We now introduce the government sector into a solow model. Let us assume that the production function is: Y = K L1 - where 0 << 1. Now Y = C + I + G and we know that G = BY with 0 < < 1. We further assume that C = c(Y - G) where ca is a constant between zero and one. The population growth rate is n. The depreciation rate is \delta. Let y = Y/L, k = K/L and c = C/L. a) Is the production function constant returns to scale (CRTS) ? Prove it. b) As is standard, k = sy - (n + \ delta )k holds. Find out the steady state values of k, y and c in this model (i.e. the values of k*, y* and c *). c) What will happen to the steady state you find in part a) if increases ? d) Find out the values of k, y, and c in the golden rule steady state (i.e. the values of k**, y** and c**). e) What saving rate can be used to support this golden rule steady state ?

We now introduce the government sector into a solow model. Let us assume that the production function is: Y = K L1 - where 0 << 1. Now Y = C + I + G and we know that G = BY with 0 < < 1. We further assume that C = c(Y - G) where ca is a constant between zero and one. The population growth rate is n. The depreciation rate is \delta. Let y = Y/L, k = K/L and c = C/L. a) Is the production function constant returns to scale (CRTS) ? Prove it. b) As is standard, k = sy - (n + \ delta )k holds. Find out the steady state values of k, y and c in this model (i.e. the values of k, y and c *). c) What will happen to the steady state you find in part a) if increases ? d) Find out the values of k, y, and c in the golden rule steady state (i.e. the values of k, y and c**). e) What saving rate can be used to support this golden rule steady state ?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Can you show me the solution for part d)
In the Solow model, population growth leads to steadystate growth in total output, but not in output per worker. Do you think this would still be true if the production function exhibited increasin g or decreasing returns to scale? Explain.
Could you show me the solution for question part b)
13 =e 2. Consider the advanced Solow model with technological progress and human capital. Recall that the production function is given by Y = Ka (AH)¹-a where H = eu. Remember that is the return to education and u is the fraction of time spent acquiring new skills. As in class, assume that both and u are exogenous constants. As usual, saving is given by Å A = n and g. Now suppose that total SSY OK. This is in contrast to S = SY assumed in class. The extra term, -OK, reflects the idea that when wealth (as measured by the capital stock) is higher, saving is lower. (Wealthier economies have less need to save for the future.) a. Derive the capital accumulation equation in terms of the state variable. b. Solve for the values of the state variables on the balanced growth path (BGP). (i.e. Solve for the steady state values). C. Solve for the value of output per worker on the BGP. d. What is the effect of an increase in on this economy? To explain the effect, draw four diagrams:
Consider the following numerical examples for the Solow Growth Model: Economy A z=1 s=0.5 F(K,N)=K0.3N0.7 n=0.01 d=0.1 Economy B z=1 s=0.2 F(K,N)=K0.3N0.7 n=0.01 d=0.1 In which economy is Consumption per capita higher in steady state? O Economy A O Economy B Not enough Information
Suppose an economy described by the Solow model is in steady state with population growth n of 1.8 percent per year and technological progress g of 1.8 percent per year. total output and total capital grow at 3.6 percent per year. suppose further that the capital share of output is 1/3. if you used the growth accounting equation to divide output growth into three sources- capital, labor, and total factor productivity- how much would you attribute to each source? compare your results to the figures we found for the united states in tables 9-2.
= 2. Consider a Solow growth model in which the production function is Yt AK²N₁¹/2, where A = 1. Moreover, assume that the depreciation rate is d = 0.02, the rate of population growth is n = 0.02, and the saving rate is s = = 0.2. a. Compute the value of the capital stock per worker in steady state. b. Draw a graph that represents the steady-state equilibrium of the model. c. Suppose that the capital-labor ration in year t is 90. What will the level of the capital- labor ratio be in year t+1? Will it increase or decrease in future periods? Explain. d. Compute the rate of change of the capital labor ratio between time t and t + 1. How does it compare to the rate of growth of the capital-labor ratio in steady state?
1. Consider Avataria, which can be described by the Solow model with the population growth. Its production function Y(K,L) = 2K¹2 L¹/2 Its investment rate is 40%, its depreciation rate is 10%, and its population growth rate is 10%. Calculate the capital-labor ratio, output per worker, and consumption per worker in the steady state. Assume that now the population growth slows down to 4%. What happens with the output per worker and consumption per worker in the new steady state? Calculate the exact values. (a) (b)
Q5 Suppose in a Solow model, we have the following parameter values: n = 0, s = 0.5, a = 0.3. There is no growth in the total factor productivity so that A, = A = 1. Moreover, we know that at time 0, the economy is at a steady state so that k = k, =1. Now imagine that a foreign power invaded this %3D country. 1% of the population was killed and another 14% of the population fleeded the country to avoid violence. Moreover, 15% of capital stocks were destroyed. All of this happens in period t=1. After that, the war ended and there was no more destruction of capital or loss of population (but the refugee permanently settled outside of the country and will never return0. What is the growth rate of per-capita output in period t =4?
Suppose in a Solow model, we have the following parameter values: n = 0, s = 0.2, a = 0.33. There is no growth in the total factor productivity so that A, = A = 1. Moreover, we know that at time 0, the economy is at a steady state so that k = k, =1. Now imagine that a deadly pandemic hits the economy at time t=1. As a result, the population at time t =1 is 10% lower than the population at time t=0. The pandemic is a one-time shock so that population growth rate remains the same, i.e., from t-2 onward, the population remains the same as the population at time t=1. The total capital stock, however, is unchanged so that K, Ko. What is the growth rate of per-capita capital in percentage (rounded to the 2 decimal places, e.g., answer 1.08 if your calculation shows the growth rate is 0.01079) at time t=3 from time t=2? %3!
Please refer to the clarification of specific questions
The Solow model is an important formal model of economic growth. Assume that the production function is Y = F(K,N) = zK° N¹-a, where 0 < a < 1. Production is constant returns to scale. We use lowercase to denote variables in per capita terms.