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Econ 105C Intermediate Quantitative Economics III,: Problem Set 7
due in Gradescope on Tuesday, May 26
1. IS-MP Model with Two Interest Rates (Romer handout, Section V, part of problem 4):
Suppose financial innovations reduce the interest rate differential at a given level of output.
How, if at all, does this development affect output, Y, and the saving real interest rate rs? How
does it affect the borrowing real interest rate rb? Draw a diagram to help illustrate your answer.
2. Growth Rate Calculations. U.S. GDP in 2025 was $30.8 trillion, and U.S. GDP/person in
2025 was about $91,100, while China’s GDP in 2025 was $19.6 trillion (converted to US$ at
market exchange rates), and China’s GDP/person in 2025 was $29,400 (converted to US$ at
PPP-adjusted exchange rates).
a) Suppose that U.S. real GDP continues to grow at its recent pace of 2.3%/yr. What will U.S.
real GDP (in 2025$) be in 2035? (Recall that if a series y grows at a constant rate g, then yt
= y0 (1+g)t.)
b) Suppose instead that U.S. real GDP grows at its longer-run historical rate of 3.25%/yr.
What would U.S. real GDP (in 2025$) be in 2035 in that case?
c) Suppose that U.S. real GDP/person continues to grow at its recent pace of 1.6%/yr. What
will U.S. real GDP/person (in 2025$) be in 2035?
d) Suppose instead that U.S. real GDP/person grows at its longer-run historical rate of 2.1%/yr.
What would U.S. real GDP/person (in 2025$) be in 2035 in that case?
e) Suppose that China’s real GDP continues to grow at its historical average rate of 9.1%/yr.
What will China’s real GDP (in 2025US$) be in 2035?
f) Suppose that China’s real GDP/person continues to grow at its historical average rate of
8.2%/yr. What will China’s real GDP/person (in PPP-adjusted 2025US$) be in 2035?
g) If the U.S. grows at the same rate as in part a, and China grows at the same rate as in part e,
in how many years from now will China’s real GDP be equal to the U.S.’s real GDP?
h) If the U.S grows at the same rate as in part c and China grows at the same rate as in part f, in
what year will China’s standard of living be equal to the U.S.’s standard of livin
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