# 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 …