The Ricardian Model: Production Possibility Frontier, Autarky Equilibrium Price Ratio And Real Return To Labour

Overview of the Ricardian Model

Consider the following hypothetical situation, described in the table, showing unit labour requirements:

	Butter	Cloth
Home	1/5 (hours) Save Time On Research and Writing Hire a Pro to Write You a 100% Plagiarism-Free Paper. Get My Paper	1 (hours)
Foreign	1 (hours)	1/3 (hours)

1. In which commodity does Home have an absolute advantage? In which commodity does
   Foreign have an absolute advantage? Why?
   b. How much will Home gain if it trades 5 units of butter for 3 units of cloth? How much would
   foreign gain from the same trade? Why?
   c. How much will Home gain if it trades 5 units of butter for 6 units of cloth? How much would
   foreign gain from the same trade?

Short Answers

1. a) Home has an absolute advantage in producing butter. Foreign has an absolute advantage in producing cloth (Dornbusch, Fischer, and Samuelson, 2017, p.830).
2. b) If home trades 5 units of butter for 3 units of cloth, home will gain 2 unit hours of butter. From this trade, foreign will gain 3 unit hours of cloth (Greenwood, Hanson and Stein, 2015, p.1685).
3. c) If home trades 5 units of butter for 6 units of cloth, home will gain 5 unit hours of butter. From this trade, foreign will gain 3 unit hours of cloth (Hanson, Lind and Muendler, 2015)

Explanation:

1. a) Home has an absolute advantage in producing butter because it takes fewer hours (1/5hours) to produce a unit of butter than foreign which takes (1hour). Foreign has an absolute advantage in producing cloth because it takes fewer hours (1/3hours) to produce a unit of cloth than home which takes (1hour) (Costinot, Donaldson, Vogel, and Werning, 2015, p.670).
2. b) If home trades 5 units of butter for 3 units of cloth, home will gain 2 unit hours of butter (Vovchenko and Zhang, 2016, p.100). This is due to the fact that it will take home 1 hour to produce 5 units of butter but it will it 3 hours to produce 3 units of cloth, hence 2 hours gain. From this trade, foreign will gain 4 unit hours of cloth. This is due to the fact that it will take foreign 1 hour to produce 3 units of cloth but it takes it 5 hours to produce 5 units of butter hence 4 hours gain (Costinot and Donaldson, 2017, p.12).
3. c) If home trades 5 units of butter for 6 units of cloth, home will gain 5 unit hours of butter (Laursen, 2015, p.110). This is due to the fact that it will take home 1 hour to produce 5 units of butter but it takes foreign 6 hours to produce 6 units of cloth hence 5 hours gain. From this trade, foreign will gain 3 unit hours of cloth since it takes foreign 2 hours to produce 6 units of cloth but it takes it 5 hours to produce 5 units of butter hence 3 hours gain (Dellas, 2017, p.130).

Question 2: The Ricardian Model (15 marks)
Consider the following hypothetical situation, described in the table, showing unit labour requirements:

	Motorbikes	Skateboards
Home	5 (hours)	2 (hours)
Foreign	3 (hours)	3 (hours)

HOME has 1000 hours of labour available. FOREIGN has 1200 hours of labour available.

a. Draw the production possibility frontier for Home and Foreign.
b. In the absence of trade, what is the relative price of motorbikes in terms of skateboards in
each country?

1. Draw the world production possibility frontier clearly showing the case of specialization in comparative advantage and comparative disadvantage.
2. Trade is believed to make each country better off by enlarging the range of consumption
   choices available to residents/consumers. Compare the consumption possibilities available to
   Home and Foreign consumers in the closed economy and, in the open/trading economy cases.
   Graph the expanded consumption opportunities. The relative price of skateboards in terms
   of motorbikes under free trade is given and equal to 4/5.

Answers

1. a)
2. b) In absence of trade, the price of either bicycle or skateboard is determined by the number of hours spend in production (Ethier, 2017, p.185). This means that, the price of bicycles in home nation will be 5 while price for skateboards will be 3. On the other hand, price of both bicycles and skateboards will be 3 each in foreign nation.
3. c) In order to maximize the production, Home should use all hours to produce skateboards while Foreign should spend all hours to produce bicycles (Hamamatsu, 2018, p.210).

