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microeconomics

Microeconomics 4th Edition David Besanko, Ronald Braeutigam - Solutions

LO23-2 Explain the cost/benefit approach the typical economist takes to analyze regulations.
LO23-1 List three reasons why economists sometimes differ and sometimes agree in their views on social policy.
In turn, as we saw in the appendix to Chapter 7, if we know the input demand functions, we can infer properties of the production function from which it was derived (and maybe even derive the equation of the production function).
Shephard’s Lemma tells us that if we know the total cost function, we can derive the input demand functions.
8.35. A firm owns two production plants that make widgets. The plants produce identical products, and each plant (i) has a production function given by for i ! 1, 2. The plants differ, however, in the amount of capital equipment in place in the short run. In particular, plant 1 has K1 ! 25, whereas
8.34. A researcher has claimed to have estimated a long-run total cost function for the production of automobiles. His estimate is that where w and r are the prices of labor and capital. Is this a valid cost function—that is, is it consistent with long-run cost minimization by the firm? Why or
8.33. A railroad provides passenger and freight service.The table shows the long-run total annual costs TC(F, P), where P measures the volume of passenger traffic and F the volume of freight traffic. For example, TC(10,300) ! 1,000.Determine whether there are economies of scope for a railroad
8.32. Suppose that the experience curve for the production of a certain type of semiconductor has a slope of 80 percent. Suppose over a five-year period that cumulative production experience increases by a factor of 8.Input prices over this period did not change. At the beginning of the period,
8.31. A railroad has two types of services: freight service and passenger service. The stand-alone cost for freight service is TC1 ! 500 " Q1, where Q1 equals the number of ton-miles of freight hauled each day and TC1 is the total cost in thousands of dollars per day. The standalone cost for
8.30. Suppose that the total cost of providing satellite television services is as follows:where Q1 and Q2 are the number of households that subscribe to a sports and movie channel, respectively. Does the provision of satellite television services exhibit economies of scope?
8.29. The following diagram shows the long-run average and marginal cost curves for a firm. It also shows the short-run marginal cost curve for two levels of fixed capital: K ! 150 and K ! 300. For each plant size, draw the corresponding short-run average cost curve and explain briefly why that
8.28. Figure 8.18 shows that the short-run marginal cost curve may lie above the long-run marginal cost curve. Yet, in the long run, the quantities of all inputs are variable, whereas in the short run, the quantities of just some of the inputs are variable. Given that, why isn’t short-run
8.27. A producer of hard disk drives has a short-run total cost curve given by Within the same set of axes, sketch a graph of the short-run average cost curves for three different plant sizes:and Based on this graph, what is the shape of the long-run average cost curve?
8.26. A short-run total cost curve is given by the equation STC(Q) ! 1000 " 50Q2. Derive expressions for, and then sketch, the corresponding short-run average cost, average variable cost, and average fixed cost curves.
8.25. The production function Q ! KL " M has marginal products MPK ! L, MPL ! K, and MPM ! 1. The input prices of K, L, and M are 4, 16, and 1, respectively.The firm is operating in the short run, with K fixed at 20 units and M fixed at 40. What is the short-run total cost of producing 400 units of
8.24. The production function Q ! KL " M has marginal products MPK ! L, MPL ! K, and MPM ! 1. The input prices of K, L, and M are 4, 16, and 1, respectively.The firm is operating in the short run, with K fixed at 20 units. What is the short-run total cost of producing 400 units of output?
8.23. The production function Q ! KL " M has marginal products MPK ! L, MPL ! K, and MPM ! 1. The input prices of K, L, and M are 4, 16, and 1, respectively.The firm is operating in the long run. What is the longrun total cost of producing 400 units of output?
