Let's solve each part of the problem step by step.### Given:Production Function:
Initial values:
,
### a. How much output does the economy produce?Substitute the initial values into the production function:
So, the economy produces 100 units of output.### b. What are the wage and the rental price of land?In the Cobb-Douglas production function
, the exponents (0.5) represent the share of output attributed to each input.- Share of output attributed to land (K) = 0.5- Share of output attributed to labor (L) = 0.5Since the total output is 100 units:- Rental price of land (R) = 0.5 * 100 = 50- Wage (W) = 0.5 * 100 = 50### c. What share of output does labor receive?As calculated above, the share of output attributed to labor (L) is 0.5, or 50%.### d. If a plague kills half the population, what is the new level of output?If half the population is killed, the new amount of labor (L) is halved:
Substitute the new values into the production function:
So, the new level of output is approximately 70.7 units.### e. What is the new wage and rental price of land?With the new amount of labor (L = 50):- Share of output attributed to land (K) = 0.5- Share of output attributed to labor (L) = 0.5Total output is now 70.7 units:- Rental price of land (R) = 0.5 * 70.7 = 35.35- Wage (W) = 0.5 * 70.7 = 35.35### f. What share of output does labor receive now?As calculated above, with the new level of output, the share of output attributed to labor (L) remains 0.5, or 50%.### Summary:a. Output: 100 unitsb. Wage: 50, Rental price of land: 50c. Share of output for labor: 50%d. New output: 70.7 unitse. New wage: 35.35, New rental price of land: 35.35f. New share of output for labor: 50%