibrium values after this shift are denoted with 1 subscripts. The red lines show how curves shift when monetary policy reacts to keep the real interest rate (and hence the exchange rate) ﬁxed. The equilibrium values after this policy response are denoted with 2 subscripts. 691 F...
expansion lowers the real interest rate which reduces the real exchange rate and stimulates net exports. This is an additional monetary transmission mechanism relative to the domestic economy. Consequently, increases in the money supply are more expansionary in the closed economy. Conversely, expansionary shifts in the...
t types of ﬁrms diﬀer slightly in the speciﬁcs of the business activities they undertake, but they all play a similar fundamental role of intermediating credit between savers (typically, households) and investors (typically, ﬁrms). In this chapter we will repeatedly refer to such an intermediary as a “bank,” even thoug...
th an outside option of just storing the $1. To make matters as simple as possible, suppose that there is no discounting of future payoﬀs relative to current payoﬀs. The household can make a loan to a ﬁrm at (real) interest rate r – in the event the project succeeds, the household gets its principal plus interest back,...
w beneﬁt (the utility from living in the house or the rents that can be earned by leasing it out), and it can be sold to generate cash. Cash, held either in the form of currency or in a checking or savings account, is also an asset for the account holder. Liabilities are debts or obligations that an individual or insti...
sibility that assets a bank holds on its balance sheet may underperform. The easiest example to think about is loans made. Some loans may default (i.e. the borrower does not pay the loan back), in which case the bank must realize a loss on its balance sheet by “writing oﬀ” the loan and accepting a reduction in equity. ...
rities: $30 Cash Reserves: $20 Equity $20 Liabilities plus Equity Deposits: $100 Borrowings: $0 With $50 in liquid assets (securities and cash reserves), the bank can meet a withdrawal of up to $50 without having to sell any loans. Its liquidity cushion therefore provides it more leeway to withstand unexpectedly high w...
meet the need for safe assets. Through what are called repurchase agreements, large institutional investors can “deposit” money with a ﬁnancial institution, and in the process receive MBS (or similar securitized loan products) as collateral. Should the ﬁnancial institution fail, the large institutional investor gets t...
isk situation we described when discussing traditional banking in Section 31.3.2. An increase in Repo haircuts, or more generally a failure for short term funding to be rolled over, creates a liquidity problem for the shadow bank which is ﬁnancing itself with this short term funding. This liquidity crisis may require t...
n the monetary base and the money supply. We will deﬁne mm as the number multiplying the monetary base and will refer to it as the money multiplier. We may then write: mm = 1 + c c + rr + er M = mm × M B (32.7) (32.8) We will think about a central bank as being able to determine M B. The central bank is a monopoly supp...
ves $1.1 million (-$0.9 million) Equity $2 million Liabilities plus Equity Deposits: $11.0 million (-$0.9 million) 733 Bank B is now just exactly satisfying its reserve requirement, like Bank A before it. Diﬀerently than Bank A, Bank B’s balance sheet has expanded in size – it now holds an addition $1 million in assets...
the physical capital stock in the economy). It is for this reason that “equity” is often referred to as “capital” or sometimes “equity capital.” For the economy as a whole, total equity equals total capital, which we can think of as comprising non-ﬁnancial assets like plant, equipment, and housing. Non-ﬁnancial assets...
is: Table 32.35: Bank C Receives Deposit Assets Loans: $8.2 million Securities: $1 million Reserves: $2.4612 million (+$0.6612 million) Equity $2 million Liabilities plus Equity Deposits: $9.6612 million (+$0.6612 million) Bank C is now holding reserves in excess of what it desires. It has received $0.6612 million in n...
ll that the experiment considered in this section involved the central bank initially swapping out $1 million in government 749 securities for $1 million in reserves, but these reserves do not stay with Bank A. From Table 32.47, we see that the total change in reserves for this particular example is: ∆RE = 0.1818 + 0.1...