Therefore, Home 8 hours on skateboards This will translate into shared demand (Taylor, 2017, p.120). That is, people living in home will purchase bicycles from foreign nation while buy skateboards from Home country. This specialization scenario will maximize the returns in both nations increasing the comparative advantage (Taylor, 2013, p.230).

The curve will look like shown below,

d.) In a closed economy, foreign nation has the capacity to produce many bicycles and skateboards quickly (Obstfeld, Rogoff and Wren, 2016). This is evidenced by the number of hours it takes to manufacture a skateboard or bicycle. However, the Home nation is disadvantaged; it takes more hours to manufacture a bicycle. Therefore, consumption possibilities in home nation will be more towards skateboards since they are easy to manufacture and hence cheap (Venables, 2017, p.710).

Question 3: The Ricardian Model

Suppose two economies H and F produce two goods, X and Y, with only one input: labour. Production technology implies that unit labour requirements are given in the following table:

amount of labour per unit of output	X	Y
H	6	12
F	4	2

Suppose that H has 2400 units of labour and F has 1800 units of labour.

(a) What is the pattern of absolute advantage? Of comparative advantage? Give a brief explanation

(b) Derive the Production Possibilities Frontier (PPF) for H and F. What is the autarky equilibrium price ratio in each country? 

(c) What is the range of feasible equilibrium world price ratios? 

(d) Suppose these countries trade with each other at some feasible world price ratio. Which country exports good X? Why? 

(e) Does trade equalize the real return to labour in Home and Foreign? Why?

Answer

As given, economy H needs 6 units of labour for 1 unit of X and 12 units of labour for 1 unit of Y, having 2400 units of labour in total. While, economy F needs 4 units of labour for 1 unit of X and 2 units of labour for 1 unit of Y, having 1800 units of labour in total.

Production Possibility Frontier and Autarky Equilibrium Price Ratio

(a)  The country exporting good X will be the country having comparative advantage of X over Y. Again, F has absolute advantage over both commodities (Weder, 2017, p.80). But because the comparative advantage of a commodity refers to lesser relative price of the commodity, as calculated according to autarky, the relative price of X is  or 0.5 in H while is 2 in F, hence, H have comparative advantage of producing X over Y.

(b) For economy H, the production possibility frontier (PPF) will have y-intercept at point if all labour is producing Y, ie  while x-intercept at point if all labour is producing X, ie  . For economy F, the production possibility frontier (PPF) will have y-intercept at point if all labour is producing Y, ie while x-intercept at point if all labour is producing X, ie  ((Taylor, 2017, p.120). The equation will be linear, as since there is no capital, the cost of increasing output at the PPF curve will be constant. Now, remember that to find a linear equation with two variables by two given points  and  , will have the slope   , and equation  , for C be y intercept at X=0 ((Taylor, 2017, p.121).

Hence, for economy H, we have the points as (0,200) and (400,0) as the intercept’s coordinate, and hence  , will have the equation   For economy F, we have the points as (0,900) and (450,0) as the intercept’s coordinate, and hence   , will have the equation   .

The graphs are as below (graphed is scaled as x from 0 to 500 and y from 0 to 1000) (Hamamatsu, 2018, p.210).

Autarky equilibrium price ratio of good X is  , ie relative price of X with respect to Y. It is the slope of the PPF, and since the slope is same as due to constant cost, we have autarky price of X in H is , and in F is   . Note, only absolute value of slope is taken to show the relation’s magnitude (Levchenko and Zhang, 2016, p.100).

(c) Range of equilibrium feasible world price ratio will be the range between the relative autarky equilibrium prices of the two economies, ie range is , for  be the world price ratio.

(d) At the feasible world price ratio the country exporting good X will be the country having comparative advantage of X over Y. As can be seen in the graph, F has absolute advantage over both commodities. But comparative advantage of a commodity refers to lesser relative price of the commodity. As calculated, autarky relative price of X is  or 0.5 in H while is 2 in F, hence, H have comparative advantage of producing X over Y. Thus, H exports the good X.

