All Matches

Solution Library

Expert Answer

Textbooks

Search Textbook questions, tutors and Books

Oops, something went wrong!

Change your search query and then try again

Result Not Found

Books FREE
Tutors
Study Help
Hire a Tutor
AI Study Help New

Search
Sign In
Register

study help
business
foundations macroeconomics

Questions and Answers of Foundations Macroeconomics

1. Show that the aggregate production function (where it is taken into account how A, depends on Y, through taxation, etc.) is:Y1= (arL)faK,, and comment.
5. Show that the model can be condensed to the two equations:,= AK~ A "' L ( 1- a )/a1 K,. 1 = sY,+ (1- (5)K, .Find the growth rate, g •' of output per worker. Comment, for instance, with respect
4. Find the expression for the growth rate, g se• of output per worker in steady state. Comment with respect to what creates growth in output per worker in this model (when < 1 ).
3. Show that the transition equation for k1 is:k = __ k[s/(a - 1+(1 -0)](1-
2. Show that in this model:A (K a
1. Show that the aggregate production function in this model is:Why have we assumed < 1 /(1 -a)? Show that the aggregate production function has increasing returns to (K, L 1) whenever ¢> 0. Show
4. According to this model, growth in GOP per worker depends positively not only on sK as tested in Fig. 8.4, but also on sH. To test this create a diagram that plots growth rates in GOP per worker,
3. Show that according to the model above the growth rates of physical and human capital, respectively, in any period tare:K - K,. , -K, g, = K, H - H,. ,-H, g, = H, and then show that as x1= K,/H1
2. Define the ratio between physical and human capital, x1"" K, /Hr Show that the model above implies the following dynamic equation for this ratio:and demonstrate that this equation has properties
1. First show that if the production function of the individual firm is:Y, = (K'/)"(H'()'"(A.J_'/) '-"-"', and an external productive effect implies:then if = 1, the aggregate production function
5. By considering again the linear approximation around steady state, etc., find, also for this model, the rate of convergence A for y, according to the linear approximation. Show that(again) A goes
4. Show that the constant levels of capital per worker and output per worker in steady state are:* ( S )1/[(1- a)(l - 9\)J k = -n+O and* = (-s-)la+~(l a)J/ (1 ")(1 )J.y n+J
3. What is the aggregate production function in this model? Is labour unproductive at the aggregate level (also when¢ < 1 )? Why is it that in this case there is no positive, semi-endogenous type of
2. Find the steady state values, k"' and f", for k, and Yu respectively. Show that in steady state the common growth rate of A" k, andy, is 0 (also when n> 0).
1. Show that now:(~\A,., _l..!il_ A, - (1 + n) ~ 'and that with the usual definitions, the transition equation is:k,. , = -- k,(sk;'- 1 - ( 1 )' - + (1 -b))~ . 1 + n Convergence to positive steady
2. Show that the rate of convergence (for tJ> < 1) is:. (1 +n) W -91> -(1-o)A= (1- aj(1 - ¢) (1 + n) 9~>= (1 - a)(1-¢)[ 1-(1 11 ~ -J].Convince yourself that in the special case tJ> = 0, this rate
1. Go through all the operations that lead to this equation yourself. (Of course, everything is the same as in Chapter 5 since there is no difference in the generic equation studied. It is important,
3. For each value of ¢, let the economy be initially in steady state for o = 0.08. After some periods, 1 0 say, o shifts permanently down too'= 0.06. Simulate the model over the periods before the
2. For each value of ¢>, compute the steady state values for K, and Y, before and after the shift in o.
1. Show that the steady state values, K* and Y*, of capital and output (also per worker), respectively, are:(s)l/{(1- a)(l - 91)1 K* =-c5 and What is the steady state value of A1?(s )la+91( 1- a)]/((
3. Assume that labour's share, {J + rp, is 0.6 with raw labour and human capital hav n~ equal shares fJ and rp, respectively, and that capital's share is 0.2, while land's and oil's shares are both
2. Define the physical capital- output ratio, z, e K,!Y,, as well as the human, q 1 e H,!Y, . Show that along a balanced growth path where both z1 and q 1 are constant, the approximate growth rate of
1. W ith usual notation like y 1 e Y, / L1, k1 e K,/L1, h1 e H1/ L1 , x1 e X/ L1, e 1e E1/ L11 and g{ e In y,- ln y,_,, etc., show that the per capita production function is:and that:g{ E;f ag~ +
Exercise 9. Further numerical evaluation of g Y in the model with both land and oil Consider equation (35), which assumes a= 0.2, f3 = 0.6, K = r. = 0.1, and (36), which assumes further n = 0.01 and
3. Find expressions for the approximate growth rates, g', g "' and gu, of the real interest rate, r11 the real wage rate, w11 and the real oil price, u11 respectively, in steady state. How does u 1