w but also through non-standard lending institutions (e.g. facilities, some of which are discussed in Chapter 37); (ii) purchases of mortgage-related debt; 754 and (iii) purchases of longer maturity US government debt. Figure 32.3 below shows the evolution of the asset side of the Federal Reserve’s balance sheet over t...
he money multiplier in turn is a function of the cash deposit ratio, the required reserve ratio, and the excess reserve ratio. The central bank only controls the second of these ratios. • The money multiplier steady declined in the 20 years prior to the Great Recession. During the Great Recession the money multiplier d...
ts r2 then the household will prefer deposits to holding cash. If the bank can oﬀer rd > 1, then it has engaged in what we will call liquidity transformation. By this we mean that, by pooling resources and playing probabilities with a large number of depositors, the bank creates an asset that is more liquid than the pr...
d the bank will become insolvent. The former is the “good” equilibrium, while the latter is the “bad” bank run equilibrium. We illustrate the outcomes of these two equilibria continuing with the example with which we have been working: Example We know from above that the cutoﬀ value H = 47.5. If G ≤ 47.50, then only th...
able 33.4: T-Account for Hypothetical Bank Assets Loans: $100 Securities: $0 Cash Reserves: $0 Equity $20 Liabilities plus Equity Deposits: $60 Borrowings: $20 In this way, through the discount window the bank can attract more liabilities (borrowings) to make up for an unexpected withdrawal, which can allow it to meet ...
In spite of these diﬀerent terms, we will refer to all three types of securities as “bonds.” In this chapter we will ﬁrst discuss the main type of cash ﬂow repayment plans oﬀered by bonds. Then we will discuss how to infer the interest rate on a bond in terms of the market price of the bond and the promised cash ﬂows. ...
s is that it makes it easier to compare bonds with diﬀerent maturities or cash ﬂow characteristics. For example, a bond with a face value of $10,000 will almost certainly trade for a higher price than a bond with a face value of $1,000. But this doesn’t necessarily mean that the $10,000 bond will provide a better expec...
𝑌𝑌1,𝑡𝑡+1) 𝑃𝑃1,𝑡𝑡 𝑌𝑌1,𝑡𝑡+1>𝑌𝑌0,𝑡𝑡+1 that the yield to maturity is the discount rate which equates the bond price with the present discounted value of expected future cash ﬂows from the bond. There is no uncertainty here, and the bond yields 1 unit of income in period t + 1. Hence, the yield must satisfy:...
ﬂuence the prices of each bond as well as the implied yields on each type of bond. = 1.1 and Y l t+1 789 34.3.1 No Income Risk First, consider a speciﬁcation of uncertainty in which there is no income risk – future income is either high with probability 1 (so p1 + p2 = 1 and p3 = 0), or low with probability 1 (so p1 = ...
nnot hold any of either the risky or the risk-free bond, and hence must be indiﬀerent between them. For the household to be indiﬀerent between the two types of bonds, the yield on the risky bond must be higher than the yield on the risk-free bond. The third row considers the opposite case – income can be high or low, b...
ﬁnal period of life. It has income from three sources – exogenous income ﬂow, Yt+2; maturing one period bonds brought from the previous period, Bt+1,t+1,t+2; and maturing two period bonds brought from the previous period, Bt+1,t,t+2. The household’s objective in period t is to pick a consumption/saving plan which maxim...
se much by making the simplifying assumption that the income draws in periods t + 1 and t + 2 are independent from one another. As when we considered default risk above, ﬂow budget constraints must hold in each possible state of the world. In period t + 1, there are two states of the world – either the 806 endowment is...
ions hypothesis as laid out in the previous subsection under certainty would hold. Otherwise, the simple expectations hypothesis does not hold exactly, though the logic of the expectations hypothesis is still at play. In particular, changes in expected future short maturity bond prices ought to be reﬂected in current l...
