The average income of farmers is less than the average income of non-farmers, but fluctuates more from year to year. Given this, how does the permanent-income hypothesis predict that estimated consumption functions for farmers and non farmers differ?
> This question asks you to use a Solow-style model to investigate some ideas that have been discussed in the context of Thomas Piketty’s recent work (see Piketty, 2014; Piketty and Zucman, 2014; Rognlie, 2015). Consider an economy described by the assumpt
> Consider the model of Section 11.4. (a) Use equations (11.65) and (11.69), together with the fact that VV =0 in equilibrium, to find an expression for E as a function of the wage and exogenous parameters of the model. (b) Show that the impact of a rise i
> Assume that both labor and capital are paid their marginal products. Let w denote ∂F(K,AL)/∂L and r denote [∂F(K,AL)/∂K]−δ. (a) Show that the marginal product of labor, w, is A[ f(k)−kf (k)]. (b) Show that if both capital and labor are paid their margina
> Suppose that investment as a fraction of output in the United States rises permanently from 0.15 to 0.18. Assume that capital’s share is 1 3 . (a) By about how much does output eventually rise relative to what it would have been without the rise in inve
> Find the elasticity of output per unit of effective labor on the balanced growth path, y∗, with respect to the rate of population growth, n. IfαK(k∗) = 1 3 , g = 2%, and δ = 3%, by about how much does a fall in n from 2 percent to 1 percent raise y∗?
> Consider a Solow economy that is on its balanced growth path. Assume for simplicity that there is no technological progress. Now suppose that the rate of population growth falls. (a) What happens to the balanced-growth-path values of capital per worker,
> Suppose that the production function is Cobb Douglas. (a) Find expressions for k∗, y∗, and c∗ as functions of the parameters of the model, s, n, δ, g, and α. (b) What is the golden-rule value of k? (c) What saving rate is needed to yield the golden-rule
> Consider an economy with technological progress but without population growth that is on its balanced growth path. Now suppose there is a one-time jump in the number of workers. (a) At the time of the jump, does output per unit of effective labor rise, f
> Describe how, if at all, each of the following developments affects the break-even and actual investment lines in our basic diagram for the Solow model: (a) The rate of depreciation falls. (b) The rate of technological progress rises. (c) The production
> Suppose that the growth rate of some variable, X, is constant and equal to a > 0 from time 0 to time t1; drops to 0 at time t1; rises gradually from 0 to a from time t1 to time t2; and is constant and equal to a after time t2. (a) Sketch a graph of the g
> Use the fact that the growth rate of a variable equals the time derivative of its log to show: (a) The growth rate of the product of two variables equals the sum of their growth rates. That is, if Z(t)=X(t)Y(t), then Z(t)/Z(t)=[X(t)/X(t)]+[Y(t)/Y(t)]. (b
> This problem asks you to show that with some natural variants on the approach to modeling agency riskin Problem10.7, consumption is not linear in the shocks, which renders the model intractable. (a) Consider the model in Problem 10.7. Suppose, however, t
> Consider the model of Section 11.4. Suppose the economy is initially in equilibrium, and that y then falls permanently. Suppose, however, that entry and exit are ruled out; thus the total number of jobs, F + V, remains constant. How do unemployment and v
> Consider Problem 10.6. Suppose, however, that the demand of the period-0 noise traders is not fully persistent, so that noise traders’ demand in period 1 is ρN0+N1,ρ0. They have no initial wealth. (a) Consider first period 1. (i) Consider a representativ
> Consider the previous problem. For simplicity, assume A0 = 0. Now, however, there is a third type of agent: hedge-fund managers. They are born in period 0 and care only about consumption in period 2. Like the sophisticated investors, they have utility U(
> Consider the following variant on the model of noise-trader risk in equations (10.15) (10.23). There are three periods, denoted 0, 1, and 2. There are two assets. The first is a safe asset in perfectly elastic supply. Its rate of return is normalized to
> (a) Show that in the model analyzed in equations (10.15) (10.23) of Section 10.4, the unconditional distributions of Ca 2t and Cn 2t are not normal. (b) Explain in a sentence or two why the analysis in the text, which uses the properties of lognormal dis
> Consider the model of Section 10.2 with a different friction: there is no cost of verifying output, but the entrepreneur can hide fraction 1−f of the project’s output from the investor (with 0 ≤ f ≤ 1). Thus the entrepreneur can only credibly promise to
> Consider the model of investment under asymmetric information in Section 10.2. Suppose that initially the entrepreneur is undertaking the project, and that (1 + r)(1−W) is strictly less than RMAX. Describe how each of the following affects D: (a) A small