2. Consider now only the steady state of the same model. Show that the approximate growth rates of Y1and K1 fulfil:Y K- fJ C g = g =--(g+n)- --SE.fJ +c fJ +t:Show that there is balanced growth in
1. Consider the Solow model with oil. State expressions for the factor reward rates, r1 , w1 and u 11 as depending, in any period, on the state variables K1, L11 A 1 and R1• Show that the income
4. Show that the grow1h rate of y in steady state is exactly:{Jg -Kn f3 +K o and compare this to the approximate grow1h rate, gY, found in Section 1 of this chapter.
3. Show that the steady state value, z*, for the capital- output ratio is:z* = s(]3 ~ K) (n + g) + b 'and show that the above differential equation implies convergence of z to z*. (For the latter you
2. Show that the law of motion for z following from the model is the following linear differential equation in z:t = (/3 + K )s - /..z, where J...,. (f3 + K)(5 + f3(n +g). (Hint: Start from the
1. Show that the per capita production function and the capital-output ratio (still in obvious notation, e.g. x ""' X/L) are, respectively:y = k" AIIx', z = k 1- a A-11 x-•.
3. Assume that n > 0, but g = 0, more or less as considered by the classical economists.Describe how the real rates, r,, w, and v, evolve over time. If there is a fixed number of landlords owning the
2. Show that the steady state of the Solow model with land is in accordance with balanced growth, not only in the respect that the capital- output ratio is constant, but also in the following
1. Show that in the Solow model with land the exact (in contrast to the approximate), common growth rate gr• of output per worker and of capital per worker in steady state is:gr• = (1 + g)~/(~H)
Exercise 4. Fighting structural unemployment Try to think of specific policies which might reduce the natural rate of unemployment. Explain why you think that these particular policies might reduce
Exercise 1 abo'le pointed to an{other) empirical shortcoming of the Solow model without human capital. The model's prediction that the investment rate in physical capital and the population growth
Exercise 10. An empirical shortcoming of the Solow model with human capital?
Exercise 9. An alternative Solow model with human capital You may have been wondering why we have built human capital into the model of this chapter in a way that is different from how it was brought
Exercise 7. Inferring a and qJ from the estimation of the convergence equation First find a way to estimate values fora. and cp from the information gathered in (39), (40) and(41 ). Then show that
Exercise 6. The effects of various parameter changes Let a base scenario be defined by the economy being, in all periods from 0 to 200 say, in steady state of the Solow model with human capital at
Exercise 5. Further simulations to investigate stability In Section 3 we ran a simulation of the Solow model with human capital to check stability of k,. h, towards the steady state k*, h*. We only
Exercise 3. Balanced growth in steady state Show that growth in the steady state of the Solow model w ith human capital in a// respects accords w ith the concept of balanced growth. In particular,
Exercise 2. Government in the Solow model with human capital When we were setting up the basic Solow model in Chapter 3 we were careful to explain that the savings rate, s, in S, = sY, could be
Exercise 1. One more empirical improvement obtained by adding human capital We opened this chapter by summarizing two main empirical shortcomings of the general Solow model. One was that its steady
Exercise 8. Growth accounting: have the growth miracle economies experienced above-normal TFP growth?Table 5.3 shows GOP per worker, y1, capital per worker, k, and average years of education in the
Exercise 7. Growth accounting: does your country keep up?Table 5.2 shows GOP per worker, y, and non-residential capital per worker, k, for some countries and years. Use formula (45), assuming a = ~.
Exercise 6. Deriving an estimate of a from the estimation of the convergence equation In this chapter we derived an estimate of a from our estimation of the steady state regression equation (29). The
Exercise 5. The effects of an increase in the rate of technological progress Assume that the economy is initially in steady state at parameter valuesa, s, n, g,b. Then from some period the rate of
4. Do all of the above once more, but now with g = 0.04 throughout. So, the base scenario is now given by a = ~. s = 0.12, n = 0.01, g = 0.04, J = 0.05 and A0 = 1, with the economy being in steady
3. From your simulations find the (approximate and rounded up) number of periods it takes forji 1 to move half the way from its old to its new steady state value. In Exercise 3 you were asked to