P B t,t,t+2u′(Ct) = β E [P B P B t,t,t+3u′(Ct) = β E [P B P B t+1,t,t+2u′(Ct+1)] t+1,t,t+3u′(Ct+1)] (34.113) (34.114) (34.115) In equilibrium, consumption will equal income regardless of date or state of nature. Hence we can impose this market-clearing condition to solve for equilibrium bond prices. (34.114) can be com...
skless interest rates, impact the economy? From a saver’s perspective, the key point is that bonds of diﬀerent types (either diﬀering in maturity or default risk) are substitutes. Purchasing bonds is simply a means by which to transfer resources intertemporally and hence to smooth consumption. In fact, once one adjusts...
P B t,t,t+2 E[Dt+2] E[Dt+2u′(Yt+2)] E[Dt+2] E[u′(Yt+2)] (34.157) (34.158) One would be tempted to distribute the expectations operator in the numerator and hence cancel out the fraction in (34.158), but as we have seen again and again, in general this is not possible. Rather, we can use the by-now-familiar relationshi...
s, so credibility is important. Quantitative easing involves purchasing, in large amounts, non-traditional securities, such as longer term government debt or private-sector risky debt. The basic idea behind quantitative easing is straightforward – if one can increase the demand for these types of debt, one ought to be ...
ctive? 838 Chapter 35 The Stock Market and Bubbles A stock is a type of ﬁnancial security that is sometimes called an equity. It is called an equity because an owner of a share of stock is an owner in the company issuing the stock. Shareholders are entitled to the current and future proﬁts generated by the company. Lik...
ginal utility beneﬁt of purchasing an additional bond in t is an additional unit of income in t + 1, which is valued at β E [u′(Ct+1)] (i.e. the expected marginal utility of consumption). Hence, the right hand side of (35.14) is the marginal utility beneﬁt of purchasing an additional unit of the bond. At an optimum, th...
ether income is high or low. Since the payout on the bond is also uncorrelated with the realization of income, and since the bond and the stock oﬀer the same expected payout, they trade for the same price and there is no diﬀerence in yields. The third row considers an intermediate case; the dividend payout is positivel...
y function be the natural log. We assume that = 0.9. Assume that the two values income can take on in the future are Y h 1+1 = 0.95. Assume the ﬁrst stock oﬀers a relatively stable dividend, with dh = 1.5 that the dividend of the second stock is much more volatile. In particular, let dh = 0.5. Let us specify the probab...
,l,h t+2 ) + q15u(C l,l,l,h t+2 ) + q16u(C l,h,l,h t+2 )] (35.69) We can again invoke terminal conditions to simplify the analysis. In particular, the household will not choose to die with positive stocks of bonds or stock in t + 2. This means that Bt+2 = 0 and SHt+2 = 0 regardless of the realization of uncertainty. It...
stock is procyclical), investors will demand a higher yield to hold the stock in comparison to the risk-free bond (i.e. the equity premium will be positive). t+1 t+2 t+1 t+2 t+1 t+2 = dl = dh = Y l = Y h t+2 = 1.1 and dl = 1.1 and Y l Let us now do a couple of quantitative experiments with actual numbers. Suppose that ...
ock (i.e. the more its payouts covary with the stochastic discount factor), the higher should be the discount rate applied to the stock, and hence such a stock should 864 trade at a comparatively low price-dividend ratio. Finally, decreases in interest rates in the economy as a whole ought to generally be good for stoc...
horizons. We can generate a simulation of the stock price by simulating a process for dividends. Suppose that β = 0.95. Suppose further that ¯d = 1, ρ = 0.98, and s = 0.02. We simulate 1000 periods of dividends. At each point, we calculate the fundamental stock price using (35.134). A hypothetical time series of the s...
argument is that central banks ought to adjust interest rates to prevent bubbles from occurring. John Taylor of Stanford university, for example, has argued that the housing market bubble was driven by the Fed keeping its policy rate too low for too long in the early 2000s. It is easy to see why low interest rates can...
