Chapter 9: Production and Cost in the Long Run
Chapter 9:
PRODUCTION AND COST IN THE LONG RUN
Essential Concepts
1. In long-run analysis of production, all inputs are variable and isoquants are used to study production
decisions. An isoquant is a curve showing all possible input combinations capable of producing a
given level of output.
2. Isoquants are downward sloping because if greater amounts of labor are used, then less capital is
required to produce a given level of output. The marginal rate of technical substitution (MRTS) is the
3. The marginal rate of technical substitution can be expressed as the ratio of two marginal products:
4. Isocost curves show the various combinations of inputs that may be purchased for a given level of
expenditure (
C
) at given input prices (w and r). The equation of an isocost curve is given by
5. A manager can minimize the total cost of producing
units of output by choosing the input
combination on the isoquant for
which is just tangent to an isocost curve. Since the optimal input
K
6. In order to maximize output for a given level of expenditure on inputs, a manager must choose the
combination of inputs that equates the marginal rate of technical substitution and the input price ratio,
which requires choosing an input combination satisfying exactly the same conditions set forth above
for minimizing cost.
Chapter 9: Production and Cost in the Long Run
7. The expansion path is the curve that gives the efficient (least-cost) input combinations for every level
8. Long-run total cost (LTC) for a given level of output
is given by
9. Long-run average cost (LAC) measures the cost per unit of output when the manager can adjust
production so that the optimal amount of each input is employed: LAC = LTC/Q. LAC is -shaped.
10. Long-run marginal cost (LMC) measures the rate of change in long-run total cost as output changes
11. When LAC is decreasing (increasing), (dis)economies of scale are present. See Figure 9.11 in your
textbook.
12. The most fundamental reason for economies of scale is that larger-scale firms are able to take greater
14. The minimum efficient scale of operation (MES) is the lowest level of output needed to reach the
minimum value of long-run average cost.
15. When economies of scope exist: (1) The total cost of producing goods X and Y by a multiproduct firm
is less than the sum of the costs for specialized, single-product firms to produce these goods:
16. Purchasing economies of scale arise when large-scale purchasing of raw materials enables large
buyers to obtain lower input prices through quantity discounts.
17. Workers, managers, engineers, and even input suppliers in these industries “learn by doing” or “learn
18. The relations between long-run cost and short-run cost can be summarized by the following points:
a. LMC intersects LAC when the latter is at its minimum point.
19. Because managers have the greatest flexibility to choose inputs in the long run, costs are lower in the
20. Since the long-run cost structure shows the lowest-possible costs a firm can achieve, business
decision makers and industry analysts are keenly interested in long-run costs.
Answers to Applied Problems
1. The consultant’s advice makes sense if BlueStar is operating on a short-run expansion path with less
than the efficient or optimal number of commercial aircraft. In the long run, the CEO should add just
enough aircraft to move BlueStar to a point of tangency on its long-run expansion path at isoquant
representing the number of travelers it wishes to serve. Such long-run restructuring lowers total costs.
2. The publishing house is not making the optimal choice because the last dollar spent on printers added
one book to total output (20/$20=1 book per dollar at the margin), while the last dollar spent on
3. Managers of government bureaus can apply the principles of efficient production by employing inputs
4. a. By purchasing one textile machine, 9 laborers must be fired to keep the level of output exactly
equal to 5,400 units per day. This reduces the labor bill by 9 $50 = $450 and increases the
5. Efficiency requires that inputs be employed so that marginal products per dollar spent are equal.
Since MPL/w (= 10/20 = 0.5) MPK/r (= 15/15 = 1), the Beta Corporation is not operating
6. a. Spreading the overhead refers to spreading total fixed cost over the number of units of output
produced; average fixed cost declines as output increases.
7. a. Since the slope of the isocost curves (w/r) are equal to 5 (= 90/18 = 60/12 = 40/8), then $200/r =
5, and r = $20.
b. 30K and 6L will minimize total cost of producing 180 units.
8. Managers of bakeries in one geographic market could specialize in the production of one product, say
bread, in order to take advantage of the scale economies in baking bread. They would then trade (or
9. While doctors have a higher marginal product than RNs, the price of RNs may be so much lower than
10. In some cases, foreign workers may be less productive than U.S. workers. Thus, the marginal product
11. a. The common or shared inputs in brake and muffler repair include such inputs as the building, the
hydraulic lift to raise the cars, a cash register, a phone, a restroom, a coffee pot, assorted hand
tools for the mechanic, and the business insurance. These are all quasi-fixed inputs that must be
purchased as a lump or fixed amount that does not vary with output and these quasi-fixed inputs
are the same for either a muffler repair shop or a brake repair shop.
Chapter 9: Production and Cost in the Long Run
g. Yes, because
LTC(5000,4000)=1,390,000 <$2,290,000 =LTC(5000,0)+LTC(0,4000)
.
h. The presence of scope economies makes it more likely that this market will be characterized in
the long run by firms that do both brake and muffler repair. Any new firm that tries to enter this
market will likely enter as a multi-service firm doing both muffler and brake repair. We are
unlikely to see new entrants survive in the long run if they only do muffler or only do brake
repairs. That said, we do see specialty firms, like Just Brakes, for example, competing quite
Answers to Mathematical Exercises
1. a. MPL = aALa-1Kb
b. MPK = bALaKb-1
c. MRTS = aK/bL
ë û
d. For all values of Q, the following derivatives are all positive:
ë û
3. a. Q = 24L0.5(121)0.5 = 264L0.5 = g(L)
b. MPL = dg(L)/dL = 132L–0.5; dMPL/dL = –66L–1.5 < 0 for all L.
4. a. K* = (w/r)L*
b. L* = (w/r)–1/2Q/24 and K* = (w/r)1/2Q/24