Consider the Solow model with the following parameters/exogenous variables: ?̅, ?̅ , ?̅, ?̅, ?̅, and ?0. In the standard model, we assume that each unit of investment can be converted into future capital one-for-one. Relative to the standard Solow model, in this exercise we include a new parameter to capture the “marginal efficiency of investment.” That is, we introduce the parameter ?̅ which reflects the rate that investment can be converted into future capital stock. This term shows up in the capital accumulation equation as ??+1 = (1 − ?̅)?? + ?̅?? .
a. Suppose the economy is in steady state in the initial period; that is, ?0 = ? ∗ . Suppose there is an increase in̅?. Plot the transition path (over time) for the rental rate of capital (MPK). Rental rate of capital on vertical axis, time on horizontal axis.
b. Suppose the economy is in steady state in the initial period; that is, ?0 = ? ∗ . Suppose there is an increase in̅?. Plot the transition path (over time) for consumption. Consumption on vertical axis, time on horizontal axis.
Consider the Solow model with the following parameters/exogenous variables: ?̅, ?̅ , ?̅, ?̅, ?̅, and...
Consider an economy that follows the dynamic as in the Solow model developed in class, with constant L. Suppose a country enacts a tax policy that discourages investment, and the policy reduces the investment rate immediately and permanently from s to s1. Assuming the economy starts in its initial steady state, use the Solow model to explain what happens to the economy over time and in the long run. Draw a graph showing how output evolves over time (put ????...
Consider an economy that follows the dynamic as in the Solow model developed in class, with constant L. Suppose a country enacts a tax policy that discourages investment, and the policy reduces the investment rate immediately and permanently from s to s1. Assuming the economy starts in its initial steady state, use the Solow model to explain what happens to the economy over time and in the long run. Draw a graph showing how output evolves over time (put Yt...
28. Consider the Solow model with exogenous growth. Assume that because of global warming the depreciation rate increases. Illustrate the change in the steady state. What happens to the growth rate of standard of living in the new steady state? 29.Suppose the government of a small open economy passes an investment tax exemption to stimulate investment. Using the classical open economy model, what will the effects of this investment tax exemption? 30.Suppose a government decides to increase taxes Using the...
3. Transition Dynamics Consider the Solow growth model with constant population and no techno- logical progress as studied in class. Suppose the economy is initially in the steady state, with the level of per-capita capital stock of kss. The per-capita production function is given by y -f (k) - Akt, 0 < α < 1. In each of the following scenarios, plot the transition time path of per capita capital stock. kt, per-capita output, yt, and per-capita consumption, ct- (1-s...
Consider an economy that is characterized by the Solow Model. The (aggregate) production function is given by: Y = 6K1/3L2/3 In this economy, workers consume 80% of income and save the rest. The labour force is growing at 2% per year while the annual rate of capital depreciation is 5.5%. a) Solve for the steady state capital-labour ratio and consumption per worker. The economy is in its steady state as described in part (a). Suppose both the stock of capital...
Consider the Solow growth model. Output at time t is given by the production function Y-AK3 Lš where K, is total capital at time t, L is the labour force and A is total factor productivity. The labour force and total factor productivity are constant over time and capital evolves according the transition equation KH = (1-d) * Kit It: where d is the depreciation rate. Every person saves share s of his income and, therefore, aggregate saving is St-s...
Consider the Solow growth model. Output at time t is given by the production function Yt = AK 1 3 t L 2 3 where Kt is total capital at time t, L is the labour force and A is total factor productivity. The labour force and total factor productivity are constant over time and capital evolves according the transition equation Kt+1 = (1 − d) ∗ Kt + It , where d is the depreciation rate. Every person saves...
3) Consider the Solow model with population growth and labor-augmenting technological progress. Suppose that the aggregate production function is Cobb- Douglas, i.e. Y = AK"(E · L)1-a, where A is a constant, while E denotes technological progress and grows at rate g. Labor grows at an exogenous rate n, and capital depreciates at rate d. As usual, people consume a fraction (1 – s) of their income. a. Use a graph similar to what we have seen in class to...
This is a question in Macroeconomics about Solow Model Consider an economy in discrete time t = 0,1,2,3,... Y denotes total output, C denotes total consumption, and S denotes total savings. At any period, total output is split between consumption and saving, i.e. Y() = C(t) + s(t) The economy is closed so that aggregate saving equals aggregate investment, S(t) = 1(t). Investment augments the national capital stock K and replaces that part of it which is wearing out. Suppose...
Malthusian Model of Growth Notation: Yt Aggregate output; Nt Population size; L¯ Land (fixed); ct Per capita consumption Production: Aggregate production function is Yt = F(Nt , Lt) = zN2/3 t L 1/3 t Population Dynamics: Nt+1 = g(ct)Nt Population growth function: g(ct) = (3ct) 1/3 Parameter Values: Land: L¯ = 1000 for all t. Productivity parameter: z = 1 ...