no population growth Assume Cob-Douglas production Yt = K (AL) E L=1), saving as a constant fractions of output, and no depreciation of capital. Now assume that At = by such that labour becomes more effective as a by-product of the quantity and gk in terms of A, K, and the parameters produced. Derive equations for SA of the model
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- Economics, physical capital represents the uildings or machines used by a business to produce product. The marginal product of physical capital presents the rate of change of output product with spect to physical capital (informally, if you increase e size of your factory a little, how much more Foduct can you create?). articular model tells us that the output product Y is given, a function of capital K, by Y = AKªL'-a ere A is a constant, L is units of labor (assumed to be stant), and a is a constant between 0 and 1. Determine marginal product of physical capital predicted by this del. ned with CamScannerIn any Econorry the production function | 1-x is y=Ka L!-xnfinity Derive ss level of output per and capital per worker. vyorkerIn the Saul model, if the per capita production function is y=k^0.7, the savings rate is 0.2, and the depreciation rate(8) is 0.1, then the steady-state level of capital per worker (k') equals O O O A. B. C. D. 4.85 8.05 10.08. 11.12
- Show that, when using a traditional economic production function,doubling our population can double our output if capital stocks alsodouble. Use the production function: Q = AK L , where A representstechnology in an economy, K capital, and L labor. Double K and L andshow that Q also doubles, assuming α=β=1/2. Now show that, when we incorporate natural capital into thediscussion, doubling the population does not increase output in thesame way (since natural capital cannot also grow). Use theproduction function: Q = AK L N , where N is natural capital. DoubleK and L and show that Q less than doubles, assuming α=β=γ=1/3.worn out in the production process. ment Now IzMe: Section 2.7 uge your comprehension of this section. To begin, please click the wnward arrow located at the top right of this box. Assignment Score: 0.00% Submit Assignment for Grading Save ns tu2et10h_Ch02_Sec07.02m « Question 2 of 3 » Check My Work Three different economies have made choices about the production of capital goods. Which of the following is most likely to produce the greatest growth in the production possibilities curve (PPC)? O a. Less production of capital goods than what is needed to replace worn-out capital. Ob. Capital goods produced at the exact rate needed to replace worn-out capital. c. More production of consumption goods that replace worn-out capital. O d. Greater production of capital goods than what is needed to replace worn-out capital. MacBook Air DD F6 EZ F8 F9 F10 F11 F12 & * 6 7 8 { P + 000Assume the rate of technological progress is constant in a SSGM with Cobb- Douglas production function. Show that a steady-state cannot be identifiede if the technological progress is capital augmented, i.e. F(K, L) = [A(t)K(t)]*L(t)'_ª, where A(t) is the efficiency term growinge with a constant rate g.t
- as Figure 11-1 D Real GDP per hour worked, YIL v $40 IC 8 T 1 60 Production function, Production function, Production function, Capital per hour worked, KIL Refer to Figure 11-1. Diminishing marginal returns is illustrated in the per-worker production function in the figure above by a movement from Production function 1 to Production function 2 from Production function 2 to Production function 1. from Production function 1 to Production function 3. up along any of the production functionsIn the Malthusian model, the population growth rate is O A. assumed to be constant. O B. not related to consumption per worker. O C. positively related to consumption per worker. D. exogenous. O E. negatively related to consumption per worker.A CES production function with physical and human capital Consider the CES production function in terms of physical capital, K, and human capital, H: where 0 a. Set up the Hamiltonian and find the first-order conditions. b. What is the optimal relation between K and H? Substitute this relation into the given production function to get a relation between Y and K. What does this “reduced-form” production function look like? c. What is the steady-state value of the ratio of physical to human capital, (K/H)∗? d. Describe the behavior of the economy over time if the initial condition is such that K(0)/H(0)? e. Suppose that the inequality restrictions IK ≥ 0 and IH ≥ 0 apply. How do these constraints affect the dynamics if the economy begins with K(0)/H(0)∗?
- Based on two period model: population growth results in a decrease in the relative amount allocated to the second period and a lower present value of the marginal user cost. True or False?Let the production function be Q = K0.®L0.2 Solow's assumptions are K = sQ – 6K The symbols s represents a (constant) marginal propensity to save, n, a (constant) rate of growth of labor and 8 constant depreciation rate. (a) Derive the fundamental equation of Solow growth model for given production function. (b) Sketch graph of with k on the vertical axis and k on the horizontal take n = 0.01, s = 0.3, 8 = 0.1.2) 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.