This question will take more time to answer This question aims to explore some of the points discussed about the Solow-Swarn with the general Cobb-Douglas production function: Y = A KO L(1-0) The equation describing capital dynamics is: Ki+1 = Kị + lị - dK Where d is a constant parameter that captures the depreciation rate. Investment fo discussed in class, ie, a constant 's' fraction of output is invested in every period. A the rate n = 0 and let s = 0.60, d = 0.10, a = 0.5, L= 1and A= 1. Which one of the following answer is correct about the steady state equilibrium? %3D
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- a. List all the equilibrium conditions of this model and Using the equilibrium conditions listed, write down an expression that describes the evolution of the aggregate capital stock, Kt over time. Briefly explain why this expression is not particularly convenient for our analysis of the model? b.Using your answer to the above question, derive the equation that describes the evo- lution of the the capital stock per effective unit of worker, kt. ' Why is the analysis in terms of the variables per effective unit of worker more useful than the one with the aggregate capital stock? c. Assume that a E (0, 1). Draw a diagram that describes the evolution of kt, and show that there exists a unique steady state, k* > 0. Label properly. Find the expressions for the steady state variables k*, y*, and c* in terms of the parameters of the model. , Now, assume that α = 1. Draw a diagram that describes the evolution of kt, and show that income per worker can grow indefinitely in this case. Label…Consider the Solow model (Y-AK1/4L3/4). Suppose that the productivity parameter is A=500, the depreciation rate is d=1/10, the savings (investment) rate is s=0.30, and the labor force is constant and equal to 2 million. ÊÊWhat is the steady state capital stock (K)? Please choose the closest answer." a. b. 48200 million C. 34341 million d. 15930 million 18340 millionsuppose the production formula is given by yt= kt ^1/3 where y is the output per worker and k is the capital per worker. futhermore assume that the saving rate is exogenous and the capital deprecitates at delta rate. if the sum of both deprectiation rate and saving rate equals 1, answer the questions below 1. find the steady state values of capital, output, investments and consumption as functions of the saving rate only? 2. in a diagram show the steady state value values in a part (a)?
- Hello I need help to find the answer for my econ 101 hw for a question as follows: Assume that the production function for a country is given by ?=√K and annual investment is given by the function ?=?×? where γ=0.270, and that the yearly depreciation rate is 4.50%. Suppose that this year, the output in the country is 1, and a neighbor country's output is 50% higher. Calculate the time it would take for the country's output to catch up with its neighbor's output. Assume the neighbor country's economy is neither growing nor shrinking. I will be also attaching the original problem for your reference as I just need to find the time that it would take the country's output to catch up with its neighbor's output. Thank You and please refer to the image to further assist with the question that I want answered.Assume there are only two producing sector Y & Z in an economy. Calculatea) Gross value added at market price by each sector b) National income from the followings:Items Amount in CroresNet factor income from abroad- 20Sales by Y= 1000Sales by Z= 2000Change in stock of Z= -200C Closingstock of Y= 50 Opening stock of Y= 100Consumption of fixed capital by Y & Z= 180Indirect taxes paid by Y & Z= 120Purchase of raw material by Y= 500Purchase of raw material by Z= 600Exports by Z= 702) 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.
- suppose that the production function is cobb douglas a. find the expression for k*, y* and c* as functions of the parameters of the model, s, n, 8 Show Transcribed Text b. what is the golden-rule value of k c. what saving rate is needed to yield the golden - rule capital stock?The saving rate is 30% and the depreciation rate is 10%. The production function of the economy is given as: Y = K05 L05 What is the steady state level of capital? Answer Choices: a. 9 units b. 10 units c. 11 units d. 12 units1. Suppose that the aggregate production function in the Solow-Swan model has the Cobb- Douglas form, y = ka. Also, assume a = 0.35, saving rate s = 15%, population growth n = 5%, technology growth g = 10%, and no depreciation ổ = 0%. (a) Show that f'(k) > 0, f"(k) < 0, and the Inada conditions limp-of"(k) = o and limz f'(k) = 0 are satisfied. (b) What are the numerical steady-state values of y* and e*? Show your workings. (c) Why is the steady state unique? (d) Assume labour and capital are paid their marginal products and the economy is on a balanced growth path at time t = 0: i) What is the real wage w(0) if A(0) = 1? ii) What is the growth rate of wages w/w along the balanced growth path? iii) What is the return to "working" capital r? iv) What are the shares of income going to capital and to labour? v) If the depreciation rate were positive (e.g., 6 = 10%), explain what would hap- pen to the return to "working" capital r and the shares of income going to (both "working" and…
- How does an increase in the capital depreciation rate & affect the steady-state consumption rate C*/Y*? What happens to this effect as a → 0?2. Assume a Cobb-Douglas production function with and alpha parameter of 0.5 for a society that saves 25% of their income but sees their capital depreciate at a rate of 5%. Complete the following table, make sure to identify which level of capital is the steady state amount. Note, after the first 4 production periods you can assume I jumped forward in time to the listed capital stock variables for year x, y, z. Assume all values to two decimals. Period 1 2 3 X y Z K* 8 16 36 Y* C* I* dk AkHouseholds across a nation face a reduction in wealth. As a result, savings will increase dispos able decrease not change and disposable income will increasedisposabledecreasenot change. This will lead to a/an increasedisposabledecreasenot change in supply of loanable funds. Therefore the equilibruim level of investment will