Week 4 – Check Your Understanding
Chapter 7:
1. From the knowledge of the relationships among the various production functions, complete the following table: (3 points)
Variable Input L 
Total Product TPL (=Q) 
Average Product APL 
Marginal Product MPL 
0 
0 
na 
na 
1 


16 
2 
56 


3 

36 

4 


52 
5 

40 

6 
216 


7 


20 
Crew Size 
Amount of Fish Caught Per Week (Hundreds of Pounds) 
2 
18 
3 
25.5 
4 
32 
5 
37.5 
6 
42 
7 
45.5 
8 
48 
9 
49.5 
10 
50 
11 
49.5 
12 
48 
13 
45.5 
2. The amount of fish caught per week on a trawler is a function of the crew size assigned to operate the boat. Based on past data, the following production schedule was developed: (3 points)
Over what range of workers are there:
a. Increasing marginal returns _______________________
b. Decreasing marginal returns _______________________
c. Negative marginal returns ________________________
3. Suppose the firm’s production function is given by the following relationship:
Q = 5 L ^{0.8} K ^{0.2}
Where the exponents of L (labor) and K (capital) are interpreted as the fixed input elasticities of labor and capital, respectively.
a. Determine the percentage increase in output (Q) if labor (L) is increased by 10 % while capital is held constant.
b. Determine the percentage increase in output (Q) if capital (K) is increased by 20 % while labor is held constant.
c. Determine the percentage increase in output (Q) if both labor (L) and capital (K) are increased by 20 %.
4. Consider the following Cobb Douglas Production function for the bus transportation system in a particular city: (3 points)
Q = aL^{b1}F^{b2}K^{b3}
Where L = labor input in worker hours
F= fuel input in gallons
K = capital input in number of buses
Q = output measured in millions of bus miles
The values of the parameters are: (Hint: See the interpretation of the exponents in Question 3.)
a = 0.0024
b1 = 0.50
b2 = 0.30
b3 = 0.15
a. Suppose that the labor input (L) is increased by 2% next year (with the other inputs held constant). Determine the approximate percentage change in output (Q).
b. Suppose that the capital input (K) is decreased by 2% next year (with the other inputs held constant). Determine the approximate percentage change in output (Q).
c. What type of returns to scale appears to characterize this bus transportation system? (Hint: add the exponents up. If the sum exceeds 1, there is increasing returns to scale, if it is less than 1, there is decreasing returns to scale, and if it equals 1, there is constant returns to scale.)
Chapter 8:
1. A certain production process employs only labor (L). Output (Q) is a function of labor given by the following relationship: (3 points)

Q = 600L^{2} – 100L^{3 } 
Where MPL = 1200L – 300L^{2}


(a) 
Determine the average product function for input L.

(b) 
Find the number of units of input L that maximizes the total product function. (Hint: set MPL equal to zero and solve for L.)

(c) 
Find the number of units of input L that maximizes the average product function. (Hint: set MPL equal to the APL equation found in part “a” and solve for L.) 


2. During the last few days the Superior Company has been running into problems with its computer system. The last run of the production cost schedule resulted in the incomplete listing shown below. From your knowledge of cost theory, fill in the blanks. (6 points)
Q 
TC 
TFC 
TVC 
ATC 
AFC 
AVC 
MC 
0 
40 


na 
na 
na 
na 
1 



52 



2 


20 




3 



21.33 



4 






4 
5 


40 




6 



15.67 



7 





10 

8 


96 




9 





15 

10 






45 