capital per efficiency worker that result from the logic of the model. (e) Working with the fundamental equation you derived in part (c), find the equilibrium solution for k algebraically. Relate this to your diagram in part (d).
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not sure how to do part E
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- Consider the endogenous growth model AK, in which the production function is given by Y = AK. Suppose s denotes the saving rate; that δ represents the depreciation rate; and that the variable that represents the population and that grows at the rate n. Calculate the growth rate of capital per capita in the same way as for the Solow model and, from there, solve the differential equation to obtain the capital per capita (denoted by k) as a function of time.Consider a numerical example of the Solow model: Assume that n=0.2 s=0.3 d=0.1 F(K,N)=K12N12 Initially, in period t=0, that z=3 N=1 and the economy is in a steady state: Suppose that at t=1, total factor productivity falls to z=1 and then returns to z=3 for periods t=2,3,4.... What is the value of per person aggregate output at period t=1?Consider the Solow model without technological progress and an economy with the following production function, Y=A[Kα+Gα]1/α where α<1, K is private capital and G is public capital that is used freely and provided by the government. The level of technology A is fixed and assumed to be equal to 1. A. Does this production function feature constant returns to scale? Explain. In order to finance public capital, the government taxes all investment on private capital at the rate 0<τ<1. So, the revenue raised by the government in each period is sKYt(1−τ) where sK is the private savings rate so that sKYt is pre-tax private savings. Public investment towards public capital is a constant fraction sG of total revenue. Then, the accumulation equations for private and public capital, respectively, are, Kt+1−Kt=sKYt(1−τ)−δKt Gt+1−Gt=sG(sKYtτ)−δGt where δ is the common depreciation rate B. Consider a balanced growth path where the growth rates of private capital is equal to the growth…
- B. The rate of technological progress rises. 2. 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 population growth falls. B. The rate of technological progress rises. C. The production function is Cobb-Douglas, F(K,AL) = K" (AL)1-" , and capital"s share, ", rises. D. Workers exert more effort, so that output per unit of effective labor for a given value of capital per unit of effective labor is higher than before.1. In the Solow model, if investment (I=sY) is lower than depreciation (dK), then…. A. Depreciation (dK) in the following period will be higher than in the current period. B. Capital stock (K) in the following period will be lower than in the current period. C. Per-capita GDP (y) in the following period will be the same as in the current period. D. Overall GDP (Y) in the following period will be higher than in the current period. The answer is B - - Can you show work for it, graph the representation for itConsider a Solow–Swan model with saving rate s = 0.4, labour force growth gL = 0.05, constant productivity A = 1, and depreciation ?δ = 0.05. If output per worker is y = Y/L = 200 and capital per worker is k = K/L = 1000, which of the following is true? Group of answer choices - Effective depreciation per worker is 80, saving per worker is 100 and k will increase towards the steady state - Effective depreciation per worker is 100, saving per worker is 80 and k will decrease towards the steady state - Effective depreciation per worker is 100, saving per worker is 80 and k is at the steady state - Effective depreciation per worker is 80, saving per worker is 100 and k will decrease towards the steady state
- Suppose the economy of an island behaves as the Solow model (Y=AK1/2L1/2), version 1.0 (constant population). Suppose that the productivity parameter is A=90, the depreciation rate is d=1/10, the savings (investment) rate is s=0.10, and the labor force is equal to 2 million (and constant over time). 1-Due to climate change, from 2011 onward, every year the island is hit by hurricanes of increasing force that destroy capital. As a result, the depreciation rate doubles. What will be the new long-run (steady state) value for income per worker (Y/L)? Pick the closest value. Also label the new steady-state GDP as point C in the diagram. Between 75 and 85 None of the other options Between 4,500 and 5,200 Between 8,000 and 8,500 Between 44 and 49 2-In year 2021 investors recognize that the depreciation rate is higher than a decade earlier. They also recognize that the actual returns to their investments in physical capital over the previous decade have consistently fallen below their…Consider the Solow model with a production function Y(t) = A*K(t)^α*L(t)^(1-α), Where A is a fixed technological parameter. Explicitly solve for the steady-state value of the per capita capital stock and per capita income. How do these values change in response to a rise in (a) the technological parameter A, (b) the rate of saving s, (c) α , (d) δ, the depreciation rate, and (e) the population growth rate n?3. In the Solow model, ________ is assumed to be constant. capital accumulation investment rates depreciation consumption
- Suppose a Solow economy is initially at its steady state k∗, and suddenly is hit by a decrease in the depreciation rate δ, from δ to δ1. This change does not alter any of the other exogenous parameters in the model Depict this situation in a graph What happens to steady state level of capital per capita in this situation? What happens to the level of capital per capita over time? Depict this in a graph and explain intuitively.Consider the Solow growth model in which we allow for long-run techno- logical progress. Assume N′ = (1 + n)N where N is the population (labor force) in the current period, N′ is the population (labor force) in the future period, and n is the pop- ulation growth rate. Assume that z = 1 for simplicity, and there is labour-augmenting technological progress. The production technology is given by Y = F(k,bN) where Y is the output of the consumption good, K is the current period capital stock, b denotes the number of units of “human capital” per worker, and bN is the “efficiency units” of labour. Assume that b′ = (1 + β)b where β > 0 is the growth rate in human capital. Consumers save a constant fraction, s, of their disposable income, where 0 < s < 1. The production function F exhibits constant returns to scale. (a) Define a variable k as the quantity of capital per efficieny units of labor (as opposed to quantity of capital per labour). Using equilibrium conditions derive the…Consider the Solow model with a production function Y(t) = A*K(t)αL(t)1-α, Where A is a fixed technological parameter. Explicitly solve for the steady-state value of the per capita capital stock and per capita income. How do these values change in response to a rise in (a) the technological parameter A, (b) the rate of saving s, (c) α , (d) δ, the depreciation rate, and the population growth rate n?