Consider a country called the North Pole that produces toy robots (R) and toy airplanes (A) in a specific-factors model setting. The production of both goods uses elf labor, but paints (T) is specific to the production of toy airplanes, and buttons (K) are specific to the production of toy robots. The price of toy airplanes is PA = 5 and the price of toy robots is PR = 100. The amounts of paints, buttons, and elf labor are T = 4000, K = 500, and L = 500, respectively. The marginal products of labor in the production of toy robots and toy airplanes are given:

MP LR = (K/LR)^1/3 (1)

MP LA = 10 (T /LA)^1/3 (2)

2.1 How many workers produce toy airplanes in equilibrium?

2.2 What is the equilibrium nominal wage?

2.3 Suppose immigration causes L to rise by 100. What is the new equilibrium nominal wage?