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Microeconomics I

Quiz #2

Winter, 2007

12/20, 2007

I. Multiple choices (30%)

1.  Which of the following statements best summarizes the law of diminishing marginal returns?

A)  In the short run, as more labor is hired, output diminishes.

B)  In the short run, as more labor is hired, output increases at a diminishing rate.

C)  In the short run, the amount of labor a firm will hire diminishes as output increases.

D)  As more labor is hired, the length of time that defines the short run diminishes.

2.  Suppose the production of VCRs can be represented by the following production function: q = L0.4 K0.4. Which of the following statements is (are) TRUE?

A)  The production function has decreasing returns to scale.

B)  The marginal productivity of labor falls as labor increases in the short run.

C)  Capital and labor can be substituted for one another.

D)  All of the above.

3.  Suppose the production function for a certain device is q = L + K. If a labor-saving technical change has occurred, which of the following could be the new production function?

A)  q = L + 5K

B)  q = 5 * (L + K)

C)  q = 5L + K

D)  All of the above are possible

4.  The slope of an isoquant tells us

A)  how much output increases when both inputs are increased.

B)  the increase in MPL when capital increases.

C)  the decrease in capital necessary to keep output constant when labor increases by one unit.

D)  the decrease in capital necessary to keep MPL constant when labor increases by one unit.

5.  Returns to scale is a concept that operates

A)  only in the short run.

B)  only in the long run.

C)  in both the long run and the short run.

D)  in either the long run or the short run but never both.

6.  Variable costs are

A)  a production expense that does not vary with output.

B)  a production expense that changes with the quantity of output produced.

C)  equal to total cost divided by the units of output produced.

D)  the amount by which a firm's cost changes if the firm produces one more unit of output

7.  The implementation of the assembly line is an example how

A)  changes in the organization of production improve productivity.

B)  neutral technical change improves productivity.

C)  non-neutral technical change can decrease productivity.

D)  labor saving technical change increases economy-wide unemployment.

8.  If a particular production process is subject to diminishing marginal returns to labor at every level of output, then at every level of output

A)  AC is upward sloping.

B)  MC exceeds AVC.

C)  AFC is constant.

D)  All of the above.

9.  If the average cost of producing a good is increasing as a firm produces more of the good, then which of the following must be TRUE?

A)  AFC is falling.

B)  AVC is rising.

C)  MC > AVC.

D)  All of the above.

10.  The production of cigarettes is highly automated; however, a worker is required to monitor each machine. Machines and workers do not interact with one another. Given this information, there are most likely

A)  economies of scale.

B)  economies of scope.

C)  constant returns to scale.

D)  increasing returns to scale.

11.  When the isocost line is tangent to the isoquant, then

A)  MPL = MPK.

B)  the firm is producing that level of output at minimum cost.

C)  the firm has achieved the right economies of scale.

D)  All of the above.

12.  Learning by doing will result in

A)  an upward sloping long-run average cost curve.

B)  a larger long-run marginal cost than long-run average cost.

C)  a rotation in the isocost curves.

D)  lower long-run costs than short-run costs.

13.  The slope of the isocost line tells the firm how much

A)  capital must be reduced to keep total cost constant when hiring one more unit of labor.

B)  capital must be increased to keep total cost constant when hiring one more unit of labor.

C)  more expensive a unit of capital costs relative a unit of labor.

D)  the isocost curve will shift outward if the firm wishes to produce more.

14.  Long-run average cost is never greater than short-run average cost because in the long run

A)  capital costs equal zero.

B)  the firm can move to the lowest possible isocost curve.

C)  wages always increase over time.

D)  wages always decrease over time.

15.  A production possibilities frontier that is a downward-sloping straight line implies

A)  economies of scale.

B)  diseconomies of scale.

C)  economies of scope.

D)  no economies of scope.

II. True or False (30%)

For the following, please answer "True" or "False" and explain why.

1.  If a given number of output is efficiently produced it is not possible to produce the same amount with less inputs.

True.

2.  If marginal productivity is decreasing as more labor is hired, then average productivity must be decreasing as well.

False.

The change in average productivity is not determined by the change in marginal productivity. Average productivity can be increasing even when marginal productivity is decreasing. Average productivity can only be decreasing when marginal productivity is below average productivity.

3.  A firm may express increasing, constant and decreasing returns to scale for various levels of output.

True.

As output increases a firm can experience all types of returns to scale.

4.  The marginal cost curve intersects the average fixed cost curve at its minimum.

False.

Marginal cost intersects average variable cost (and average cost) at its minimum.

5.  Short-run average cost exceeds long-run average cost only when there are economies of scale.

False.

Short-run average costs exceed long-run average costs because the firm is locked into a certain input mix in the short run that may not be cost minimizing when all inputs are variable. This condition holds regardless of the presence of economies of scale.

III. Problems (40%)

1.  Provide a graph and an explanation to show that the production function

Q = L0.5 K0.5 has diminishing marginal product of labor but has constant returns to scale.

See the above figure. The MPL = .5 * L-0.5 K0.5 so as the amount of labor increases the MPL falls. The convex shape of the isoquants illustrates the diminishing marginal product of labor. Doubling both capital and labor will result in output doubling.

2.  Describe the relationship between marginal productivity and average productivity. Use calculus or a graph to support your answer.

AP = Q(L)/L. dAP/dL = ([L * MP] - Q) / L2 = MP - AP/L. Thus, if MP = AP, AP is constant. If MP > AP, AP will rise. If MP < AP, AP will fall.

3. 

At Albert's Pretzel Company, MPL = 1/L, and MPK = 1/K. The isoquant for 100 pounds of pretzels daily is shown in the above figure. Albert minimizes the cost of producing 100 pounds of pretzels daily by hiring 5 units of labor and 10 units of capital when w = 50 and r = 25. When r rises to 100, what is the minimum cost of producing 100 pounds of pretzels daily in the short run? in the long run?

In the short run, the input mix cannot change. The short-run cost is (5 * 50) + (10 * 100) = 1250. In the long run, Albert will change the input mix. From the graph, the new mix will be L = 10 and K = 5. To check, the MRTS = K/L and costs are minimized when MRTS = w/r which equals 1/2. As a result, the long-run cost of 100 pretzels is (10 * 50) + (5 * 100) = 1000.

4.  What are the functions for MC and AC if TC = 100q + 100q2? Are the returns to scale increasing, decreasing, or constant?

MC = 100 + 200q

AC = 100 + 100q

Since AC increases with an increase in output, there are decreasing returns to scale.