In this problem we're given a simple production function, a partially parameterized Cobb-Douglas Production Function. We derive output/production, then find the real wage rate (finding the marginal product of labor) and the rental rate of capital (finding the marginal product of capital along the way... actually the marginal product of land, but it's the same steps to find MPK). Lastly, finding the labor share of income, and the capital share of income. Plus a "trick" to find the factor share of income by just looking at the Cobb-Douglas production function.

Part 1 of 3 - This video solves parts a and b below.



More Intermediate Macro Video: https://sites.google.com/site/curtisk...
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Suppose the production function in medieval Europe is Y=K^0.5 L^0.5, where K is the amount of land and L is the amount of labor. The economy begins with 100 units of land and 100 units of labor. Use a calculator and equations in the chapter to find a numerical answer to each of the following questions.
a. How much output does the economy produce?
b. What are the wage rate (skip to 5:33) and the rental price of land (skip to 18:00)?
c. What share of output does labor receive?
d. If a plague kills half the population, what is the new level of output?
e. What is the new wage and rental price of land?
f. What share of output does labor receive now?

From Mankiw "Macroeconomics" (Intermediate level), 8th edition, Chapter 3 (The Open Economy) - Problem 2
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