Midterm, Microeconomic, Erasmus School of Economics
Microeconomics FEB11001X MIDTERM 2 7 December 2010
Name and Sirname: Student number GROUP number
Calculators and dictionaries are NOT allowed.
1
Of Land, Capital and men (5 points)
Consider a …rm that uses optimally its three inputs: land, capital and labor. Argue, in your own words (15 lines max!) why, in the optimal point, we must have equality between the marginal productivity of land, capital and labor.
2
Mono and Duo
The …rm “Mono” is a …rm operating on a market with the following inverse demand function: P (Q) = a bQ: The total cost function of Mono is T C (q) = 10 + cq where q is Mono’ output. s Assume that a > c > 0 and b > 0: 1. Compute Mono’ pro…t. (5 points; if you do not like letters, you can replace s them by the following numbers, but then you can score 4 points maximum only: a = 140; b = 2 and c = 20); 2. Suppose another …rm, “Duo” with the same cost function, enters this market , and competes in quantites with Mono. Compute Mono’ pro…t in this Cournot s competition game (5 points; 4 points if you replace the letters with the above numbers)
3
Techies
Q (K; L) = K 1=4 L2=3 1. Determine (using the appropriate de…nition) whether there are increasing, constant or decreasing returns to scale in this industry. (2.5 points) 2. Do you expect many or few …rms to be present in this market? Why? Justify your answer. (2.5 points) 1
Consider an industry in which all …rms use the same technology:
Name and Sirname: Student number GROUP number
Calculators and dictionaries are NOT allowed.
1
Of Land, Capital and men (5 points)
Consider a …rm that uses optimally its three inputs: land, capital and labor. Argue, in your own words (15 lines max!) why, in the optimal point, we must have equality between the marginal productivity of land, capital and labor.
2
Mono and Duo
The …rm “Mono” is a …rm operating on a market with the following inverse demand function: P (Q) = a bQ: The total cost function of Mono is T C (q) = 10 + cq where q is Mono’ output. s Assume that a > c > 0 and b > 0: 1. Compute Mono’ pro…t. (5 points; if you do not like letters, you can replace s them by the following numbers, but then you can score 4 points maximum only: a = 140; b = 2 and c = 20); 2. Suppose another …rm, “Duo” with the same cost function, enters this market , and competes in quantites with Mono. Compute Mono’ pro…t in this Cournot s competition game (5 points; 4 points if you replace the letters with the above numbers)
3
Techies
Q (K; L) = K 1=4 L2=3 1. Determine (using the appropriate de…nition) whether there are increasing, constant or decreasing returns to scale in this industry. (2.5 points) 2. Do you expect many or few …rms to be present in this market? Why? Justify your answer. (2.5 points) 1
Consider an industry in which all …rms use the same technology: