Question

Problem 1. (10 points.) This problem is based on the Ricardian Model. Assume that 2 countries, Gryffindor and Slytherin, use troll labor to produce 2 goods, magic wands and chocolate frogs (a) In Gryffindor, 1 troll can produce 6 magic wands or 10 chocolate frogs, while in Slytherin the production of 1 magic wand requires 2 trolls and the production of 1 chocolate frog requires 1 troll. Assume that there are 10 trolls in Gryffindor and 20 trolls in Slytherin. Draw a PPF for each country. b) Which country has a comparative advantage in magic wands and why (c) What is the possible maximum relative price of a magic wand in the trade equilibrium? What is its possible minimum price? (d) Suppose that in the trade equilibrium the relative price of a magic wand is Pw/Pf 1.8, where Pw is the world price of the magic wand and Pf is the world price of a chocolate frog. Which good will each country export? (e) For each country, calculate the real wage in terms of magic wands and in terms of chocolate frogs. (f) For each country, compare the values you obtained in part (e) with the real wage in terms of either good in the no-trade equilibrium. Do trolls in each country gain from trade?

Answer 1

a) For Gryffindor,

Max Magic wands production = 6 * 10 = 60

Max chocolate frog production = 10 * 10 = 100

For Slytherin,

Max Magic wands production = 0.5 * 20 = 10

Max chocolate frog production = 1 * 20 =20. The PPF for each country is as follows:

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b) For gryffindor, Opportunity cost of producing magic wands is = 100/60 = 5/3 = 1.667

  For slytherin, Opportunity cost of producing magic wands is = 20/10 = 2

As we can see, it is costlier for slytherin to produce magic wands as compared to gryffindor as its opportunity cost is higher. Thus, gryffindor has COMPARATIVE ADVANTAGE in producing Magic Wands.

c) Relative price of magic wands in gryffindor = P_mw/P_cf = 60/100 = 0.6

Relative price of magic wands in slytherin = P_mw/P_cf = 10/20 = 0.5

Therefor max rel. price is 0.6 and min rel. price is 0.5 in equilibrium.

d) P_W/P_F= 1.8 (GIVEN) or, P_F/ P_W = 1/1.8= 0.55

a_{w /} a_f = 0.60 for gryffindor and a_{w /} a_f = 0.50 for slytherin.

since, 0.60>0.55>0.50 according to ricardian model, gryffindor should export magic wands and slytherin should export chocolate frogs.

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NOTE: For further reference, ricardian model says the following:

IF P_W/P_F >a_{w /} a_{f ; then one should produce and export w}  

IF P_W/P_F<a_{w /} a_{f ; then one should produce and export f}

_{IF they are equal, any combination works.}