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Outline of Answers to Problem Set 1
(1) A traded good is one that can be bought and sold through the international market.
A nontraded good cannot. Of course, these are extreme descriptions of reality, and some goods may be partially but not fully tradeable. Equilibrium exchange rates are determined by the supply of and demand for a country’s currency. The supply of a country’s currency is determined by that country’s purchases of imports on the world market. The demand for its currency is determined by the purchase of that country’s exports by the world. The exchange rate acts to equalize these two (thereby creating trade balance). Notice that a rich and productive country is likely to have a stronger currency and a higher income. The higher income, in turns, pulls up the prices of those products within the country that are nontraded.
Thus measured in terms of exchange rate income, a rich country looks richer than it really is, because, we are not accounting for the fact that it faces (on average) higher donestic prices for the nontraded goods. This is why PPP measurements typically bring down the relative income of a rich country, and pull up the relative income of a poor country.
(2) The price of a Big Mac is, to a large extent, determined by the prices in competing restaurants. Thus Big Macs will sell for a higher price in rich countries (where nontraded restaurant prices are likely to be higher). Thus Big Mac prices incorporate, to some extent
— and often to a better extent than exchange rates do — the “true” cost of living within a country. Therefore, using the relative prices of Big Macs to create “exchange rates” across country currencies will often serve as a good approximation of relative PPP income.
(3) The setting up of infrastructure or industrial standards involves a “sunk cost” and a
“variable cost”. The sunk cost is the cost of the entire infrastructure: in the example of tv systems, this would be all kinds of interconnected senders and receivers that broadcast at a particular type and reﬁnement of resolution. The variable cost refers to the individual purchase of tv sets. Now given that the infrastructure is not set up for it, it makes a little sense for customers to buy high-deﬁnition tv sets. Moreover, given the huge sunk costs, countries which have already invested in a particular standard may not want to tear up this standard and start all over again, unless the new technology is much, much better. However, a country that is starting afresh will obviously want to use the latest technology: there is no past, no sunk cost, to be borne in mind. This is why countries which have been early innovators are often saddled with older systems, and newcomers can leapfrog over them with the newer technology. Television and telephone systems are only two examples of these.
In the problem that accompanies the question, the value of the existing technology is xT
(without any discounting). The value of the new technology is yT , and net of cost it is yT − C. Therefore the new technology will be installed if yT − C > xT . Clearly, the larger the current value of x the less likely it is that this inequality will hold, so it is entirely possible that a country with x = 0 today will adopt while a country with x > 0 today will not.
(4) Exponential growth
(a) 5%: double 2 = (1 + 0.05)t , t = 14 quadruple: t = 28
10%: double 70/10 = 7 quadruple: t = 14
(b) Approximation: y = Y − P
ˆ ˆ y = 5 − (−1) = 6
After 20 years: (1 + 0.06)20 = 3.207
(c) compounding: (1.3)12 = 23.29, or 2329% per year
(5) No mobility