Question

There are 100 workers both in Home and Foreign to produce ice and tea. Home needs 1 worker to produce 1 unit of ice and 2 workers to produce 1 unit of tea. Foreign needs 2 workers to produce 1 unit of ice and 1 worker to produce 1 unit of tea. (a) Which country has a comparative advantage in ice? Which country has a comparative advantage in tea? The consumers in Home and Foreign have different preferences. Home's preference can be represented by a Cobb-Douglas utility function:

UH(CHI,CHT)=(CHI)0.5(CHT)0.5
The consumers in Foreign, however, have a Leontief preference:
UF(CFI,CFT)=min(CFI,CFT).

Assume that there exists an equilibrium with complete specialisation.
(b) What is the equilibrium production of ice and tea?
(c) Let tea be the numeraire (PT=1). What is the equilibrium consumption as a function of the price of ice (PI) ?
(d) Find the equilibrium price. Why is this an equilibrium? Suppose now migration is free (we assumed that migration is infinitely costly).
(e) What do you expect to happen?
We have assumed free trade. Therefore, PHI=PFI. Now suppose that because of climate change, ice melts when transported. Only a fraction of the starting amount arrives at the destination. In other words, in order to export 1 unit of ice to Foreign, Home needs to transport τ(>1) units of ice. This is what trade economists call the iceberg trade cost.
(f) With an iceberg trade cost τ, if the price of ice in Home is PHI and Home specialises in ice, what would be the price of ice in Foreign PFI ?
(g) If τ=1.2, find the new equilibrium price with complete specialisation. (h) What do you expect to happen if τ=3 ?

Answer 1

Comparative advantage is determined by the ability of a country to produce a good at a lower opportunity cost than other countries. Home has a comparative advantage in ice, while Foreign has a comparative advantage in tea. In the equilibrium with complete specialization, Home will produce ice and Foreign will produce tea, resulting in an efficient allocation of labor and increased production of both goods.

Step-by-step explanation:

Comparative advantage refers to a country's ability to produce a good or service at a lower opportunity cost than other countries. In this case, Home has a comparative advantage in ice because it only needs 1 worker to produce 1 unit of ice, while Foreign needs 2 workers. On the other hand, Foreign has a comparative advantage in tea because it only needs 1 worker to produce 1 unit of tea, whereas Home needs 2 workers.

(b) In the equilibrium with complete specialization, Home will produce ice and Foreign will produce tea. To find the equilibrium production, we can compare the labor requirements for producing ice and tea in each country. Since Home needs 1 worker for 1 unit of ice and Foreign needs 2 workers, Home will produce ice. Similarly, since Home needs 2 workers for 1 unit of tea and Foreign needs 1 worker, Foreign will produce tea.

(c) If tea is the numeraire (the price of tea is 1), then the equilibrium consumption as a function of the price of ice (PI) is given by the ratio of the prices of tea and ice: CHT/CHI = PFT/PIT.

(d) The equilibrium price is determined by the intersection of the demand and supply curves in the market. In this case, since there is complete specialization, the demand for tea in Home and the demand for ice in Foreign will be zero. As a result, the equilibrium price will depend on the supply of tea in Foreign and the supply of ice in Home.

(e) If migration is free, workers can move between countries freely. This will lead to a more efficient allocation of labor, as countries can specialize in producing goods for which they have a comparative advantage.

(f) With an iceberg trade cost τ, the price of ice in Foreign (PFI) will be higher than the price of ice at Home (PHI). The exact relationship between the prices depends on the trade cost parameter τ.

(g) If τ=1.2, the new equilibrium price with complete specialization will depend on the specific values of the Cobb-Douglas utility function and the Leontief preference function.

(h) If τ=3, the new equilibrium price with complete specialization will be higher than the previous equilibrium price. This is because the trade cost τ increases the cost of production and transportation, which in turn affects the supply and price of ice.