> Consider the model of Section 10.1. Suppose, however, that there are M households, and that household j’s utility is Vj = U(C1) + βs jU(C2), where βs j > 0 for all j and s. That is, households may have heterogeneous preferences about consumption in diffe
> Consider deposit insurance in the Diamond Dybvig model of Section 10.6. (a) If fraction φ>θof depositors withdraw in period 1, how large a tax must the government levy on each agent in period 1 to be able to increase the total consumption of the non with
> Consider the Diamond Dybvig model described in Section 10.6, but suppose that ρR < 1. (a) In this case, what are ca∗ 1 and cb∗ 1 ? Is cb∗ 1 still larger than ca∗ 1 ? (b) Suppose the bank offers the contract described in the text: anyone who deposits one
> Consider modeling the noise traders in the model of equations (10.15) (10.23) of Section 10.4 in terms of shocks to the quantity they demand of the risky asset rather than to their expectations of the price of the asset. Specifically, suppose the demand
> Consider the steady state of the Diamond Mortensen Pissarides model of Section 11.4. (a) Suppose that φ =0. What is the wage? What does the equilibrium condition (11.70) simplify to? (b) Suppose that φ =1. What is the wage? What does the equilibrium cond
> Consider the model of Section 10.1. Assume that utility is logarithmic, that β =1, and that there are only two states, each of which occurs with probability one-half. In addition, assume there is only one investment project. It pays RG in state G and RB
> Let H denote the stock of housing, I the rate of investment, pH the real price of housing, and R the rent. Assume that I is increasing in pH, so that I =I(pH), with I(•) > 0, and that H =I − δH. Assume also that the rent is a decreasing function of H: R=
> Consider the model of investment in Sections 9.2 9.5. Suppose it becomes known at some date that there will be a one-time capital levy. Specifically, capital holders will be taxed an amount equal to fraction f of the value of their capital holdings at so
> Consider the model of investment in Sections 9.2 9.5. Describe the effects of each of the following changes on the K = 0 and q = 0 loci, on K and q at the time of the change, and on their behavior over time. In each case, assume that K and q are initiall
> Consider the Romer model of Section 3.5. For simplicity, neglect the constraint that LA cannot be negative. Set up the problem of choosing the path of LA(t) to maximize the lifetime utility of the representative individual. What is the control variable?
> Consider the social planner’s problem that we analyzed in Section 2.4: the planner wants to maximize∞ t=0 e−βt[c(t)1−θ/(1−θ)]dt subject to k(t)=f (k(t))−c(t)−(n+g)k(t). (a) What is the current-value Hamiltonian? What variables are the control variable,
> Consider an individual choosing the path of G to maximize∞ t=0 e−ρt− a 2G(t)2dt, a > 0, ρ>0.Here G(t) is the amount of garbage the individual creates at time t; for simplicity, we allow for the possibility that G can be negative. The individual’s creatio
> The major feature of the tax code that affects the user cost of capital in the case of owner-occupied housing in the United States is that nominal interest payments are tax-deductible. Thus the after-tax real interest rate relevant to home ownership is r
> Corporations in the United States are allowed to subtract depreciation allowances from their taxable income. The depreciation allowances are based on the purchase price of the capital; a corporation that buys a new capital good at time t can deduct fract
> Consider the analysis of the effects of uncertainty about discount factors in Section 9.7. Suppose, however, that the firm finances its investment using a mix of equity and risk-free debt. Specifically, consider the financing of the marginal unit of capi
> Describe how each of the following affects steady-state employment in the Diamond Mortensen Pissarides model of Section 11.4: (a) An increase in the job breakup rate, λ. (b) An increase in the interest rate, r. (c) An increase in the effectiveness of mat
> Consider a firm that is contemplating undertaking an investment with a cost of I. There are two periods. The investment will pay off π1 inperiod1and π2 inperiod2. π1 is certain, but π2 is uncertain. The firm maximizes expected profits and, for simplicity
> Consider the model of investment with kinked adjustment costs in Section 9.8. Describe the effect of each of the following on the q =0 locus, on the area where K = 0, on q and K at the time of the change, and on their behavior over time. In each case, as
> Consider the model of investment under uncertainty with a constant interest rate in Section 9.7. Suppose that, as in Problem 9.10, π(K) = a −bK and that C(I) = αI 2/2. In addition, suppose that what is uncertain is future values of a. This problem asks y
> Suppose that π(K)=a −bK and C(I)= αI 2/2. (a) What is the q =0 locus? What is the long-run equilibrium value of K? (b) What is the slope of the saddle path? (Hint: Use the approach in Section 2.6.)
