1) Trisha's Fashion Boutique production function for dresses is q(K, L) = , where K is the number of sewing machines and L is the amount of labor hours employed.  Trisha pays $15 per labor hour, $7.5  per capital hour, and sells each dress for $87.50.  Also, Trisha currently has 4 sewing machines.

a.    Fill in the table below.

b.      How many units of labor will Trisha employ to maximize her profit?

c.      Derive the (short-run) cost function (TC) of Trisha's Fashion Boutique as a function of the output (q)

d.     Find the average total cost (ATC), average fixed cost (AFC), average variable cost (AVC), and the marginal cost (MC)

e.     Find the number of dresses Trisha should produces if she wants to minimize her average total cost (hint:  ATC reached minimum at the point where MC = ATC)

Answer:

.

b. As the above table illustrates, when Trisha moves from employing 1 labor hours to 20 labor hours, the value of the marginal product of labor falls under the marginal cost of labor at $15 (the exact answer is    that Trisha will employ 7 workers – you can use Excel or a little bit of algebra to find it).

c.  TC(q) = 30 + (15/8)q3

d.  ATC = TC/q = 30/q + (15/8)q2;  AFC = 30/q;  AVC = (15/8)q2;  MC = (45/8)q2 .

e.  q = 2

2) Use the following two statements to answer this question:

I.    Isoquants cannot cross one another.

II.   An isoquant that is twice the distance from the origin represents twice the level of output.

A) Both I and II are true.

B) I is true, and II is false.

C) I is false, and II is true.

D) Both I and II are false.

Answer:  B

3) A firm uses two factors of production.  Irrespective of how much of each factor is used, both factors always have positive marginal products which imply that:

A) isoquants are relevant only in the long run.

B) isoquants have negative slope.

C) isoquants are convex.

D) isoquants can become vertical or horizontal.

E) none of the above

Answer:  B

4) An upward sloping isoquant:

A) can be derived from a production function with one input.

B) can be derived from a production function that uses more than one input where reductions in the use of any input always reduces output.

C) cannot be derived from a production function when a firm is assumed to maximize profits.

D) can be derived whenever one input to production is available at zero cost to the firm.

E) none of the above

Answer:  C

5) Use the following two statements to answer this question:

I.    If the marginal product of labor is zero, the total product of labor is at its maximum.

II    If the marginal product of labor is at its maximum, the average product of labor is falling.

A) Both I and II are true.

B) I is true, and II is false.

C) I is false, and II is true.

D) Both I and II are false.

Answer:  B

6) The marginal rate of technical substitution is always equal to:

A) the absolute value of the slope of an isoquant.

B) the ratio of the marginal products of the inputs.

C) the ratio of the prices of the inputs.

D) all of the above

E) A and B only

Answer:  E

7) A firm's marginal product of labor is 4 and its marginal product of capital is 5.  If the firm adds one unit of labor, but does not want its output quantity to change, the firm should:

A) use five fewer units of capital.

B) use 0.8 fewer units of capital.

C) use 1.25 fewer units of capital.

D) add 1.25 units of capital.

Answer:  B

8) A straight-line isoquant:

A) is impossible.

B) would indicate that the firm could switch from one output to another costlessly.

C) would indicate that the firm could not switch from one output to another.

D) would indicate that capital and labor cannot be substituted for each other in production.

E) would indicate that capital and labor are perfect substitutes in production.

Answer:  E

9) An L-shaped isoquant:

A) is impossible.

B) would indicate that the firm could switch from one output to another costlessly.

C) would indicate that the firm could not switch from one output to another.

D) would indicate that capital and labor cannot be substituted for each other in production.

E) would indicate that capital and labor are perfect substitutes in production.

Answer:  D

10) A construction company builds roads with machinery (capital, K) and labor (L).  If we plot the           isoquants for the production function so that labor is on the horizontal axis, then a point on the isoquant with a small MRTS (in absolute value) is associated with high ________ use and low ________ use.

A) labor, capital

B) capital, labor

C) concrete, gravel

D) none of the above

Answer:  A

11) Suppose the production of long-distance airline flights is described by a fixed proportion production process in which three crew members (i.e., labor) are required for each aircraft (i.e., capital).  If the airline operates with four crew members per plane, then we know that:

A) the production process violates diminishing margin returns.

B) production at this point is technically inefficient.

C) the isoquants for this production process are upward sloping.

D) the airline will have negative profits.

Answer:  B

12) Joe's Organic Cereal Company produces granola breakfast cereal under a fixed proportion production system in which 22 ounces of cereal are packaged in each cardboard box.  However, the plant production manager decides to reduce the amount of cereal per box to 20.5 ounces at the start of the next year.  For     the isoquant map, cereal is plotted in the vertical axis, and boxes are on the horizontal axis.  What              happens to the curves in the isoquant map as a result of this change?

A) Shift upward

B) Shift downward

C) Shift rightward

D) Shift leftward

Answer:  B

13) Use the following two statements to answer this question:

I.    "Decreasing returns to scale" and "diminishing returns to a factor of production" are two phrases that mean the same thing.

