PRODUCER DECISION MAKING

PRODUCER DECISION MAKING: SINGLE VARIABLE INPUT 
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.