8.22. Consider a production function of three inputs, labor, capital, and materials, given by Q ! LKM. The marginal products associated with this production function are as follows: MPL ! KM, MPK ! LM, and MPM !LK. Let w ! 5, r ! 1, and m ! 2, where m is the price per unit of materials.a) Suppose
8.21. When a firm uses K units of capital and L units of labor, it can produce Q units of output with the production function Each unit of capital costs 2, and each unit of labor costs 1.a) The level of K is fixed at 16 units. Suppose What will the firm’s short-run total cost be? (Hint: How much
8.20. When a firm uses K units of capital and L units of labor, it can produce Q units of output with the production function Each unit of capital costs 20, and each unit of labor costs 25. The level of K is fixed at 5 units.a) Find the equation of the firm’s short-run total cost curve.b) On a
8.18. A firm has the linear production function Q !3L " 5K, with MPL ! 3 and MPK ! 5. Derive the expression for the 1ong-run total cost that the firm incurs, as a function of Q and the factor prices, w and r.8.19. A firm uses two inputs: labor and capital. The price of labor is w and the price of
8.17. A packaging firm relies on the production function Q ! KL " K, with MPL ! K and MPK ! L " 1.Assume that the firm’s optimal input combination is interior (it uses positive amounts of both inputs). Derive its long-run total cost curve in terms of the input prices, w and r. Verify that if the
8.16. A hat manufacturing firm has the following production function with capital and labor being the inputs:Q ! min(4L, 7K)—that is, it has a fixed-proportions production function. If w is the cost of a unit of labor and r is the cost of a unit of capital, derive the firm’s long-run total cost
8.15. Tricycles must be produced with 3 wheels and 1 frame for each tricycle. Let Q be the number of tricycles, W be the number of wheels, and F be the number of frames. The price of a wheel is PW and the price of a frame is PF.a) What is the long-run total cost function for producing tricycles,
8.14. Consider a production function of two inputs, labor and capital, given by The marginal products associated with this production function are as follows:Let w ! 2 and r ! 1.a) Suppose the firm is required to produce Q units of output. Show how the cost-minimizing quantity of labor depends on
8.13. A firm produces a product with labor and capital.Its production function is described by Q ! L " K. The marginal products associated with this production function are MPL ! 1 and MPK ! 1. Let w ! 1 and r ! 1 be the prices of labor and capital, respectively.a) Find the equation for the
8.12. A firm produces a product with labor and capital.Its production function is described by Q ! min(L, K). Let w and r be the prices of labor and capital, respectively.a) Find the equation for the firm’s long-run total cost curve as a function of quantity Q and input prices, w and r.b) Find
8.11. A firm produces a product with labor and capital as inputs. The production function is described by Q !LK. The marginal products associated with this production function are MPL ! K and MPK ! L. Let w ! 1 and r ! 1 be the prices of labor and capital, respectively.a) Find the equation for the
8.10. For each of the total cost functions, write the expressions for the total fixed cost, average variable cost, and marginal cost (if not given), and draw the average total cost and marginal cost curves.a) TC(Q) ! 10Q TC(Q) ! 1000Q1 2.b) TC(Q) ! 160 " 10Qc) TC(Q) ! 10Q2, where MC(Q) ! 20Qd)
8.9. A firm’s long-run total cost curve is TC(Q) ! 40Q$ 10Q2 " Q3, and its long-run marginal cost curve is MC(Q) ! 40 $ 20Q " 3Q2. Over what range of output does the production function exhibit economies of scale, and over what range does it exhibit diseconomies of scale?
8.8. A firm’s long-run total cost curve is TC(Q) !1000Q $ 30Q2 " Q3. Derive the expression for the corresponding long-run average cost curve and then sketch it. At what quantity is minimum efficient scale?
8.7. A firm’s long-run total cost curve is Derive the equation for the corresponding long-run average cost curve, AC(Q). Given the equation of the longrun average cost curve, which of the following statements is true?a) The long-run marginal cost curve MC(Q) lies below AC(Q) for all positive
8.6. A firm’s long-run total cost curve is TC(Q) !1000Q2. Derive the equation for the corresponding longrun average cost curve, AC(Q). Given the equation of the long-run average cost curve, which of the following statements is true?a) The long-run marginal cost curve MC(Q) lies below AC(Q) for
8.5. A firm produces a product with labor and capital, and its production function is described by Q ! LK. The marginal products associated with this production function are MPL ! K and MPK ! L. Suppose that the price of labor equals 2 and the price of capital equals 1. Derive the equations for the
8.4. The following incomplete table shows a firm’s various costs of producing up to 6 units of output. Fill in as much of the table as possible. If you cannot determine the number in a box, explain why it is not possible to do so.
8.3. The following incomplete table shows a firm’s various costs of producing up to 6 units of output. Fill in as much of the table as possible. If you cannot determine the number in a box, explain why it is not possible to do so.
8.2. The following incomplete table shows a firm’s various costs of producing up to 6 units of output. Fill in as much of the table as possible. If you cannot determine the number in a box, explain why it is not possible to do so.
8.1. The following incomplete table shows a firm’s various costs of producing up to 6 units of output. Fill in as much of the table as possible. If you cannot determine the number in a box, explain why it is not possible to do so.
12. What is an experience curve? What is the difference between economies of experience and economies of scale?
11. What is the difference between economies of scope and economies of scale? Is it possible for a twoproduct firm to enjoy economies of scope but not economies of scale? Is it possible for a firm to have economies of scale but not economies of scope?
10. Suppose that the minimum level of short-run average cost was the same for every possible plant size.What would that tell you about the shapes of the longrun average and long-run marginal cost curves?
9. Suppose the graph of the average variable cost curve is flat. What shape would the short-run marginal cost curve be? What shape would the short-run average cost curve be?
8. Explain why the short-run marginal cost curve must intersect the average variable cost curve at the minimum point of the average variable cost curve.
7. Could the output elasticity of total cost ever be negative?
6. Sketch the long-run marginal cost curve for the“flat-bottomed” long-run average cost curve shown in Figure 8.11.
5.a) If the average cost curve is increasing, must the marginal cost curve lie above the average cost curve?Why or why not?b) If the marginal cost curve is increasing, must the marginal cost curve lie above the average cost curve? Why or why not?
4. How would an increase in the price of labor shift the long-run average cost curve?
3. If the price of labor increases by 20 percent, but all other input prices remain the same, would the long-run total cost at a particular output level go up by more than 20 percent, less than 20 percent, or exactly 20 percent? If the prices of all inputs went up by 20 percent, would long-run
2. Explain why an increase in the price of an input typically causes an increase in the long-run total cost of producing any particular level of output.
