Question

Consider an economy where production follows the O-ring theory: Y = q₁q₂. Suppose country A has 3 people with q = 1 and 1 person with q = 1/2, country B has 2 people with q = 1 and 2 people with q = 1/2 , and country C has 3 people with q = 0 and 1 person with q = 1/2 .

1. If you think of q as "probability of success" for each worker, how would you interpret this production function?
2. Show that, in country B, positive assortative matching will lead to the highest possible total output.
3. Explain why this is the case.
4. Suppose, in each country, a worker with q = 1/2 is considering getting an education to improve her quality to 1. Assume that her salary will rise by the amount that this increased education raises total production. Show that the salary rise in country A will be the highest and the salary rise in country C will be the lowest.

Answer 1