dividends. Hence: Using (35.150), we can write (35.153) as: Vt = Dt + QtSHt Vt = Dt + βu′(Ct+1)dt+1 u′(Ct) SHt (35.153) (35.154) But from (35.148), we know that βu′ u′ we can write the total value of the ﬁrm as: (Ct+1) (Ct) = 1 1+rt . Furthermore, dt+1SHt = Dt+1. Hence, Vt = Dt + Dt+1 1 + rt (35.155) In other words, th...
t summarizes a couple of special cases. When γ → ∞, we must have Yt = Y f t and the model collapses to the Neoclassical Model. When γ = 0, in contrast, we have the simple sticky price model. For values of γ lying in between we have the partial sticky price model. The endogenous variables are Yt, Ct, It, Nt, wt, rt, it,...
ill be a reduction in investment. This results in the AD curve shifting in to the left. To the extent to which the AS curve is non-horizontal, the price level falls. The fall in the price level causes the LM curve to shift out to the right somewhat. In equilibrium, rt is lower and Yt is lower. Lower Yt must be met by l...
f this shift as resulting from an increase in Gt, but qualitatively we would get the same picture if we considered a reduction in Gt+1, an increase in At+1, or a reduction in ¯ft. 897 𝑌𝑌𝑡𝑡 𝑟𝑟𝑡𝑡 𝑌𝑌𝑡𝑡 𝑃𝑃𝑡𝑡 𝐼𝐼𝐼𝐼 𝐿𝐿𝐿𝐿(𝑃𝑃0,𝑡𝑡) 𝐿𝐿𝐿𝐿(𝑃𝑃1,𝑡𝑡) 𝐿𝐿𝐿𝐿(𝑃𝑃2,𝑡𝑡) 𝑃𝑃0,𝑡𝑡 𝑃𝑃1,𝑡𝑡 𝑃𝑃2,...
ds? Typically, ﬁnancial crises are preceded by asset price booms and busts. Although popular in the ﬁnancial press, we hesitate to associate the term “bubble” with such boom and bust episodes, because what a “bubble” is in from an economists’ perspective is slightly diﬀerent than what the ﬁnancial press typically means...
s (ourselves included) believe that the Great Recession was not as bad as it might have been because of the extraordinary policy actions taken by the Fed. We will discuss some of these extraordinary policy actions in more depth below. 37.2 The Great Recession: Some More Speciﬁcs on the Run In this section we provide a ...
earing that their counterparties were at risk and that the underlying collateral was not valuable, short term funders (like Fidelity in the example) began demanding haircuts on repurchase agreements. Prior to the crisis, haircuts were zero. At the height of the crisis, haircuts rose to more than 40 percent. A 40 percen...
was the ﬁnancial crisis, which began in late 2007 and intensiﬁed throughout 2008. The third and most virulent stage is the further intensiﬁcation of the ﬁnancial crisis at the end of 2008 and into the ﬁrst half of 2009, exacerbated by the fact that the zero lower bound on interest rates had become binding by the end o...
ee that monetary policy should be the ﬁrst line of defense against a recession. During a time where monetary policy is constrained by the ZLB, ﬁscal policy may not only be the only available tool but might also be more eﬀective in comparison to normal times. Finally, the third set of policies involved unconventional mo...
hift of the IS curve because of “crowding out” associated with increases in the real interest rate. At the ZLB, in contrast, the vertical AD curve ought to shift out horizontally to the right by the same amount as the shift of the IS curve because there is no crowding out if the interest rate is ﬁxed at its lower bound...
e related debt securities and/or longer maturity Treasury 933 𝑃𝑃𝑡𝑡𝐵𝐵 𝐵𝐵𝑡𝑡 𝐷𝐷 𝑆𝑆 𝑃𝑃0,𝑡𝑡𝐵𝐵 𝐵𝐵0,𝑡𝑡 securities.1 The Fed would create base money by creating reserves to purchase these securities from private banks. Quantitative easing (or QE, for short) proceeded in three distinct waves. The ﬁrst wa...
