# Capital per capita Investment to capital ratio Output per capita kt it /kt yt t United States China United States China United States China 2 3 5 6

and ﻿

﻿ and ﻿

where Yt denotes output, Kt denotes the stock of physical capital, L denotes population, St denotes savings, and It denotes investment. The subscripts us and ch denote, respectively, the United States and China. Suppose that the parameters A, α, σ, and δ are the same in the United States and China. In particular, assume that α = 0.3, σ = 0.25, and δ = 0.1.

(a) Suppose that the capital to GDP ratio in the United States in 2014 was 2.5, that is, ﻿ in 2014. Use this information and the production technology given above to deduce the value of A. Use this value throughout the remainder of this exercise.

(b) Given the information above, calculate the 2014 capital to labor ratios in the United States and China, ﻿ and ﻿ in 2014.

(c) Produce the equilibrium dynamics of capital per capita, investment per capita, and output per capita in the United States and China predicted by the Solow model starting in 2014. Speciﬁcally, ﬁll out the table on the last page. In the table, ﻿ denotes capital per capita, ﻿ denotes output per capita, and ﻿ denotes investment per capita. The year 2014 is normalize to t = 1.

(d) Let us say that China’s GDP per capita has converged to that of the U.S. when the latter is less than 10 percent larger than the former (i.e., when ﻿ ). In what year does the Solow model predict this to happen? Compare your answer to the one you gave to a similar question in homework 1.

(e) Comment on the equilibrium dynamics for the United States.

(f) Using a software of your choice (for example, Matlab), produce a graph showing the time period, t, on the horizontal axis and output per capita, yt, in the U.S. and China as predicted by the Solow model on the vertical axis. Comment.

(g) Make a graph like the one in the previous question, but with the ratio of investment per capita to capital per capita ﻿ instead of output per capita on the vertical axis. Comment.

Capital per capitaInvestment to capital ratioOutput per capitaktit /ktyttUnited StatesChinaUnited StatesChinaUnited StatesChina235610111213141516171819202122

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