2. Simulate the model using appropriate parameters and initial values, thus creating computed time series for relevant variables according to the alternative scenario. Extend Diagram 1 so that it
1. Compute the s1eady state values k* and ji* for k1 and ji1 in the base scenario (all definitions are standard and as in the chapter). Illustrate the base scenario in three diagrams. Diagram 1
3. Now derive the steady state value z'" directly from (51). Sketch the transition diaQram for z,, and establish properties of the transition equation that imply global, monotone convergence to z*,
2. Show, using the per capita production function, that z,= (k,/A,) ' - ".Then show, by writing this equation for period t + 1, using the definition k,. 1 "' K,. ,I L ,. ,. and then using the model's
1. Show that z, as just defined fulfils: z, = k,/y, =k,/y, = i
5. To solve the general Solow model analytically one can apply a trick as in Exercise 3 of Chapter 3. Define z "' k1 - a . Show that z is the capital- output ratio, k/y. Then show that:z = (1
4. Show that {it follows from the model that) the growth rate ink at any time is:k - ..,.. = sk"- 1 -(n + g + o). k Illustrate this in a modified Solow diagram. Show that the growth rate, Yfy, of
3. Compute the steady state values, k* and Ji*, for capital per effective worker and income per effective worker. Compare to the parallel expressions found in this chapter for the model in discrete
2. Illustrate the above Solow equation in a Solow diagram with k along the horizontal axis.Demonstrate {from the Solow diagram) that from any initial value, k0 > 0, capital per effective worker, k,
1. Applying methods similar to those used in Exercise 2 of Chapter 3, show that the law of motion fork following from the general Solow model in continuous time can be expressed in the Solow
6. Show that the steady state values for GOP per capita, the wage rate, wealth per capita and national income per capita all decrease in response to the increase in 1:. (Hint: You don't have to solve
5. Show that an increase in 1: implies a decrease in w* + rk*, whenever 1: > 0 initially. How is the transition equation affected by an increase in r ?
4. Using the above expressions fo r k* and w*, show that:w* +rk* = 1 +-_---(1 -a) -- - . [1: a ] ( a )a/(1 - a)r+r 1 -a r+r
3. Show that the transition equation for national wealth per capita is:1 + sr s(w* + r k*) v = --v + --'-----'- /+ 1 1 + n 1 1 + n
2. Show that domestic capital per capita and the wage rate, respectively, adjust immediately to:* ( a ')1/(1-a) k =-f'+E'and w* = (1 -a) -_- . (a )'l/(1 - a)f+ E
1. W rite down the complete model (for your convenience) and show that in any period t, GOP per capita is:y, = w1+(l'+ E)k1,
Exercise 7. Long-run national income in the small open economy as depending on domestic and international savings propensities A certain restatement of (27) can be of interest. As argued in this
4. Now simulate each of the transition equations from period zero and onwards (for a number of periods of your own choice, but be sure to have quite a few), thereby creating a sequence (v 1)for the
3. Compute the steady state values, y n* = r: and u* = k;, under these specifications. Assume that both economies, the open and the closed, start in their steady states and then, as from period one,
2. Consider the transition equation for the open economy (v,. , as a function of v,) and show that under our assumptions its slope is:1 + (J.n 1 + n
1. Show from (27) that under these assumptions steady state national income per capita is:Then show, by comparing to the relevant formula in Chapter 3, that this y"* is equal to the steady state GOP
4. How is the long-run functional income distribution in the open economy affected by a permanent international interest rate shock, where r increases permanently to a new and higher level? Explain
1. Show, using (16) and the fact that w, jumps immediately tow*, that labour's share in any period tis:w, u, v, - = 1-r- = 1-r--- Y7 Y~ w* + rv, 'and show that as national wealth, v,, converges
Exercise 3. The income distribution in the small open economy As stated in this chapter, in any period t, the share of labour income in GOP, w,/y, is equal to V'1 -a., while the share of income
Exercise 2. Golden rule in the open economy?Show that in the small open economy's steady state consumption per capita, is:1 c* = (1 -s) w*1 - (s/n)r 'where the expression for w* of ( 19) could be
Exercise 1. The elasticity of long-run national income per capita with respect to the savings rate in the small open economy This exercise investigates how strongly national income per capita is
Exercise 11. Endogenous population growth and club convergence in the basic Solow model Consider a growth model that consists of the same equations as the basic Solow model except that then in Eq.
