Euler Equation Consider the following (almost identical) two-period economies (t = 1,2) K₁ a zF(K) B 8 u(c) Economy 1 Economy 2 1 0.3 1 zkº 0.9 0.5 log(c) 1 0.3 1 zKa 0.9 1 log(c) Suppose that at the end of t = 2 the depreciated stock of capital (1-6) K₂ is sold. Which economy experiences higher consumption growth between period 1 and period 2? Show why! Hint: Combine Euler Equation with Resource Constraint at t = 1 and t=2 to solve for K2; plug back into euler equation
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- 2) Consider an economy with depreciation 6=.2, saving rate s = .1. Worker productivity grows at rate g = .1. The economy starts with 5 units of capital per worker. The productivity function is given by: 2tnioq S) m6x9 grit no bazzim 23 0 2 2 19 0 f(k) = 3* k1/3 (1916978 zi 19verlɔirlw how to two lapiolandotdwong noitsluqoq TUOHTIW lebom wolo2011 ( The Marginal Product of capital is therefore 100037950 1 ritwong ytivitoub 1910 190 stign .6 MPK = 3* know 19q gniv brs (19) a. Using the above parameters, what is the golden rule steady state capital per (effective) worker? Please show your work below.12. Consider an economy without technological progress and population growth. The production function is given as Y = K²/³N\/3. Both the saving rate and the capital depreciation rate are assumed to be 0.1. Which of the following saving rate delivers the highest consumption per worker in the steady-state: (a) 1/3 (Ь) 1/2 (c) 2/3 (d) none of above is correct4. If the production function is given by Y=K2L'3 and the saving rate saving rate (s) equals the depreciation rate (8). Find the numerical values of the steady state capital and output?
- Suppose the production function is given by Y= VK\N, where Y is the amount of output, K is the amount of capital, and N is the number of workers. Suppose further that there are no technological progress and population growth. What is the expression in terms of the saving rate, s, and the depreciation rate, 8, for the level of consumption per worker in the steady state? Oa. 2(1 – s) Ob. 4(1 – s) O c. All of the answers here are incorrect * 4s(1 – s) Od. O* 2s(1 – s)QUESTION 2 If Z = (XY)2, and we know that the annual growth rate of Z is 3%, and the annual growth rate of X is 2%, the annual growth rate of Y is а. - 1% b. - 0.5% C. 0.5% d. 1.0%1. Consider the variables x. V. and z. Assume that the growth rates of these variables aire given by g(x) = 0.04, g(y) = 0.12 and g(z) = 0.008. Then the growth rate of the variable w = %3D (yx)3/4(z)1/4 is approximately equal to a. 16% b. -10% с. 12% d. 12.5%
- I have worked on 1-3, but am stuck on 4-6, could you please assist? Suppose that the economy is summarized by the following: Technology (Production Function): Yt = 10 (Kt)0.3 (Lte)0.7 Consumption function: Ct = 0.8Yt Depreciation rate: 8% (i.e. δ= 0.08) Population growth: 2% (i.e. n = 0.02) Technological growth: 4% (i.e. g = 0.04) QUESTIONS: Find the steady state (long run) equilibrium values of kte, yet, and cet. Show graphically what would be the effect of a increase of the saving rate to s=0.4? Show graphically what would be the effect of an increase in population growth to 0.04? Assuming that in 2013 the US economy is in the steady state and L2013 = Le2013 = 8, what is the value of ke2014, ye2014, ce2014 , k2014, y2014, and c2014 ? Use your answer to e) to calculate the growth rate of ket, yet, cet , kt, yt, and ct Based on your answers to the previous questions and on your knowledge of how the Solow growth model works, explain what policies should a less-developed country…Question 2Assume production function is given by:Y= K(1/2) L(1/2)a. Write the production function in per worker terms (y=f(k))b. Assume that the per worker level of capital in the steady state is 4, the depreciation rate is 5% per year, and population growth is 5% per year. Does this economy have “too much” or “too little” capital? How do you know? [Show your work].An economy has production function Y = K¹/2L¹/2, a savings rate of 60 percent. There is no technological progress or labour force growth. The depreciation rate initially 10 percent, increases to 40 percent. There are 400 workers in this economy. When the depreciation rate is 40 percent, output will be equal to dollars.
- suppose the production formula is given by yt= kt ^1/3 where y is the output per worker and k is the capital per worker. futhermore assume that the saving rate is exogenous and the capital deprecitates at delta rate. if the sum of both deprectiation rate and saving rate equals 1, answer the questions below 1. find the steady state values of capital, output, investments and consumption as functions of the saving rate only? 2. in a diagram show the steady state value values in a part (a)?Be the production function Q (K, L) - : (K} +213), that depends on the quantitiess Used from inputs Kand L; and be the point (K, L) = (1,2). (a) What is the effect on the production of an increase of a unit in the amount used of INPUT L, L, Other things being equal?? (b) What is the effect on the production of an increase of 1% in the amount used of INPUT L, Ceteris paribus?J 7 Given a production function Yt = AKt1 /3L2 /3 , if K0=8, A = 2, L = 4, s = 0.2, and d = 0.05: (a) Calculate the steady-state level of capital and output. (b) Calculate K1 , I 1 , Y1 and C1 .