II    Diminishing returns to all factors of production implies decreasing returns to scale.

A) Both I and II are true.

B) I is true, and II is false.

C) I is false, and II is true.

D) Both I and II are false.

Answer:  D

Figure 6.4.3

14) Refer to Figure 1. The situation pictured is one of:

A) constant returns to scale, because the line through the origin is linear.

B) decreasing returns to scale, because the isoquants are convex.

C) decreasing returns to scale, because doubling inputs results in less than double the amount of output.

D) increasing returns to scale, because the isoquants are convex.

E) increasing returns to scale, because doubling inputs results in more than double the amount of output.

Answer:  C

15) A farmer uses M units of machinery and L hours of labor to produce C tons of corn, with the following production function This production function exhibits:

A) decreasing returns to scale for all output levels.

B) constant returns to scale for all output levels.

C) increasing returns to scale for all output levels.

D) no clear pattern of returns to scale.

Answer:  C

16) A farmer uses M units of machinery and L hours of labor to produce C tons of corn, with the following production function This production function exhibits:

A) decreasing returns to scale for all output levels.

B) constant returns to scale for all output levels.

C) increasing returns to scale for all output levels.

D) no clear pattern of returns to scale.

Answer:  A

17) Consider the following statements when answering this question:

I.     If a technology exhibits diminishing returns then it also exhibits decreasing return to scale.

II.    If a technology exhibits decreasing returns to scale then it also exhibits diminishing returns.

A) I is true, and II is false.

B) I is false, and II is true.

C) Both I and II are true.

D) Both I and II are false.

Answer:  D

18) Use the following statements to answer this question:

I.    We cannot measure the returns to scale for a fixed-proportion production function.

II.   Production functions with inputs that are perfect substitutes always exhibit constant returns to scale.

A) I and II are true.

B) I is true and II is false.

C) II is true and I is false.

D) I and II are false.

Answer:  D

19) Many mining and mineral extraction processes tend to exhibit increasing returns to scale.  Suppose      copper mines have increasing returns, and the existing copper mines reduce their capital and labor inputs by 25 percent in response to a global recession.  What is the expected impact on copper output?

A) Output increases by less than 25 percent.

B) Output decreases by less than 25 percent.

C) Output decreases by exactly 25 percent.

D) Output decreases by more than 25 percent.

Answer:  D

20) Bridget's Brewery production function is given by where K is the number of vats she uses and L is the number of labor hours.  Does this production process exhibit increasing, constant or     decreasing returns to scale?  Holding the number of vats constant at 4, is the marginal product of labor  increasing, constant or decreasing as more labor is used?

Answer:  Since we know the production process exhibits constant returns to scale.  Holding the number of vats constant at 4 will still result in a               downward sloping marginal product of labor curve.  That is the marginal product of labor decreases as more labor is used.

21) Michael's Dairy farm production function is given by where K is the number of     machine milkers and L is the amount of labor hours he uses.  Does this production function exhibit        increasing, constant or decreasing returns to scale?  Holding the number of machine milkers constant at 16, is the marginal product of labor increasing, constant or decreasing as more labor is used?

Answer:  Since we know the                    production process exhibits decreasing returns to scale.  Holding the number of machine milkers constant at 16 will still result in a downward sloping marginal product of labor curve.  That is, the marginal             product of labor decreases as more labor is used.

22) Farmer Jones bought his farm for $75,000 in 1975.  Today the farm is worth $500,000, and the interest   rate is 10 percent.  ABC Corporation has offered to buy the farm today for $500,000 and XYZ Corporation has offered to buy the farm for $530,000 one year from now.  Farmer Jones could earn net profit of $15,000 (over and above all of his expenses) if he farms the land this year.  What should he do?

A) Sell to ABC Corporation.

B) Farm the land for another year and sell to XYZ Corporation.

C) Accept either offer as they are equivalent.

D) Reject both offers.

Answer:  A

23) The total cost (TC) of producing computer software diskettes (Q) is given as: the average total cost?

A) 500

B) 5Q

C) 5

D) 5 + (200/Q)

E) none of the above

Answer:  D

24) The total cost (TC) of producing computer software diskettes (Q) is given as: the average fixed cost?

A) 500

B) 5Q

C) 5

D) 5 + (200/Q)

E) none of the above

Answer:  E

25) Which of the following statements demonstrates an understanding of the importance of sunk costs for decision making?

I.    "Even though I hate my MBA classes, I can't quit because I've spent so much money on tuition."

II.   "To break into the market for soap our firm needs to spend $10M on creating an image that is unique to our new product.  When deciding whether to develop the new soap, we need to take this marketing    cost into account."

A) I only

B) II only

C) Both I and II

D) Neither I nor II

Answer:  B

Scenario 1:

The average total cost to produce 100 cookies is $0.25 per cookie.  The marginal cost is constant at $0.10 for all cookies produced.

26) Refer to Scenario 1.  The total cost to produce 50 cookies is:

A) $20

B) $25

C) $50

D) $60

E) indeterminate

Answer:  A