Question

Consider two countries, indexed by j∈{1,2}. The representative household in each of these two countries inelastically supplies Hⱼ > 0 units of labor, for j∈{1,2}. Labor can only be used domestically. There are two tradable goods, indexed by n∈{1,2}. And there is one non-tradable good in each of the two countries, indexed by n=0 for both countries.

Everyone has the same preferences over consumption vectors (c₀ ,c₁ ,c₂), determined by the utility function
U(c₀ ,c₁ ,c₂)=c0β0​​c1β1​​c2β2​​. The parameters βₙ
​are strictly positive and ∑²n=0, βₙ=1
Country j has Aⱼ > 0 units of land. It can use L₀,ⱼ ≥ 0 units of labor to produce y₀,ⱼ = A¹ ⁻ ᵃⱼLᵃ₀.ⱼ
​
units of its non-tradable good, where α∈(0,1) is a parameter. Country j can also use Lⱼj ≥0 units of labor to produce yⱼ = LⱼZⱼ

units of good j. Country 1 cannot produce good 2 and country 2 cannot produce good 1. Write wⱼ
for the wage and p₀,ⱼ
for the price of the non-tradable good in country j∈ {1,2}. The prices of the two tradable goods are p₁ and p₂
​
, respectively.
a. Give the demand curves for the consumption goods n∈{0,1,2} in each of the two countries. You may use what you know about the preferences specified in this question, without deriving the result from scratch.
b. In any equilibrium, what has to be true about the relative prices p₁/w₁ and p₂/w₂?
What does profit maximization in the non-tradable goods sector tell you about the factor shares wⱼL₀,ⱼ/(p₀,ⱼy₀,ⱼ ) for j∈{1,2} ?
c. Use non-tradable goods market clearing and the definition of income as the total value of goods sold to explain why
p₀,ⱼy₀,ⱼ/(pⱼyⱼ) = B₀/(1 - B₀)
​. Combine this with your answer to b and labor market clearing to determine L₀,ⱼ and Lⱼ
​
. d. Use the market clearing conditions for tradables to determine p₁/p₂ . Determine the wage ratio w₁/w₂
​
e. Find p₀,₁/p ₀,₂, the real exchange rate, and the ratio of real per-capita income across the two countries.

Answer 1

An increase in trade between Germany and the Czech Republic can lead to higher jobs and wages in exporting industries while decreasing them in industries facing increased imports. Total unemployment will not rise if labor can move efficiently between sectors. Sticky wages and prices can cause temporary unemployment when aggregate demand decreases.

Step-by-step explanation:

Trade between countries can have significant income distribution effects. If the trade between Germany and the Czech Republic increases due to reduced trade barriers, with Germany exporting house paint and the Czech Republic exporting alarm clocks, we can expect industry-specific impacts on jobs and wages. In Germany, increased exports could lead to higher employment and wages in the paint industry, while potentially decreasing them in the alarm clock industry due to increased imports. Conversely, the Czech Republic may see an increase in jobs and wages in the alarm clock industry but a decrease in the paint industry.

For there to be no increase in total unemployment in both countries, the workers who lose jobs in one industry must be able to find employment in another sector, potentially the export industry of each country. This transition can be facilitated by factors such as the mobility of labor, the similarity of skills required in growing industries, and the overall demand for labor in the economy.

Regarding the sticky wages and prices in the economy, the inability of wages and prices to adjust quickly can lead to temporary unemployment if the aggregate demand in the economy declines. This is depicted in labor and goods market graphs where the equilibrium shifts due to a shift in demand, but wages and prices remain at their original level for a time.