wer ft, and hence the relevant interest rate for investment spending, without adjusting the short term Federal Funds Rate. If successful, the decrease in ft would shift the IS curve to the right with a resulting rightward shift of the AD curve. The desired eﬀects of these interventions are shown in Figure 37.23 3The wo...
m?” Journal of Monetary Economics 60(5):535–549. Cubas, German, B. Ravikumar, and Gustavo Ventura. 2016. “Talent, labor quality, and economic development.” Review of Economic Dynamics 21:160 – 181. URL http://www. sciencedirect.com/science/article/pii/S109420251500040X. Delong, Bradford. 1998. “Estimating World GDP, On...
. . . . 64 4.5 Return on capital in the US 1950-2011. 4.6 Wages in the US 1950-2011. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 4.7 Relationship Between Human Capital and Income per Person . . . . . . . . . . 69 5.1 Plot of Central Equation of Solow Model . . . . . . . . . . . . . . . . . . . . . . ...
ilibrium in the Money Market . . . . . . . . . . . . . . . . . . . . . . . . . . . 428 19.3 Increase in At . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430 19.4 Increase in At: The Money Market . . . . . . . . . . . . . . . . . . . . . . . . . . 431 19.5 Increase in At+1 . . . . . . . ....
. . . . . . . . . . 640 28.10IS Shocks and the Natural Rate of Interest . . . . . . . . . . . . . . . . . . . . . 641 28.11Y f t Shocks and the Natural Rate of Interest . . . . . . . . . . . . . . . . . . . . . 642 28.12Using Fiscal Policy to Combat an IS Shock . . . . . . . . . . . . . . . . . . . . . 644 28.13Actual...
. . . . . . . . . . . 1010 . . . . . . . . . . . . . . . . . . . . . 1012 D.2 The Sticky Wage AS Curve: Increase in At 957 D.3 The Sticky Wage AS Curve: Increase in ¯Wt . . . . . . . . . . . . . . . . . . . . . 1013 D.4 Sticky Wage IS-LM-AD-AS Equilibrium . . . . . . . . . . . . . . . . . . . . . . . 1016 D.5 Eﬀects of...
44 32.42Bank D Makes a Loan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745 32.43Non-Bank Public Gets a Loan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 745 32.44Non-Bank Public Withdraws Cash . . . . . . . . . . . . . . . . . . . . . . . . . . 745 32.45Funds are Withdrawn from Ban...
cally refers to gX t as the “net growth rate” and 1 + gX t as the “gross growth rate.” The gross growth rate is just equal to the ratio of a variable across time. A useful fact is that the log of one plus a small number is approximately equal to the small number. In particular: ln(1 + α) ≈ α (A.20) Table A.2 shows the ...
lls you how Yt changes as both variables change. Furthermore, whereas a partial derivative only tells you how Yt changes for a small change in Xt, the total derivative can be used to approximate the eﬀects on Yt of a large change in Xt. Formally, the total diﬀerential can be derived using a ﬁrst order Taylor series app...
e problem an unconstrained one in just choosing X: max X ln X + ln(1 − X) 981 The ﬁrst order condition is: Now solve for XA.52) (A.53) We can then solve for the optimal value of Z by plugging this back into the constraintA.54) An alternative way to solve a constrained optimization problem is to use the method of Lagran...
e arithmetic mean of all possible realizations is 5. It is important to weight potential realizations by their probability of occurring. (B.3) piXi However, the arithmetic mean of a sample of realizations of a random variable ought to correspond to its expected value in a large enough sample. Suppose that you are a sta...
ext, i.e. how much does a series tend to move around over time) and a measure of dispersion (in a cross-sectional context, i.e. how diﬀerent do individuals on average look from one another at a point in time). There are a couple of useful properties of variance. First, the variance of a constant times a random variable...
