Problem Set 3 MSU EC 410 Prof. Ahlin due 11/8/16 1a. Use the H-augmented Solow model to determine the a) instantaneous impact on GDP per capita, b)...
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Problem Set 3
MSU EC 410
Prof. Ahlin
due 11 /8/16
1a. Use the H -augmented Solow model to determine the a) instantaneous impact on GDP per capita, b)
instantaneous impact on consumption per capita, c) long -run impact on GDP per capita, d) long -run impact on
consumption per capita, e) impact on long -run GDP per capita growth rate, and f) impact on long -run GDP
growth rate of a permanent and instantaneous increase in the fraction of national resources devoted to
investment in human capital, q . Assume the country begins at its steady state values of k * and h * before this
event occurs. Justify your answer by use of graph and/or equation.
1b. How does each answer compare to the answer the original Solow model would give when s increases,
both qualitatively ( whether the amou nt goes up or down) and quantitatively (the amount by which it goes up or
down)?
2. Growth Simulations contin ued . See GrowthSimulationQuestion b.xlsx posted on D2L. Fill in 200 years of
data using the H -Solow model using the functions and parameters given in the “GrowthCalculations”
worksheet. The savings rate increases to 30% at year 25. The H -Solow model is columns W -AE . Specifically:
f(k,h) = k1/3 h1/3 , A=5, n=0.01, d=0.04, q = 0.1, and s=0.2. Physica l capital per person starts at $4000, human
capital per person starts at $2000. Fill out k, h, y, c, k, h, and g y for 200 years.
Note that the savings rate s switches t o 0.3 at the 25th year. Make sure to incorporate this in your answers.
[Hint: it will only affect the consumption formula and the k col umn formula for the H -Solow model.]
a. Give the formulas used for all columns (in mathemat ical syntax, not Excel syntax) :
k, h, y, c, k, h, and g y
b. Give the income and consumption levels in year 2 4 and in year 200 . How does the effectiveness of the
increase in s in the H-Solow model compare to its effectiveness in the H-D and Solow models ? Justify your
answer.
c. Look at the graphs for the models (which are in the other worksheets in the Excel file, and should be filled
out automatically from the data you generate in the G rowthCalculations worksheet). Look at both H -D graphs,
but focus on the one using logs. Discuss one significant way in which all three models’ graphs are similar.
How do the Solow and H -Solow graphs differ? Do not turn in your spreadsheet, but along with answer ing the
questions here, also print out the H -Solow graph and turn it in.
3a. If total factor productivity growth were based solely on domestic invention and innovation, divergence in
GDP per capita across countries would be likely proceed very r apidly, since rates of invention and innovation
are highly skewed across countries. What force tends to keep divergence in GDP per capita lower than this
scenario would imply? How?
3b. What might be a drawback of infinite -duration intellectual property p rotection? What might be a drawback
of no intellectual property protection?
4. Imagine that a bank will only lend if it can earn a rate of return of 6% on a loan. Further, imagine it
incurs administrative costs of $40 per loan it makes, regardless of the size of the loan. Throughout the problem,
assume for simplicity that the loans are all repaid with certainty, i.e. there is no risk.
a. If the bank makes five loans – of $100, $200, $500, $1000, and $10,000 – what are the respective
interest rates it must char ge to break even on each loan?
b. Imagine the bank makes the same five loans as in part a., but must charge all borrowers the same interest
rate. What interest rate will it charge to break even overall? Which borrowers pay less, which pay more in this
case than in p art a.? This practice of making losses on some loans and profits on others is called “cross -
subsidization”. 2
c. How might competition between banks eliminate any one bank’s ability to cross -subsidize smaller
borrowers? Specifically, ci) could a rival lend er lure away any of the customers of a bank carrying out the
policy of part b., and cii) how would this affect the ability of a bank carrying out the policy of part b. to cross -
subsidize smaller borrowers ?
d. It may not be accurate to assume that every loan incurs the same administrative cost, irrespective of size.
Larger loans may require more work. Redo part a. under the assumption that the administrative cost of
servicing a loan is $40 per loan plus 1% of the size of the loan. (Thus a loan of $5000 would cost the bank $40
+ 1%*$5000 = $90, while a loan of $500 would cost the bank $40 + 1%*$500 = $45.)
