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A: The production function explains the relationship between input and output.
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- Suppose Westeros produces output according to the production function: Y = √K The fraction of output that is saved and invested in new capital is 20%. The depreciation rate is 5%. Use this information to answer the following questions. Macmillan Learning a. What is the steady-state amount of capital (K) in Westeros? b. What is the steady-state amount of output (Y*) in Westeros? c. If Westeros had started out with 25 units of capital, what would the Solow model predict would happen to its output in the long run? O It will decrease, since that is above its steady state level of output of 4 It will decrease, since that is above its steady state level of output of 16 It will increase, since that is below its steady state level of output of 16 It will increase, since that is above its steady state level of output of 41 It will remain at 25, since that is its steady state level of outputWhich of the following explains the importance of education in economic growth? Group of answer choices All the other answers investing in education strengthens human capital investing in education strengthens physical capital investing in education strengthens technology1. Many endogenous growth models feature so called scale effects: per capita growth rises when population growth rises. Some economists have criticized these models for this reason, since countries with faster population growth do not in general appear to also experience faster per capita income growth. Consider an economy that has access to a production technology Y = AKª L¹-a where Y is output, A is the level of technology, K is capital and L is the amount of labor in the economy. Capital evolves according to K = SY (thus, the depreciation rate 6 = 0). The population growth rate is n. (Throughout, gx, where x can be any of the variables in the model). i. Assume that technology is determined by A =BK What sort of endogenous growth model is this? Find gk in terms of the K, L, and other parameters of the model. ii. Write an expression for gy in terms of gk and g₁. What must be true for a balanced growth path to exist in this model? Solve for the balanced growth path value of gy and gy,…
- 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)∗?y=zk^2/3 For this economy, derive the competitive equilibrium, and derive the equation that solves for a steady state capital stock per worker.) The goal is to analyze further the two-sector endogenous growth model. Write down the equation of motion for k, which shows delta k as saving minus break-even investment. (Break-even investment is the amount of investment needed to keep capital per effective worker constant.) Draw a graph that determines the steady-state k. In this economy, what's the steady-state growth rate of output per work? How do the saving rate and fraction of labor force in universities (u) affect this steady-state growth rate?
- > Consider the data in the table below: Per capita GDP, 2017 Saving rate (%) TFP (Ā) United States 1.000 23.5 1.000 Switzerland 1.151 28.8 1.052 Answer the following questions using the Solow growth model. 9. Assuming no differences in TFP (ignore the last column) and no differences in the rate of depreciation between the U.S. and Switzerland, use the data in the table to predict the ratio of per capita GDP of Switzerland relative to that of the U.S. in the steady states. How much percent richer is Switzerland than the U.S. in steady state? 10. Now do the same exercise assuming TFP is given by the levels in the last column. Now how much percent richer is Switzerland than the U.S. in steady state? Consider the data in the table below: Per сapita GDP, 2017Which of the following is an incorrect statement about the variable ‘s’ in the Solow Growth Model? a.s is the fraction of income that is saved b.s is an exogenous factor c.s is referred to as saving per worker d.s determines how income is allocated between consumption and investmentSuppose you add a variable rate of population growth to a two-sector model of growth. Draw and properly label a graph on how the production function, investment requirement line, and saving line look like. Does the addition of the variable rate of population growth to this model help you explain anything that a simpler two-sector model with a fixed rate of growth, or a one sector model with variable population growth, cannot? Expound.
- Please assist to solve the below question. Suppose an economy is on a balanced growth path in a simple Romer model, as described in the text, where aggregate output is: Y, = A,Lyt, law of motion of ideas (idea production function) is: AA++1 = ZA“, Lat ; labour resource constraint is: Ly +Lat = L, and the allocation of labour is: La = IL, %3D where z is a productivity parameter of the researchers, Ao is the existing stock of ideas at time, t = 0, L is the total population and assumed to be constant, and i is the constant fraction of population who works in the research sector. Suppose in year 2030, research productivity z rises immediately and permanently to the new level z'. а. How would the growth rate of ideas behave if a <1? b. Assuming a = 1, solve for the new growth rate of knowledge and growth rate of output per capita. С. Assuming a = 1, sketch the graph of Iny against time t. d. Why might research productivity increase in an economy?What must be the relationship between the rate of growth of technological change (g) and the population growth rate (L/L) for income per capita to continue to increase?