Jim Whitney Economics 250

Homework exercises #11: KEY
Due: __________________________

Circle section: 12:50 / 1:55

 Name: ______________________________
     
 

1.

(From Frank, Chapter 10) The Preservation Embalming Company's cost data have been partially entered in the table below. Following the sudden and unexpected death of the company's accountant, you are called on to fill in the missing entries.
 
Bodies
embalmed
Q		 Total
cost
TC		 Total
fixed
cost
TFC		 Total
variable
cost
TVC		 Average
total
cost
ATC		 Average
fixed
cost
AFC		 Average
variable
cost
AVC		 Marginal
cost
MC
0 24 24 0 --- --- --- ---
1 40 24 16 40 24 16 16
2 74 24 50 37 12 25 34
3 108 24 84 36 8 28 34
4 160 24 136 40 6 34 52
5 220 24 196 44 4.8 39.2 60
6 282 24 258 47 4 43 62
 
2. This question concerns the supplementary readings selection: F-22 Production OKs for Takeoff, http://faculty.oxy.edu/whitney/classes/ec250/tasks/h11_app.htm
a. Suppose the cost information in Passage A and Passage B applies to an output level of 295 planes, with Passage A reporting ATC and Passage B reporting a constant value for MC and AVC:
ATC = $ 173 million
AVC = MC = $ 84 million
AFC = $ 89 million		 axes.gif (4118 bytes)
b.  TFC = $ 26,255 million
c. Given the F-22's cost information, decide whether ATC at Q=295 is rising, falling, constant, or moving in an uncertain direction, and briefly indicate how you decided: 
Falling, since MC < ATC.

 
d. In the diagram to the right, sketch the  MC, AVC and ATC curves for the F-22, and use numerical values to clearly label the F-22's MC and ATC values at its current output level of 295.
 

 

3. Consider the QKL Company with the production function:
        Q = 6.25·K1L1/2 where Q = output, K = quantity of capital, L = quantity of labor.
a. Suppose QKL currently has a fixed quantity of 8 units of capital. (1) What is the short run production function for Q? (In other words, what is Q as a function of L, given K?) (2) What is the formula for MPL?
    (1) K=8 => Q = 50.L1/2
    (2) MPL = dQ/dL = 25.L-1/2 = 25/L1/2

 
b. Invert your short run production from part a to express L as a function of desired output. What formula do you get?
    L = (Q/50)2

 
c. Use your answer to part b to calculate the labor needed for each of the output levels listed in the table below, and complete the K and L columns of the table:
Q K L TFC TVC TC AFC AVC ATC MC*
100 8 4 1280 40 1320 12.80 .40 13.20 .80
300 8 36 1280 360 1640 4.27 1.20 5.47 2.40
500 8 100 1280 1000 2280 2.56 2.00 4.56 4.00
700 8 196 1280 1960 3240 1.83 2.80 4.63 5.60
900 8 324 1280 3240 4520 1.42 3.60 5.02 7.20
    * MC = PL/MPL = $10/(25·L-1/2) = $.40·L1/2
    Answer key checklist: Did you use PL/MPL for MC? Since you can use calculus to derive a precise estimate of MPL, you should use this precise formula for MC.
d. Suppose the wage is $10, and the rental cost of capital is $160 per machine. Complete the rest of the table above. (For MC, use the precise marginal cost formula based on the wage rate and the marginal product of labor where the marginal product of labor is the derivative of the short-run production function with respect to labor).  See the table above.
e. Graph QKL's AVC, ATC, and MC curves: See the diagram below (Ignore the "profit box" for now--that's part of a later question).