. Consider a Solow growth model where the saving rate is 0.5 and the production function is given by Y; = K (y*L)'-«, where a = 1/3 and y= 1.02. In addition assume that the depreciation rate of capital is 8 = 0.01. Finally, assume that the capital stock at time 0 is such that the economy is on the balanced growth path from the beginning of time. Calculate the interest rate and the capital-output ratio.

. Consider a Solow growth model where the saving rate is 0.5 and the production function is given by Y; = K (y*L)'-«, where a = 1/3 and y= 1.02. In addition assume that the depreciation rate of capital is 8 = 0.01. Finally, assume that the capital stock at time 0 is such that the economy is on the balanced growth path from the beginning of time. Calculate the interest rate and the capital-output ratio.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Question

4. Consider a Solow growth model where the saving rate is 0.5 and the production function
is given by
Y; = K°(^'L)'-«,
where a =
1/3 and y =
1.02. In addition assume that the depreciation rate of capital
is 8 = 0.01. Finally, assume that the capital stock at time 0 is such that the economy
is on the balanced growth path from the beginning of time. Calculate the interest rate
and the capital-output ratio.

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) 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?
An economy's production function as follows Y = 8 (K)¹/2 (EL)¹/2 If depreciation rate is 10%, population growth rate is 4%, tech progress grows 6%, and saving rate is 20%. a. b. C. d. e. f. Write production function in term of per effective worker variables. Find steady state capital per effective worker, output per effective worker, consumption per effective worker, investment per effective worker. Find growth rate of capital per worker and output per worker at steady state. Find growth rate of capital stock and total output at steady state. Propose policies to encourage long run growth of total output and living standard? Draw relevant graph for the above questions.
Q1 The steady state Consider the Basic Solow Model without exogenous growth: Y-AKOL-a C= (1-8)Y Y=C+I K' I (1-8)K where labor is constant. Assume the following values for the rest of this question: A=100 a = 0.35 s=0.12 8=0.10 L=25 For each question that follows, if the answer depends on the answer(s) to previous question(s), use unrounded answers in do calculations. If you do not, rounding error will accumulate. Q1.1 Compute steady state capital per worker. Round your answer to at least three decimal places.
Consider our graph of the basic Solow growth model. On the graph above: y represents real output (or income) per worker; y=F(k) is the production function; k is the capital stock per worker; s is the savings rate; δ is the rate of depreciation of capital; ‘i’ represents business investment (purchases of capital) per worker); ‘LF’ stands for Loanable Funds. (For purposed of intuition, think of capital as ‘machines.’) If we started out with a capital (per worker) stock lower than the steady-state stock ( , above), we would expect to see which of the following happen over time? Group of answer choices A) Positive growth rates while the capital stock increases. B) Negative growth rates while the capital stock increases. C) Negative growth rates while the capital stock decreases. D) Positive growth rates while the capital stock stays less than the steady-state level. E) Positive growth rates while the capital stock decreases.