> Suppose the costs of adjustment exhibit constant returns in κ and κ. Specifically, suppose they are given by C(κ/κ)κ, where C(0) = 0, C(0) = 0, C(•) > 0. In addition, suppose capital depreciates at rate δ; thus κ(t) = I(t)−δκ(t). Consider the representat
> Consider a firm that produces output using a Cobb Douglas combination of capital and labor: Y=KαL1−α,0
> Consider the setup of the previous problem without the assumption that lims→∞ Et [Pt+s/(1+r)s]=0. (a) Deterministic bubbles. Suppose that Pt equals the expression derived in part (b) of Problem 8.8 plus (1+r)tb, b > 0. (i) Is consumers’ first-order condi
> Consider a stock that pays dividends of Dt in period t and whose price in period t is Pt. Assume that consumers are risk-neutral and have a discount rate of r; thus they maximize E[∞ t=0 Ct/(1+r)t ]. (a) Show that equilibrium requires Pt = Et[(Dt+1 + Pt+
> Consider the two-period setup analyzed in Section 8.4. Suppose that the government initially raises revenue only by taxing interest income. Thus the individual’s budget constraint is C1 +C2/[1+(1− τ)r] ≤ Y1 +Y2/[1+(1− τ)r], where τ is the tax rate. The g
> Suppose that Ct equals [r/(1+r)]{At +∞ s =0 Et [Yt+s]/(1+r)s}, and that At+1 =(1+r )(At +Yt −Ct). (a) Show that these assumptions imply that Et[Ct+1]=Ct (and thus that consumption follows a random walk) and that ∞ s=0 Et [Ct+s]/(1 + r )s =At + ∞ s=0 Et [
> In the setup described in Problem 11.10, suppose that w is distributed uniformly on [μ−a,μ+a] and that C V, and rejects it if ˆw
> Suppose instantaneous utility is of the constant-relative-risk-aversion form, u(Ct)=C1−θ t /(1−θ),θ>0. Assume that the real interest rate, r, is constant but not necessarily equal to the discount rate, ρ. (a) Find the Euler equation relating Ct to expect
> In the model of Section 8.2, uncertainty about future income does not affect consumption. Does this mean that the uncertainty does not affect expected lifetime utility?
> Actual data do not give consumption at a point in time, but average consumption over an extended period, such as a quarter. This problem asks you to examine the effects of this fact. Suppose that consumption follows a random walk: Ct = Ct−1 +et, where e
> Consider the following seemingly small variation on part (b) of Problem 8.16. Choose an N, and define e ≡ 200/N. Now, assume that Y can take on only the values 0,e,2e,3e,...,200, each with probability 1/(N+1). Likewise, assume that C can only take on the
> Consider the dynamic programming problem that leads to Figure 8.4. This problem asks you to solve the problem numerically with one change: preferences are logarithmic, so that u(C) = lnC. Specifically, it asks you to approximate the value function by val
> Consider an individual who lives for three periods. In period 1, his or her objective function is lnc1 +δ lnc2 +δ lnc3, where 0
> Consider an individual who lives for two periods and has constant-absolute risk-aversion utility, U =−e−γC1 − e−γC2,γ>0. The interest rate is zero and the individual has no initial wealth, so the individual’s lifetime budget constraint is C1 +C2 = Y1 +Y2
> Suppose that the utility of the representative consumer, individual i, is given by T t=1 [1/(1+ρ)t](Cit/Zit)1−θ/(1−θ), ρ>0,θ>0, where Zit is the ‘‘reference” level of consumption. Assume the interest rate is constant at some level, r, and that there is n
> Suppose that, as in Section 8.2, the instantaneous utility function is quadratic and the interest rate and the discount rate are zero. Suppose, however, that goods are durable; specifically, Ct =(1−δ)Ct−1 + Xt, where Xt is purchases in period t and 0≤ δ
> Consider a worker searching for a job. Wages, w, have a probability density function across jobs, f (w), that is known to the worker; let F(w) be the associated cumulative distribution function. Each time the worker samples a job from this distribution,
> Consider an economy with two possible states, each of which occurs with probability one-half. In the good state, each individual’s consumption is 1. In the bad state, fraction λ of the population consumes 1−(φ/λ) and the remainder consumes 1, where 0
> Suppose the only assets in the economy are infinitely lived trees. Output equals the fruit of the trees, which is exogenous and cannot be stored; thus Ct = Yt, where Yt is the exogenously determined output per person and Ct is consumption per person. Ass