en a sample of observed data. Let µX and µY denote the sample arithmetic means of X and Y , and σX and σY denote the sample standard deviations (all deﬁned above). Then the sample covariance is: ̂cov(X, Y ) = ∑T i=1 (Xi − µX)(Yi − µY ) T (B.34) The “hat” appears atop the covariance operator in (B.34) to refer to the fa...
age rises by more, and labor input rises by less. Indeed, it is conceivable that Nt could 1005 𝑤𝑤𝑡𝑡 𝑟𝑟𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑁𝑁𝑡𝑡 𝑁𝑁𝑡𝑡 𝑌𝑌𝑡𝑡𝑑𝑑 𝑌𝑌𝑠𝑠 𝐼𝐼𝐼𝐼 𝑤𝑤0,𝑡𝑡 𝑟𝑟0,𝑡𝑡 𝑌𝑌0,𝑡𝑡 𝑁𝑁0,𝑡𝑡 𝑁𝑁𝑑𝑑(𝑤𝑤𝑡𝑡,𝐴𝐴0,𝑡𝑡,𝐾𝐾𝑡𝑡) 𝑁𝑁𝑠𝑠(𝑤𝑤𝑡𝑡,𝜃𝜃𝑡𝑡,𝑟�...
elevant for the position of the AS curve here, and that is ¯Wt. Suppose that ¯Wt were to increase. Holding the price level ﬁxed at P0,t, this would result in a higher real wage. Along the 1013 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑌𝑌𝑡𝑡 𝑁𝑁𝑡𝑡 𝑁𝑁𝑡𝑡 𝑤𝑤𝑡𝑡 𝑃𝑃𝑡𝑡 𝑃𝑃0,𝑡𝑡 𝑊𝑊�𝑡𝑡𝑃𝑃0,𝑡𝑡� 𝑌𝑌𝑡𝑡=𝑌𝑌𝑡𝑡 𝑌𝑌�...
market. The higher price level results in the real wage rising. This means that the increase in labor input will be smaller than if the price level were ﬁxed (put another way, the change in equilibrium output is smaller than the horizontal shift of the AS curve). Depending on the relative slopes of the AD and AS curve...
higher than it would be if the nominal wage were ﬂexible, Y f output, Y sr 0,t. This is depicted in Figure D.11. The AD and AS curves intersect to the right of the hypothetical ﬂexible wage AS curve. This means that labor input is higher than it would be if wages were ﬂexible. Put diﬀerently, this means that the equili...
n Variable Yt Nt wt rt it Pt Exogenous Shock ↑ IS curve - ↑ Mt - ↑ At + - + + + + - + + + + + - - - - 1038 Appendix E Replacing the LM Curve with the MP Curve E.1 The AD Curve when the MP Curve Replaces the LM Curve In Chapters 24, 26, and 28 we characterize monetary policy with the money supply, Mt. When drawing the L...
al neoclassical Pt = ¯Pt + γ(Yt − Y f t ) (E.8) 1045 𝑟𝑟𝑡𝑡 𝑟𝑟𝑡𝑡 𝑌𝑌𝑡𝑡 𝜋𝜋𝑡𝑡 𝜋𝜋𝑡𝑡 𝜋𝜋𝑡𝑡 𝜋𝜋𝑡𝑡 𝑌𝑌𝑡𝑡 𝐼𝐼𝐼𝐼 𝜋𝜋𝑡𝑡=𝜋𝜋𝑡𝑡 𝑟𝑟̅𝑡𝑡 𝐴𝐴𝐴𝐴 𝜋𝜋0,𝑡𝑡 𝜋𝜋1,𝑡𝑡 𝜋𝜋2,𝑡𝑡 𝑌𝑌0,𝑡𝑡=𝑌𝑌0,𝑡𝑡′ 𝑌𝑌2,𝑡𝑡 𝑟𝑟0,𝑡𝑡=𝑟𝑟0,𝑡𝑡′ 𝑟𝑟1,𝑡𝑡 𝑟𝑟2,𝑡𝑡 𝑀𝑀𝑀𝑀 (𝜙𝜙𝜋𝜋 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠...
