ECON 0028: The Economics of Growth Term 1 (Fall 2022) ASSIGNMENT 4
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ECON 0028: The Economics of Growth
Term 1 (Fall 2022)
ASSIGNMENT 4
Due on December 11 (Sunday), 12noon
1. Consider the Romer model in which the standing on the shoulders effect exactly offsets the fishing out effect. Assume that population grows at a constant rate n.
(a) What is the value of parameter that guides the diminishing returns to accumulating knowledge and ideas? What is gA , the long-run growth rate of the economy?
(b) Under this value of the parameter, write down the ideas produc- tion function, with the growth rate of ideas (i.e. 
) on the left hand side. Mathematically, what kind of equation is this?
(c) Solve this equation graphically: set up a graph with the growth rate of technology on the y-axis and LA /A on the x-axis. Plot first the right-hand side of your ideas production function. Then plot the value of 
in the long-run that you calculated in (a). Mark with X1 the point on your diagram that corresponds to the BGP of this economy.
(d) Starting from that BGP, consider a permanent one-off jump up in the value of sR , the share of labor resources devoted to R&D. This could happen for a variety of reasons – come up with a couple of examples (but assume that parameters n and θ do not change). Do any of the curves you plotted shift as a result of the increase in sR ? Why or why not?
(e) Mark the point that denotes the position of the economy imme- diately after the increase with X2. At this point, what is growing faster: LA or A? (remember that sR jumps up one day, but does not change thereafter). Based on this answer, what is happening to LA /A?
(f) Trace out the transition path of the economy to the new BGP. Int he long-run, is there a growth rate effect? Is there a level effect?
Explain your answer by plotting 
and log A over time, starting from t = − 10 and assuming that sR jumped up at t = 0.
2. Consider the simple model of imitation that we discussed in the lecture. Assume that the growth rate of frontier knowledge is gA = 1% per annum.
(a) Provide some economic intuition for the role of parameter µ . What values of µ guarantee that h/A is less than one?
(b) Provide some intuition for the parameter γ . Fill in the gaps: γ is an elasticity of .......... with respect to .......... . (If you don’t know
what an elasticity is, you can google it).
(c) Assume that µ = 0.005 and γ = 2. How much richer are people in the frontier countries, relative to the developing country you are analyzing, on the BGP? What happens to this gap as γ increases? Plot a graph of the technological gap on the BGP as a function of the elasticity γ (the gap on the y-axis, γ on the x-axis).
(d) Assume that γ = 1 so that 
= µ 
. Solve this equation graph- ically: construct a diagram with 
on the y-axis and 
on the x-axis and plot the right hand side, as well as the (horizontal) line that denotes the value of the growth rate of h on the BGP (what is this value?).
(e) Assume that µ = 0.005 and γ = 1. Starting from the BGP, trace out the effects of a visitor program that sends managers of domestic firms to the US, thus permanently increasing their ability to imitate frontier technologies by 50% (thus raising µ by this proportion). In the long-run, are there growth rate effects? Are there level effects?
3. There are two countries X and Z . Productivity in Country X is twice as high as productivity in Country Z . Technology in Country X is four times as high as technology in Country Z . How does efficiency in the two countries compare?
4. Consider a country in which ther are two sectors, called Sector 1 and Sector 2. The production functions in the two sectors are:
Y1 = L 1(1)/2
Y2 = L2(1)/2
where L1 is the number of workers employed in Sector 1 and L2 is the number of workers employed in Sector 2. The total number of workers in the economy is L. The only difference between the sectors is that in Sector 1 workers are paid their marginal products, while in Sector 2 they are paid their average products. Workers move freely between sectors so that the wages are equal. Calculate how many workers will work in each sector. Is the allocation efficient? If not, characterize the efficient allocation and calculate the percentage increase in output per worker.
2023-04-28