Westerhold
Econ 330
Name:_____________________________
Review Packet for Second Part of Exam II—Short Run Production and Cost
1. Suppose a firm currently has 100 units of capital available for its production process. The short run
production function is given by the following TP equation:
Q= 825L + 5.3L2 –0.05L3
A. Derive the expression for the marginal productivity of labor?
B. What is the marginal productivity of the 4th worker?
C. At what Labor Unit is output maximized? How much output (Q or TP) is produced at the maximum?
D. At what labor unit does “negative marginal returns” begin?
E. Derive the expression for the average productivity of labor?
F. What the Average Productivity of the first 20 workers?
G. At what labor unit is average productivity maximized? What is the average productivity at this
maximum?
H. What is the value of marginal productivity at the average productivity maximum? Is this what you
expected? Why or why not?
2. Joey cuts lawns during the summers. Let q equal the number of acres mowed per day, and let L be the
number of hours worked per day. Joey never works more than 8 hours per day and his short run
production function during that time is q=0.2L. Which of the following statements is false?
A. Joey’s marginal productivity equals his average productivity.
B. Joey’s marginal productivity diminishes by 0.2 for each additional hour worked.
C. Joey’s average productivity is constant.
D. Both A and C.
3. Jennifer is the only employee of her sole proprietorship. She is considering hiring an additional
employee. She knows that on her own she can produce 100 units per day. With Applicant A she would
be able to produce 175 units per day. With Applicant B she would be able to produce 155 units per day.
Which of the following statements is not accurate?
A. Applicant B has a marginal product of 75 units.
B. Applicant B has an average product of 87.5 units.
C. Applicant A has a marginal product of 75 units.
D. Applicant A has an average product of 77.5 units.
4. A typical professional National Football League team has three quarterbacks on its roster. One reason
they might not have a fourth quarterback is:
A. The 4th quarterback has a marginal product of zero.
B. the 4th quarterback marginal product is approximately 10.
C. The 4th quarterback’s marginal product is less than the first quarterback’s marginal product.
D. The 4th quarterback’s average product is less than the first quarterback’s.
5. Suppose our total costs (TC) is given by the following equation: TC=400 +10Q + .2Q2
A. The dollar value for the firm’s Total fixed costs (TFC) would be:
B. The general equation for this firm’s Total Variable Costs (TVC) would be:
C. The general equation for this firm’s Average Total Cost (ATC) would be:
D. The general equation for this firm’s Marginal Cost (MC) would be:
E. The firm’s total cost of producing 25 units would be (Show your work):
F. The firm’s TFC of producing 25 units would be:
G. The firm’s TVC of producing 25 units would be (Show using your equation from B):
H. The firm’s average total cost (ATC) would be minimized at what output level? You may round the
output level to a whole number. What would the per unit cost be at this output level? Show your work.
6. A competitive firm has the short-run cost function c(y)= y3 - 2y2 + 5y + 6. Write down equations for:
a. The firm’s average variable cost function
b. The firm’s marginal cost function
c. At what level of output is average variable cost minimized?
7. The marginal cost curve of a firm is MC = 6q. Total variable costs to produce 10 units of output are
a. $120.
b. $300.
c. $80.
d. $400.
e. $26.
8. A firm has the short-run total cost function c(y) = 4y2 + 100. At what quantity of output is short-run
average cost minimized?
a. 5
b. 2
c. 25
d. 0.40
e. None of the above.
9. Mr. Dent Carr’s total costs are 2s2 + 40s + 40. If he repairs 10 cars, his average variable costs will be
a. $60.
b. $64.
c. $80.
d. $120.
10. If Green Acres Turf Farm’s total cost of producing
acres of sod is TC = 5Q2 + 25Q + 40, the marginal cost
of producing the 10th acre of sod is
a. $125.
b. $40.
c. $25.
d. $75.
e. $275.
Answers:
1A. MPL = 825 + 10.6L -0.15L2
1B. plug in L=4; MP=865
1C. set MP=0; L=117 Q=88997
1D. at the next labor unit; MP < 0 (no calculation)
1E. APL = 825 + 5.3L -0.05L2
1F. plug in L=20; AP = 911
1G. L=53; AP=965
1H. MP=965; expected MP=AP at APmax
2.D
3. A
4. A
5A. $400
5B. 10Q + .2Q2
5C. (400+10Q+.2Q2)/Q
5D. 10 + .4Q
5E. $775
5F. $400
5G. $375
5H. Q=44.72 units; ATC=$27.89
6. a. y2 -2y + 5.
b. 3y2 - 4y + 5.
c. y = 1.
7. Variable Cost must be 3q2 so for q=10; TVC= $300.
8. MC=8q and ATC or AC= (100 + 4Q2)/q ; costs are minimized where MC=AC. Q=5
9. AVCs=10 = 2s+ 40 = 2(10)+ 40 = $60.
10. MC=10Q + 25 or 10(10) + 25 = $125.