Question:
Please put all answers on a separate paper, either written neatly or word-processed. Draw graphs on graph paper or using a worksheet program (Excel).
1. The following table indicates, on a per-acre basis, the total amount of corn (Y) that a farmer can produce with various levels of labor, a variable input (X). All other inputs are held constant.
X Y
0.0 0
2.5 5
4.7 10
6.4 15
7.9 20
9.0 25
10.0 30
10.7 35
11.3 40
11.8 45
12.3 50
12.8 55
13.3 60
13.9 65
14.6 70
15.6 75
16.7 80
18.2 85
19.9 90
22.1 95
24.6 100
27.6 105
31.1 110
35.2 115
39.9 120
42.3 118
Create a graph with Total Physical Product (the output Y) on the vertical axis and the input X on the horizontal axis. Is the Law of Diminishing productivity evident from the TPP? How do you know?
2. For each level of input (X) in the table, calculate:
Average Physical Product (APP)
Marginal Physical Product (MPP)
On a second graph, plot APP and MPP on the vertical axis and the input X on the horizontal axis. Across which stages of production (I, II or III) does this range of production extend? How do you know? Identify the boundary between stages I and II.
3. If the price of the input (rX) is $6.50/unit and the price of corn (PY) is $2.50/bushel, calculate the following for each level of input X in the table:
Marginal Value Product (MVP)
Marginal Factor Cost (MFC)
On a third graph, plot MVP and MFC with dollars ($) on the vertical axis and the input X on the horizontal axis. Using this graph, identify the profit-maximizing amount of the input X to use. Explain why this is the optimum amount.
On the third graph, mark (highlight or color) the farmer's demand curve for the variable input X.
Save a copy of your calculations and graphs for use with a future assignment.
4. New Castle County owns a piece of property (500 acres) that it wants to allocate between two uses: a trash removal company wants it for a landfill (dump for trash) and an industrial firm wants to build a new plant on it.
You are hired by the county to determine an economic optimum allocation of the land between the two uses.
a) Indicate the information you will need.
b) Indicate, explain and graph the conditions that must be satisfied for an optimum allocation of the property. Explain why the allocation is an optimum. Explain how society's wants are represented in this optimum.
c) If the demand (and price) of the industrial firm's product increases, explain what effect this will have on the allocation of the property. Graph this new situation.