# Production function, growth rates, demand function

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Production function, growth rates, demand function 1 answer below » Question 1 Growthistan has a very technologically advanced neighboring
country, Techistan, whose initial level of technology is A­*=10. Suppose that the
economy operates with a production function of the form Y(t) = A x
[K(t)] 0.5 . Let’s compare the growth of both countries from 2005 to
2100. (a) Suppose that both Techistan and
Growthistan have s=0.1, d=.05, and initial level of capital K 0= 2.
Growthistan’s level of technology is 2. Plot Y(t), ln[Y(t)] and the growth
rate for both countries. What happens to
the level of Y(2100), and what happens to the growth rate of the economy toward View complete question » Question 1 Growthistan has a very technologically advanced neighboring
country, Techistan, whose initial level of technology is A­*=10. Suppose that the
economy operates with a production function of the form Y(t) = A x
[K(t)] 0.5 . Let’s compare the growth of both countries from 2005 to
2100. (a) Suppose that both Techistan and
Growthistan have s=0.1, d=.05, and initial level of capital K 0= 2.
Growthistan’s level of technology is 2. Plot Y(t), ln[Y(t)] and the growth
rate for both countries. What happens to
the level of Y(2100), and what happens to the growth rate of the economy toward
the year 2100? Compare the difference. Techistan has just decided to start trading liberally with
Growthistan. As those two countries
trade over time, technology diffuses from Techistan to Growthistan. The rate of diffusion depends on the
proportionate technology gap between these two countries, and is governed by this
equation: A­(t+1) = A(t)
+ g x [A* –
A(t)] Where A(t) is Growthistan’s technology level, and A* is
Techistan’s technology level. The
starting value of Growthistan’s technology, A(2005) = 2. g is a constant of technological diffusion whose value is
0.05 The production function is Y(t) = A(t) * [K(t)] 0.5 s = 0.2; d = 0.05; g = 0.05; K 0 = 5 (b) Graph Growthistan’s GNP for
2005 to 2100. (c) Compare the two graphs for GNP
for Techistan and Growthistan. What is
the difference in the final value of GNP for each country? (1 paragraph) (d) Plot the growth rate for
Techistan and Growthistan on one plot.
How do these rates compare? Why? (1 paragraph) (e) Can you think of two real-world
countries whose growth paths have been similar to this? Who and why? (1
paragraph) Question
2 Following
the example in section, we will look at an intertemporal problem of
nonrenewable resource depletion. Assume
that the remaining oil supply in the world is S =
6,000 units The
energy demand during each period is D =
100,000 / P And
the annual interest rate is 3.5% so that R = 1 over 20 years (like in the lecture
slides). a) We
are now interested in three periods: today (period 1), 20 years from now
(period 2), and 40 years from now (period 3).
Assume that there is a backstop technology currently available, and its
price is \$100. Solve for the price of
energy and the consumption of energy in the three periods, as well as how much
of it in every period comes from oil versus the backstop technology. b) We
will now compare scenario (a) with one where today’s society can forego some
consumption in the present to develop alternative technologies for the
future. Assume that solar power can be
made available for period 2 at a price of \$50 only if we choose today to pay
the equivalent of 1000 energy units into R&D (assume that consumption is
equal to the amount of energy consumed minus the amount put into R&D). Under this scenario, when will we begin to
use solar power? Is any time period
better off (in terms of consumption) compared to time period (a)? Will the present generation choose to invest
in the R&D, assuming it cares about its own well-being much more than about
the future? c) Now
assume that the price of solar technology made available by R&D for period
2 is \$35. What is the new energy use for
the three periods? Will today’s
generation invest in the R&D, assuming it …