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 amount goes up or down) and quantitatively (the amount by which it goes up or down)?
2. Consider the Solow model with total factor productivity At constantly growing at rate g>0.
a. Determine the a) instantaneous impact on GDP per capita, b) instantaneous impact on consumption per capita, c) long-run impact on GDP per capita (i.e. compare the level of GDP per capita with and without the parameter change, in the long-run), d) long-run impact on consumption per capita (i.e. compare the level of consumption per capita with and without the parameter change, in the long-run), and e) impact on long-run GDP per capita growth rate of a one-time and instantaneous increase (jump) in productivity At, through a significant and non-repeatable invention. Assume the country begins at its "steady state value" of k* before this event occurs. Justify your answer by use of graph and/or equation. [Hint: this should not be considered a change in g, since productivity resumes growth at rate g after the one-time jump; it should be modeled as a one- time jump in At.]
b. Graph the path of yt and ct against time (or better yet, ln(yt) and ln(ct), which will be linear) for the event analyzed in part a.
c. Repeat parts a&b for a permanent, instantaneous increase in the growth rate of productivity, g.
3. a. 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 rapidly, 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?
b. What might be a drawback of infinite-duration intellectual property protection? 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 charge to break even on each loan?
b. Imagine the bank makes the same loans 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 part a.? This practice of making losses on some loans and profits on others is called "cross-subsidization".
c. How might competition between banks eliminate any one bank's ability to cross-subsidize smaller borrowers? Specifically, ci) could a rival lender lure away any of the customers of a bank carrying out the policy of part b., and cii) how would this affect the ability to cross-subsidize of a bank carrying out the policy of part b.?
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 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. The cost structure is still linear, but with a positive intercept and slope.)