Real Return to Labour

(e) Real returns to labour refer to how much the workers consume in amount of commodities (Ethier, 2017, p.185). Suppose their nominal wage is w, they would consume of X or  of Y. It can be seen as the number of X or Y the economy consumes is the number of X or Y it produces. Since output per labour is given in the table, the labour productivity is the reciprocal of it, and hence we can have the following table.

Real return of labour	of X	of Y
H	1/6 = 0.167	1/12 = 0.083
F	1/4 = 0.25	1/2 = 0.5

The table can also be interpreted as amount of output per unit of labour, in autarky.

After trade, the wages (real return of labour) will remain same as that of autarky for goods with comparative advantage, but wages will depend on world price ratio for goods not produced due to comparative disadvantage (Ethier, 2017, p.182). For this second case, the wage will be taken as  . The table is as below.

Real return of labour	of X	of Y
H	1/6 = 0.167
F		1/2 = 0.5

Hence, as can be seen, the real returns of labour in H was 0.167 and 0.083, but now is 0.167 and  and for  . Also, the real returns of labour in F was 0.25 and 0.5, but now is  and 0.5, and for  . Hence, workers are better off in both nations producing both goods (Ethier, 2017, p.180).

Hence, real return to labour has increased in both nations because of trade. The actual comparison can be made only if the world price ratio is stated, but in theory, real returns to labour become more equal throughout the world as nations do free trade.

References

Costinot, A., Donaldson, D., Vogel, J. and Werning, I., 2015. Comparative advantage and optimal trade policy. The Quarterly Journal of Economics, 130(2), pp.659-702.

Costinot, A. and Donaldson, D., 2017. Old idea, new insights: The Ricardian revival in international trade. NBER Reporter, (3), pp.11-15.

Dellas, H., 2017. Discussion About “The Main Contribution of the Ricardian Trade Theory”. In 200 Years of Ricardian Trade Theory (pp. 129-132). Springer, Cham.

Dornbusch, R., Fischer, S. and Samuelson, P.A., 2017. Comparative advantage, trade, and payments in a Ricardian model with a continuum of goods. The American Economic Review, 67(5), pp.823-839.

Ethier, W.J., 2017. The Relevance of Ricardian Trade Theory for the Political Economy of Trade Policy. In 200 Years of Ricardian Trade Theory (pp. 185-187). Springer, Cham.

Greenwood, R., Hanson, S.G. and Stein, J.C., 2015. A Comparative?Advantage Approach to Government Debt Maturity. The Journal of Finance, 70(4), pp.1683-1722.

Hisamatsu, T., 2018. Robert Torrens and the Ricardian model of dynamic equilibrium growth. The European Journal of the History of Economic Thought, 25(2), pp.203-226.

Hanson, G.H., Lind, N. and Muendler, M.A., 2015. The dynamics of comparative advantage (No. w21753). National bureau of economic research.

Levchenko, A.A. and Zhang, J., 2016. The evolution of comparative advantage: Measurement and welfare implications. Journal of Monetary Economics, 78, pp.96-111.

Laursen, K., 2015. Revealed comparative advantage and the alternatives as measures of international specialization. Eurasian Business Review, 5(1), pp.99-115.

Taylor, M.S., 2017. Comments on the “The Main Contribution of the Ricardian Trade Theory” by Ronald W. Jones. In 200 Years of Ricardian Trade Theory (pp. 117-127). Springer, Cham.

Taylor, M.S., 2013. ‘Quality ladders’ and Ricardian trade. Journal of International Economics, 34(3-4), pp.225-243.

Obstfeld, M., Rogoff, K.S. and Wren-lewis, S., 2016. Foundations of international macroeconomics (Vol. 30). Cambridge, MA: MIT press.

Venables, A.J., 2017. Trade and trade policy with differentiated products: A Chamberlinian-Ricardian model. The Economic Journal, 97(387), pp.700-717.

Weder, R., 2017. The Ricardian Trade Model: Implications and Applications. In 200 Years of Ricardian Trade Theory (pp. 73-97). Springer, Cham.