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Unformatted text preview: 10 out of 18 5 Consider an economy with the production function: Y= 2K0”6 (AN)°'4
Suppose, A, the productivity of labor (technological progress), rises at 3% per year. Labor force,
N, grows at 2% a year, depreciation rate is 7%, and saving rate is 50%. (Total 25 points) a) Derive the per effective worker production function. b) Write the dynamic equation of capital accumulation (fundamental Solow equation) for this
economy, in terms of per effective worker variables. c) Draw a wellmarked graph with all curves, which shows the steady state equilibrium of the
economy. Calculate the steady state per effective worker capital, output and consumption. d)— What are the growth rates of per effective worker capital, and output in steady state? Why?
e) What are the growth rate of per worker capital, and output in steady state? Why?
1) What are the growth rates of total capital, and output in steady state? Why? g) Find the golden rule per effective worker capital, per effective worker output, and saving rate.
Find the maximum possible per effective worker consumption in this economy. h)— Starting from part (c), suppose the saving rate increases. By drawing a new graph show how
the steady state variables change. (Only a complete graph and one sentence explanation) i) While the economy in the steady state equilibrium, suppose a natural disaster destroys only part
of the capital stock. By drawing a new graph show how the steady state variables change.
(Only a complete graph and one sentence explanation) j) Starting from part (c), suppose the technological growth rate increases. By drawing a new
graph show how the steady state variables change. Are people better off?
(Only a complete graph and a few sentences of explanation) You can use the back of this page for your answers 11 outof 18 12 out of 18 You can use this page and its back for your answers 13 out of 18 14 out of 18 6 Suppose an economy can be characterized by the following equations: (Total 25 points) Okun’s law: ut — ut.1 = — 0.05 (th — 4%)
Phillips curve: at — me = — 10 (ut — 7%)
Aggregate Demand: gyt =gm — nt Currently the unemployment rate is 7% (ut = 7%), and the inﬂation rate is 20% (1t:= 20%). The
government authorities have planned to reduce the inﬂation rate to 2%, by reducing the grth rate
of money supply to 6% a year, starting next year (gm =6%). a) What are the natural rate of unemployment, and nonaccelerating inﬂation rate of
unemployment (NAIRU) for this economy? (1 point) Combine aggregate demand and Okun’s law, to get one equation. Considering this equation and
the Phillips curve, answer following questions. b) Suppose people do not believe government in its disinﬂationary policies. Therefore they form
their expected inﬂation as: me = 1m. Find the unemployment rate, inﬂation rate, and output grth
rate for years 1, 2 (i.e. um, um, gy m, 11 H2, 1cm, gyt+2). Calculate the sacriﬁce ratio after 2 years of
disinﬂationary policy. (10 points) c) In this part, assume that half the people do not believe government, while the rest believe that
the inﬂation rate would be 2%. Find the unemployment rate, inﬂation rate, and output grth rate
for years 1, 2 (i.e. um, 7cm, gym, um, um, gy H2). Calculate the sacriﬁce ratio after 2 years of
disinﬂationary policy. (7 points) d) In this part, assume that everybody believes that the inﬂation rate would be 2%. Using the above
relations ﬁnd the unemployment rate, inﬂation rate, and output grth rate for years 1. (i.e. u m,
at“, gy m). How much is the sacriﬁce ratio in this case. (4 points) e) Using your results in parts (b) to (d), explain why it is believed that the disinﬂationary policies can
be costly for the economy, and how credibility of the policies can affect the size of the cost. (3 points) You can use the back of this page for your answers 15 out of 18 16 out of 18 You can use this page and its back for your answers 17 out of 18 18 out of 18 ...
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This note was uploaded on 04/10/2010 for the course ECO ECO202 taught by Professor Masoudanjamshoa during the Spring '10 term at University of Toronto.
 Spring '10
 MasoudAnjamshoa
 Macroeconomics

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