9781118041581

impacts on the availability of can scrap. Finally, technology might

matter; new can-making processes might reduce the amount of

leftover scrap generated.

Chapter 5

1. Maximizing average output is typically nonoptimal. First, we should
   emphasize that maximizing total output and maximizing average output
   are two different things. For instance, in Table 5.2, the firm’s maximum
   output is 403 units using 120 workers. In contrast, the firm would
   maximize its average product by using 10 workers producing only 93
   units. Second, optimal use of an input requires comparing extra output
   (and revenue) against the input’s extra cost. As we have seen, optimum
   input use typically means producing below the level of maximum output.


2. The production function, Q 10L  .5L^2 24K K^2 , has marginal
   products: MPL 10 L and MPK 24 2K. Both marginal products
   decline; therefore, there are diminishing returns. Starting from any L
   and K, doubling the use of both inputs generates less than double the
   level of output. Thus, the production function exhibits decreasing
   returns to scale.


3. The law of diminishing returns states that an input’s marginal product
   declines as one increases its use past some point (holding other inputs
   constant). Decreasing returns to scale states that increasing all inputs in
   proportion generates a less-than-proportional increase in output. A
   production function can exhibit diminishing returns without decreasing
   returns to scale, or vice versa.


4. a. The isoquant for the 200-pound steer has the usual convex curvature.
   b. The cost of the 68–60 mix is: ($.10)(68) ($.07)(60) $11.00 per
   day. The cheapest diet is a 56–70 mix; its cost is $10.50 per day.
   c. For a 200-pound steer, the cheapest mix is 56–70. Given constant returns
   to scale, feeding a 250-pound steer would require (250/200)  125
   percent of this amount. A 70–87.5 mix (at a cost of $13.125) is needed.


5. a. Production of steel by electric furnace has the lowest average cost per
   ton ($325). Therefore, its share of production would be expected to
   increase over time.
   b. A tripling of energy prices would leave continuous casting ($400) as
   the least-cost production method.
   c. A fall in the price of steel scrap would favor production by electric
   furnace (the only process that uses scrap).


6. Here is a graphical explanation. The firm’s initial (optimal) input mix
   occurs where the lowest isocost line is tangent to its isoquant. If the price

8 Answers to Odd-Numbered Problems

BMAns.qxd 9/26/11 11:18 AM Page 8