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Problem Set 1

2022

Question 1:  The Law of Comparative Advantage (Lecture 1)

The proof of the Law of Comparative Advantage in the lecture is for endow- ment economies.  Suppose now that the countries are not endowed with goods (which we denoted as Ei  for country i in the lecture.) but have to produce each good (using factor inputs such as labour). Let’s denote the output vector by Yi  for country i.  Suppose the outputs are produced by proﬁt maximizing rms. Prove the Law of Comparative Advantage:

(pia _ pW )Ti  < 0

while Ti  = Yi _ Di . (Hint: what does proﬁt maximization imply?)

Question 2:  2 x 2 Ricardian Model (Lecture 2)

Consider the 2 x 2 Ricardian Model, what does the model predict when there is

(a) Balanced Productivity Growth:  aL(*)C   and aL(*)W   fall proportionately, leaving aL(*)C /aL(*)W  unchanged

(b) Import-Biased Productivity Growth: aL(*)W  falls but aL(*)C  doesn’t

(c) Population Growth: Home country labor supply L increases

(Hint: how do the shocks aﬀect the RS curve? Use the RS-RD graph for the analysis.)

Question 3:  The DFS Model (Lecture 2)

Consider the DFS model discussed in class, assuming that the relative unit labor requirement A(z) =  = 1 _ z, the expenditure share is constant

b(z) = b(z)*  = 1, and the size of home is three times as large as the foreign L = 3L* .

(a) Can you determine B(z) =   given the assumptions above?

(b) Putting A(z) and B(z) together, can you determine the industry that both countries produce  and the equilibrium relative wage ω = ?

(c) What if the size of home country becomes even larger, say L = 4L* , how does the patten of production and welfare respond to the shock?