1.] The entire economy consists of two industries, Industry 1 and Industry 2. Their production functions are as follows:

Y1 = A1K1^1/3L1^2/3 and Y2 = A2K2^1/3L2^2/3

Assume that the price, P₁, and P₂, A₂, K₁, and K₂ are fixed.

[a] Show mathematically the real wages of the two industries.

[b] Suppose that the two industries initially offer the same nominal wage rate, i.e., w₁ = w₂. Now if the technological progress of Industry 1 rises, (i.e., A₁ rises), how does that affect w₁?

[c] If there are no unemployed people and the two industries compete with each other in terms of labor demand, Industry 2 has to offer the same wage rate that Industry 1 offers. How does that affect the quantity of labor Industry 2 hires and, in turn, the size of its output? [Hint: assume that A₂ and K₂ are fixed.]

[d] Suppose that A₁ = 3, K₁ = 1280, L₁ = 20, P₁ = 30, A₂ = 2, K₂ = 1080, L₂ = 40, P₂ = 60. Calculate w₁ and w₂. If A₁ increases from 3 to 6, what is the new nominal wage rate offered by Industry 1? If Industry 2 offers the same wage rate, what is the new quantity of labor Industry 2 hires? How much does the output of Industry 2 fall? [Hint: K₁, L₁, P₁, A₂, K₂, and P₂ stay unchanged]

[e] According to part [d], how many jobs does Industry 2 lose? Which type of unemployment is this? Is the entire economy better off or worse off in the short run due to the increase in A₁? How to prove it? What about the long run?

[f] If the people in the economy still want the same amount of output which used to be produced by Industry 2, what should they do? Is your conclusion consistent with the statement that foreign competition kills jobs in the United States? Briefly explain.

[g] Consider the situation that the unemployment rate of the economy has already been high. Briefly explain how it would change your conclusions above. Does this provide the justification for trade protection policies?