Exercise 1. On a weekend I decided to prepare a table with different types of costs to present it during last Thursday's class. My daughter Solomia, who was playing around, erased most of the numbers. Please help me to recover the missing numbers by filling in missing values in the table below.
|
Output, Q
|
FC
|
V C
|
T C
|
MC
|
AFC
|
AV C
|
ATC
|
|
0
|
120
|
0
|
|
-
|
-
|
-
|
-
|
|
1
|
|
|
|
|
|
60
|
|
|
2
|
|
|
|
30
|
|
|
|
|
3
|
|
105
|
|
|
|
|
|
|
4
|
|
|
|
|
|
|
65
|
|
5
|
|
|
300
|
|
|
|
|
|
6
|
|
|
|
120
|
|
|
|
Exercise 2. This time I decided to prepare to the class in the office. Unfortunately, some of my students who came during office hours erased several numbers from the board. Please help me to find out missing numbers. Also, answer the questions that follow after the table.
|
Capital, K-
|
Labor, L
|
Output, Q
|
MPL
|
APL
|
| 8 |
0
|
0
|
-
|
-
|
|
8
|
1
|
4
|
|
|
|
8
|
2
|
|
6
|
|
|
8
|
3
|
|
|
6
|
|
8
|
4
|
|
10
|
|
|
8
|
5
|
35
|
|
|
|
8
|
|
42
|
2
|
6
|
(a) With which unit of labor does diminishing marginal returns set in?
(b) For which unit of labor marginal product of labor MPL equals to average product of labor APL?
(c) What is the slope of a straight line from the origin to the point on the total product curve for the L = 3.
Exercise 3. Suppose firm's production function is given by Q = ALαKβ . Thus, the marginal product of labor is given by: MPL = αALα-1Kβ. Since it is in the short run, capital is constant at the value K = 9. Also, suppose that A = 2, α = β = 1/2 and w = $3.
a) What are the marginal cost and the average cost of production when the firm is producing 30 units of output?
b) Does the economy exhibit constant, increasing or decreasing returns to scale?
Exercise 4. Suppose that Ann and Bill are growing Apples and Pears. Ann can produce either 70 Apples (good X) or 15 Pears (good Y) on the land she owns and Bill can produce either 35 Apples (good X) or 15 Pears (good Y) on the land he owns.
The Ann's utility function is UA(X, Y ) = XY and UB(X, Y ) = XY. You may find useful to know that MUAX = Y , MUAY = X, MUBX = Y and MUBY = X.
a) Suppose both Ann and Bill do not trade. How much of each good does Ann consume? How much of each good does Bill consume? Assume utility maximization behaviour for all consumers.
b) How much utility each consumer gets?
c) Suppose now that Ann and Bill decide to trade. Normalize price of good X to $1. Assume that each of them produces only the good in which he or she has comparative advantage in. What is an equilibrium price of good Y?
[Hint: you should treat the quantity of each good produced as initial allocation in exchange economy. You may want to review Exercise 1 from Homework 3.]
d) How much of each good does Ann consume? How much of each good does Bill consume?
e) What is the new level of utilities each consumer gets?
f) Which consumer (if at all) strictly benefits from trade?