> Consider an individual who lives from 0 to T, and whose lifetime utility is given by U =T t=0 u(C(t))dt, where u(•) > 0,u(•) < 0. The individual’s income is Y0 +gt for 0 ≤ t < R, and 0 for R ≤ t ≤ T. The retirement age, R, satisfies 0 < R < T. The intere
> Consider the new Keynesian Phillips curve with indexation, equation (7.76), under the assumptions of perfect foresight and β=1, together with our usual aggregate demand equation, yt =mt −pt. (a) Express pt+1 in terms of its lagged values and mt. (b) Cons
> Consider a continuous-time version of the Taylor model, so that p(t)=(1/T )T τ=0 x(t−τ)dτ, where T is the interval between each firm’s price changes and x(t−τ) is the price set by firms that set their prices at time t−τ. Assume that φ =1, so that p∗ i (t
> Consider an economy like that of the Caplin Spulber model. Suppose, however, that m can either rise or fall, and that firms therefore follow a simple two-sided Ss policy: if pi − p∗ t reaches either S or −S, firm i changes pi sothat pi−p∗ t equals 0. As
> Consider the experiment described at the beginning of Section 7.4. Specifically, a Calvo economy is initially in long-run equilibrium with all prices equal to m, which we normalize to zero. In period 1, there is a one-time, permanent increase in m to m1.
> Repeat Problem 7.4 using lag operators. Data from Problem 7.4: Consider the Taylor model with the money stock white noise rather than a random walk; that is, mt =εt, where εt is serially uncorrelated. Solve the model using the method of undetermined co
> Consider the Taylor model with the money stock white noise rather than a random walk; that is, mt =εt, where εt is serially uncorrelated. Solve the model using the method of undetermined coefficients.
> Consider the Taylor model. Suppose, however, that every other period all the firms set their prices for that period and the next. That is, in period t prices are set for t and t +1; in t +1, no prices are set; in t +2, prices are set for t+2 and t+3; and
> Suppose there are two sectors. Jobs in the primary sector pay wp; jobs in the secondary sector pay ws. Each worker decides which sector to be in. All workers who choose the secondary sector obtain a job. But there are a fixed number, Np, of primary-secto
> Consider the efficiency-wage model analyzed in equations (11.12) (11.17). Suppose, however, that fraction f of workers belong to unions that are able to obtain a wage that exceeds the nonunion wage by proportion μ. Thus, wu = (1+μ)wn, where wu and wn den
> Moulton Corporation engaged in the following seven transactions during December, Year 12, in preparation for opening the business on January 1, Year 13. We continue with data for Moulton Corporation in Chapter 3, Problem 3.22. You will not need some of t
> Express the following transactions of Winkle Grocery Store, Inc., in journal entry form. If an entry is not required, indicate the reason. You may omit explanations for the journal entries. The store: (1) Receives $30,000 from John Winkle in return for 1
> Assume that during Year 14, Inheritance Brands, a U.S. manufacturer and distributor, engaged in the following five transactions. Inheritance Brands applies U.S. GAAP and reports its results in millions of U.S. dollars ($). You may round to one significan
> Assume that during Year 15, Bullseye Corporation, a U.S. retailer, engages in the following six transactions. Bullseye Corporation applies U.S. GAAP and reports its results in millions of U.S. dollars ($). Do not be concerned that after these transaction
> GAAP classifies items on the balance sheet in one of the following ways: Asset (A) Liability (L) Shareholders’ equity (SE) Item that would not appear on the balance sheet as conventionally prepared under GAAP. (N/A) Using the abbreviations, indicate the
> GAAP classifies items on the balance sheet in one of the following ways: Asset (A) Liability (L) Shareholders’ equity (SE) Item that would not appear on the balance sheet as conventionally prepared under GAAP. (N/A) Using the abbreviations, indicate the
> When will a firm’s fiscal year differ from a calendar year?
> Cement Plus, a firm specializing in building materials, engaged in the following four transactions during 2014: (1) purchased and received inventory costing $14,300 million, of which $12,000 million was on account with the rest paid in cash; (2) purchase
> This chapter introduces both U.S. GAAP and International Financial Reporting Standards (IFRS). Which of these systems may U.S. firms use, and which may non-U.S. firms that list and trade their securities in the United States use?
> Consider the following information reported by DairyLamb, a New Zealand firm; all figures are in millions of New Zealand dollars ($). The firm reported revenues of $13,882, cost of goods sold of $11,671, interest and other expenses of $2,113, and tax exp
> Financial statements include amounts in units of currency. What is the most common determinant of a firm’s choice of currency for financial reporting?
> Heckle Group began operations as an engineering consulting firm, on June 1, 2013. On that date it issued 100,000 shares of common stock for €920,000. During June, Heckle used €600,000 of the proceeds to purchase office equipment. It acquired a patent for
> Kenton Limited began retail operations on January 1, 2013. On that date it issued 10,000 shares of common stock for £50,000. On January 31, Kenton used £48,000 of the proceeds to rent a store, paying in advance for the next two years. Kenton also purchas
> The statement of cash flows for Buenco, a firm in Argentina, showed a net cash inflow from operations of Ps427,182 and a net cash outflow for financing of Ps21,806. The comparative balance sheets showed a beginning balance in cash of Ps32,673 and an endi
> The statement of cash flows for Bargain Purchase, a retailer, showed a net cash inflow from operations of $4,125, a net cash outflow for investing of $6,195, and a net cash inflow for financing of $3,707. The balance sheet showed a beginning-of-year bala
> The balance sheet of Delvico, an Indian firm, showed retained earnings of Rs26,575 at the start of a year and Rs70,463 at the end of that year. The firm declared dividends during the year of Rs3,544. All amounts are in millions of Indian rupees (Rs). Com
> The balance sheet of Veldt, a South African firm, showed a balance in retained earnings of R5,872.4 at the end of 2013 and R4,640.9 at the end of 2012. Net income for the year was R2,362.5 million. All amounts are in millions of South African rand (R). C
> The income statement of AutoCo, a U.S. automotive manufacturer, reported revenues of $207,349, cost of sales of $164,682, other operating expenses, including income taxes, of $50,335, and net financing income, after taxes, of $5,690. Amounts are in milli
> Fresh Foods Group, a European food retailer that operates supermarkets in seven countries, engaged in the following three transactions during 2013: (1) purchased and received inventory costing €678 million on account from various suppliers; (2) returned
> The income statement of GrandRider, a U.K. automotive manufacturer, reported revenues of £7,435, cost of sales of £6,003, other operating expenses of £918, a loss of £2 on the sale of a business, and ne
> The balance sheet of GoldRan, a South African mining company, shows current assets of R6,085.1, noncurrent assets of R49,329.8, noncurrent liabilities of R13,948.4, and current liabilities of R4,360.1. GoldRan reports in millions of South African rand (R
> The balance sheet of EuroTel, a European Union communications firm, shows current assets of €20,000 million, current liabilities of €15,849 million, shareholders’ equity of €17,154 million, and noncurrent assets of €29,402 million. What is the amount of
> A firm recorded various transactions with the journal entries shown below. Using the notation O/S (overstated), U/S (understated), or No (no effect), indicate the effects on assets, liabilities, and shareholders’ equity of any errors in
> Refer to Exhibit 1.10, which contains income statement information that is based on the financial report of Capcion, an Austrian paper and packaging manufacturer. Capcion reports all amounts in thousands of euros (€). Answer the followin
> Refer to Exhibit 1.9, which contains balance sheet information from the financial report of Palmer Coldgate, a U.S. consumer products manufacturer. This firm reports all amounts in millions of U.S. dollars ($). Answer the following questions that pertain
> Using the notation O/S (overstated), U/S (understated), or No (no effect), indicate the effects on assets, liabilities, and shareholders’ equity of failing to record or recording incorrectly each of the following transactions or events. For example, a fa
> Whitley Products Corporation begins operations on April 1. The firm engages in the following transactions during April: (1) Issues 25,000 shares of $10 par value common stock for $15 per share in cash. (2) Acquires land costing $25,000 and a building cos
> Veronica Regaldo creates a new business in Mexico on January 1, Year 8, to operate a retail store. Transactions of Regaldo Department Stores during January Year 8 in preparation for opening its first retail store in February Year 8 appear below. Regaldo
> Patterson Corporation begins operations on January 1, Year 13. See the assumptions given at the end of the list. Problem 3.23 continues this problem. The firm engages in the following transactions during January: (1) Issues 15,000 shares of $10 par value
> Who prepares a firm’s financial statements?
> Why does every accounting transaction have two effects?
> Investing activities pertain to the acquisition of productive capacity to enable a firm to carry out its activities. Examples of this capacity include (1) land, buildings, and equipment and (2) patents and licenses. How are these two kinds of capacity th