noted above we can think about the central bank eﬀectively determining the slope of the AD curve through its choice of the parameter φπ. As φπ gets bigger, the AD curve gets ﬂatter, as shown above in Figure E.5. In the limiting case, as φπ → ∞, the AD curve becomes completely horizontal. With a horizontal AD curve, sh...
college level textbook. The impetus for this project was the recognition that, while any college level introductory textbook can be adapted for use in an AP Economics course, no existing textbook is sufficient for the task. The existing textbooks cover large amounts of material that is not included on the AP Course Out...
tion of inputs. The last module in the section discusses the marginal productivity theory of income distribution and various sources of wage differentials. Section 14: Market Failure and the Role of Government This section focuses on the conditions under which markets fail and explains public and private approaches to ...
ces had risen to levels far beyond what people who actually wanted to live in houses were willing to pay The abrupt collapse of the housing market pulled the local economy down with it, as the process that had created the earlier boom operated in reverse. The boom and bust in Ft. Myers illustrates, on a small scale, th...
e and a shift in demand, providing a clear presentation of a difficult topic. Price of coffee beans (per pound) $2.00 1.75 1.50 1.25 1.00 0.75 0.50 A shift of the demand curve . . . A C B . . . is not the same thing as a movement along the demand curve. D1 D2 0 7 8.1 9.7 10 15 13 Quantity of coffee beans (billions of p...
n adapt this approach to problems involving any macroeconomic model, including models of aggregate demand and supply, production possibilities, money markets, and the Phillips curve. By the end of this module you will be able to combine mastery of the principles of macroeconomics with problem solving skills to analyze ...
ose input helped guide the second edition of Krugman and Wells’ Economics. Carlos Aguilar, El Paso Community College; Terence Alexander, Iowa State University; Morris Altman, University of Saskatchewan; Farhad Ameen, State University of New York, Westchester Community College; Christopher P. Ball, P R E F A C E xxxiii ...
ok, people whose hard work, creativity, dedication, and patience continue to amaze us. Thank you all: Tracey Kuehn and Kerry O’Shaughnessy for producing this book; Kevin Kall, Lissi Sigillo, and TSI Graphics for their beautiful interior design and the absolutely spectacular cover; Barbara Seixas, who worked her magic o...
duction with choices about consumption, and distributes goods and services to the people who want them. The United States has a market economy, in which production and consumption are the result of decentralized decisions by many firms and individuals. There is no central authority telling people what to produce or whe...
whether or not they are monetary costs, of making that choice. The choice to go to college at all provides an important final example of opportunity costs. High school graduates can either go to college or seek immediate employment. Even with a full scholarship that would make college “free” in terms of monetary costs,...
utation come from? One important answer is that media coverage tends to exaggerate the real differences in views among economists. If nearly all economists agree on an issue—for example, the proposition that rent controls lead to housing shortages—reporters and editors are likely to conclude that there is no story wort...
ooverville”? These shantytowns were named after President Herbert Hoover, who had been elected president in 1928. When the Depression struck, people blamed the president: neither he nor his economic advisers seemed to understand what had happened or to know what to do. At that time, the field of macroeconomics was stil...
regard price stability—meaning that the overall price level is changing either not at all or only very slowly—as a desirable goal because it helps keep the economy stable. Economic Growth In 1955 Americans were delighted with the nation’s prosperity. The economy was expanding, consumer goods that had been rationed dur...
shows a hypothetical production possibilities curve for Tom, a castaway alone on an island, who must make a trade-off between fish production and coconut You make a trade-off when you give up something in order to have something else. The production possibilities curve illustrates the trade-offs facing an economy that ...

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