Consider a Ricardian trade model with two countries A and B which produce goods x and y from labour. The countries’ labour endowments are given by LA=50 and LB=60. The marginal products of labour for producing good x are MPLxA=4 and MPLxB=2, respectively, in countries A and B. The marginal products of labour for producing good y are MPLyA=3 and MPLyB= μ, respectively, in countries A and B. [20%]
(a) Give the range of μ for which country A will export good x to country B. (Hint: compare opportunity costs.)
(b) Assume now that the international relative price of good x (terms of trade) is τ. Provide the ranges of μ and τ that allow country A to import good x from country B. (Hint: compare opportunity costs and international price.)
(c) Given the ranges of μ and τ provided in part (b), evaluate country A's gains from trade in terms of real wages, measured in good x. (Hint: calculate the real wages before and after trade, measured in good x.)
(d) Given the ranges of μ and τ provided in part (b), evaluate for country B's gains from trade in terms of consumption opportunities, measured in good y. (Hint: compare the maximum quantities of y country B can consume before and after trade.)
Previously I have answered parts a) and b) of this multiple-question post.
Here I will go on to answer parts c) and d), which require the results from part b) (see previous answer referenced below).
From part b) we calculated that the ranges for mu and tau are given by
mu < 6/4 , that is mu < 3/2
mu/2 < tau <3/4
c) Now, in the Ricardian model we find that if country B has a comparative advantage over A in producing goods x and A has a comparative advantage over B in producing goods y, then each country specialises in the goods they have a comparative advantage in, and so make one good only (x or y) and import the other.
So we have the situation, if B exports goods x to A, that B makes goods x only and A makes goods y only.
Before a trade relationship between the two countries is set up, A can only make goods x using its own labour force. Since the marginal product of labour for producing x is MPL(A,x) = 4, each labourer added to the workforce making x can produce 4x in unit time. If he/she is paid in terms of x (as currency), providing they take 100% of the goods, they can earn a maximum of 4x per unit time. Before trade then, a labourers real wages in x is 4 per unit time.
After trade however, in a unit of time the same labourer (who now exclusively works in making the goods y) can produce 3 units of y. Exchanging this job lot of y for x at the international price exchange rate (Py = Py/Px . Px, that is the price of y is Py/Px times the price of x, where Py/Px is equivalent to the international relative price of y to x, =1/tau), the labourer can earn (if earnings are 100%) 3Py, which in terms of real wages in x is equal to 3Py/Px = 3/tau.
So country A's gains in trade in terms of real wages in x is equal to the difference between the real wages after trade and that before trade, that is
3/tau - 4
Using the results found from part b) given above, country A's gains from trade in real wages in x, G(A,x) are such that
G(A,x) = 3/tau - 4
and since mu/2 < tau < 3/4,
3/(3/4) - 4 < G(A,x) < 3/(mu/2) - 4 giving
0 < G(A,x) < 6/mu - 4
So for the trade relationship to be in existence, there must be a positive gain for country A in terms of real wages in x. If there were no gain, they would not trade with B.
d) For country B, we are interested in the gain in consumption opportunities in terms of y as a result of trade with country A.
Before trade, the most country B can consume in y is the total amount it can produce when devoting all of its labour force (labour endowment L(B)) to making y. Country B's labour force is given as L(B) = 60. The marginal labour product of one labourer making y is MPL(B,y) = mu, so that if all the workforce are producing y, 60mu of goods y can be produced for consumption per unit time.
After trade with country A, given B would be specialising in making goods x only, the maximum amount of x it can produce with all of its labour force per unit time is equal to L(B)MPL(B,x) = 60(2) = 120. If B trades this maximum output of goods with A at the international relative price of x to y, tau = Px/Py, then in a unit of time B can earn for its own consumption 120Px which in terms of consumption of y is 120Px/Py = 120tau of goods y per unit time.
So country B's gains in trade in terms of consumption opportunities in goods y is equal to the difference between that after trade and that before trade, that is
120tau - 60mu
Using the results found from part b) given above, country B's gains from trade in consumption opportunities in y, C(B,y) are such that
C(B,y) = 120tau - 60mu
and since mu/2 < tau < 3/4,
120(mu/2) - 60mu < C(B,y) < 90 - 60mu giving
0 < C(B,y) < 90 - 60mu
So as with country A's gains in real wages, for the trade relationship to be in existence, there must be a positive gain for country B in terms of consumption opportunities in goods y. In the same way, if there were no gain, they would not trade with A.