Exercise 1 0. The recovery of Japan after the Second World War Table 3.2 shows GDP per worker for the USA and Japan for the period 1959 to 1996, measured in a common, purchasing power-adjusted
Exercise 9. Further empirically testing the steady state prediction of the basic Solow model This exercise anticipates some issues taken up in succeeding chapters, and it is a very useful empirical
Exercise 8. Balanced growth in the steady state Show that all the requirements for balanced growth, as these are stated in Chapter 2, are fulfilled in the steady state of the basic Solow model. Why
Compute the particular value k** of k, that maximizes this distance. Illustrate the point in your Solow diagram: the slope of Bk;' should equal the slope of (n + o)k,. Explain this.What is the
Exercise 7. Golden rule In this chapter it was stated that the golden rule savings rate that maximizes steady state consumption per person as given by (35) is s** = a . Show this. To illustrate, draw
Exercise 6. A one shot increase in L1 Analyse in the Solow diagram, the qualitative effects of a one shot increase in L,, starting in steady state at the prevailing parameter values. The event we are
Exercise 5. The effects of an increase in technology Do all you were asked to do in the previous exercise (there for a decrease in n) only this time for an increase in B. First analyse the
4. In Chapter 2 it was shown that developed economies have experienced relatively constant positive growth rates in GOP per worker (annual rates around 2 per cent) and relatively constant capital-
3. Show that with the CES production function, the income share of labour under competitive market clearing is:wL 1 -a - = ---,-,----y (K)(
2. Find the marginal rate of substitution between capital and labour for the CES production function, and show that the elasticity of substitution is -a, independent of rand w.The CES function is
1. Find the marginal rate of substitution between capital and labour (the marginal product of capital divided by the marginal product of labour) for the Cobb- Douglas production function.Show that
Exercise 7. Galton's Fallacy 14 It is an implication of convergence that a lower initial GOP per worker should, other things being equal, imply a higher subsequent growth in GOP pe· worker. This was
Exercise 6. Growth and trade This chapter has presented the stylized facts of growth that are most important for the theoretical developments in subsequent chapters. There is at leas! one more
Exercise 5. Level convergence among the rich?Commenting on Fig. 2.3 in Section 3 we said that it showed a tendency towards convergence to a common growth path with constant growth. Perhaps we were
Exercise 4. Growth against ultimo level In Section 3 there were figures showing across countries the log of GDP per worker in an initial year along the horizontal axis, and average annual growth in
Exercise 3. Time to double Assume that in a specific country GOP per capita, or per worker, grows at the rate g each year over many years, where g is written as a percentage, e.g. 2 per cent. Show
Exercise 2. The income distribution for the rich part of the world Table 2.4 shows GOP per worker {in 1996 US dollars) and population size for 1960 and 2000 for the rich part of the world (defined
Exercise 1. GOP per capita versus GOP per worker Give some arguments why GOP per worker, rather than GOP per capita, should be used for a comparison of standards of living between countries.
Exercise 5. Menu costs and real and nominal rigidities Explain and discuss the type of costs included in the concept of 'menu costs'. Explain why and in what sense so-called real rigidities are
Exercise 3. Macroeconomic policies for the short run and for the long run Explain the difference between structural policies and demand management policies. Explain the concepts of 'nominal
Exercise 2. Short-run versus long-run macroeconomics Explain the different assumptions underlying macroeconomics for the short run and macroeconomics for the long run. Do you find these assumptions
Exercise 1. Aggregation in macroeconomics Discuss why macroeconomists typically work with aggregate variables and explain the arguments they use to defend this procedure. Do you find the arguments
11.22. (Cagan, 1956.) Suppose that instead of adjusting their real money holdings gradually toward the desired level, individuals adjust their expectation of inflation gradually toward actual

Showing 1200 - 1300 of 3705

First
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Last

Services

Sitemap
Fun
Definitions
Become Tutor
Study Help Categories
Recent Questions
Expert Questions

Company Info

Security
Copyrights
Privacy Policy
Terms & Conditions
SolutionInn Fee
Scholarship

Get In Touch

About Us
Contact Us
Career
Jobs
FAQ
Campus Ambassador

Secure Payment

Download Our App

© 2024 SolutionInn. All Rights Reserved