1. What is the relationship between the solution to the firm’s long-run cost-minimization problem and the longrun total cost curve?
If average cost is neither increasing nor decreasing as quantity is increasing, then average cost is equal to marginal cost: AC(Q) ! MC(Q).
If average cost is increasing as quantity is increasing, then average cost is less than marginal cost: AC(Q) ( MC(Q).
If average cost is decreasing as quantity is increasing, then average cost is greater than marginal cost: AC(Q) # MC(Q).
Identify several common functional forms used to estimate total cost functions.
Discuss how a learning curve illustrates economies of experience.
Explain the meaning of economies of scope.
Explain and distinguish between the concepts of short-run average cost, short-run marginal cost, average variable cost, and average fixed cost.
Derive a short-run average cost curve and a short-run marginal cost curve from a short-run total cost curve.
Illustrate graphically the relationship between a short-run total cost curve and a long-run total cost curve.
Determine the short-run total cost curve from a production function.
Describe and a graph a short-run total cost curve.
Distinguish between economies of scale and diseconomies of scale.
Explain the difference between average cost and marginal cost.
Derive a long-run average cost curve and a long-run marginal cost curve from the long-run total cost curve.
Demonstrate how the graph of a long-run total cost curve changes when an input price changes.
Determine the long-run total cost curve from a production function.
Describe and graph a long-run total cost curve.
7.34. This problem will enable you to apply a revealed preference argument to see if a firm is minimizing the total cost of production. The firm produces output with a technology characterized by a diminishing marginal rate of technical substitution of labor for capital. It is required to produce a
7.33. Suppose that in a given production process a blueprint (B) can be produced using either an hour of computer time (C) or 4 hours of a manual draftsman’s time (D). (You may assume C and D are perfect substitutes. Thus, for example, the firm could also produce a blueprint using 0.5 hour of C
7.32. A firm operates with a technology that is characterized by a diminishing marginal rate of technical substitution of labor for capital. It is currently producing 32 units of output using 4 units of capital and 5 units of labor. At that operating point the marginal product of labor is 4 and the
7.31. Acme, Inc., has just completed a study of its production process for gadgets. It uses labor and capital to produce gadgets. It has determined that 1 more unit of labor would increase output by 200 gadgets.However, an additional unit of capital would increase output by 150 gadgets. If the
7.30. Consider the production function in LearningBy-Doing Exercise 7.6: For this production function, the marginal products of labor, capital, and materials are and Suppose that the input prices of labor, capital, and materials are w ! 1, r !1, and m ! 1, respectively.a) Given that the firm wants
7.29. Suppose that the firm uses three inputs to produce its output: capital K, labor L, and materials M. The firm’s production function is given by For this production function, the marginal products of capital, labor, and materials are and MPM ! . The prices 1 3K 1 3L 13M$2 MP 3 L ! 1 3K 1 3L$2
7.28. A plant’s production function is Q ! 2KL " K.For this production function, MPK ! 2L " 1 and MPL !2K. The price of labor services w is $4 and of capital services r is $5 per unit.a) In the short run, the plant’s capital is fixed at K ! 9.Q ! 10KL K. 1 3.Find the amount of labor it must
7.27. Suppose that the firm’s production function is given by The firm’s capital is fixed at What amount of labor will the firm hire to solve its short-run cost-minimization problem?
7.26. A bicycle is assembled out of a bicycle frame and two wheels.a) Write down a production function of a firm that produces bicycles out of frames and wheels. No assembly is required by the firm, so labor is not an input in this case. Sketch the isoquant that shows all combinations of frames and
7.25. A firm has the production function Q ! LK. For this production function, MPL ! K and MPK ! L. The firm initially faces input prices w ! $1 and r ! $1 and is required to produce Q ! 100 units. Later the price of labor w goes up to $4. Find the optimal input combinations for each set of prices
7.24. Consider the production function For this production function, and Derive the input demand curves for L and K, as a function of the input prices w (price of labor services)and r (price of capital services). Show that at an interior optimum (with K # 0 and L # 0) the amount of L demanded does
7.23. Suppose a production function is given by Q !10K " 2L. The factor price of labor is 1. Draw the demand curve for capital when the firm is required to produce Q ! 80.
7.22. Suppose a production function is given by Q !K " L—that is, the inputs are perfect substitutes. For this production function, MPL ! 1 and MPK ! 1. Draw a graph of the demand curve for labor when the firm wants to produce 10 units of output and the price of capital services is $1 per unit (Q
7.21. A firm’s production function is Q ! min(K, 2L), where Q is the number of units of output produced using K units of capital and L units of labor. The factor prices are w ! 4 (for labor) and r ! 1 (for capital). On an optimal choice diagram with L on the horizontal axis and K on the vertical
7.20. Suppose a production function is given by Q !min(L, K)—that is, the inputs are perfect complements.Draw a graph of the demand curve for labor when the firm wants to produce 10 units of output (Q ! 10).
7.19. A manufacturing firm’s production function is Q !KL " K " L. For this production function, MPL ! K " 1 and MPK ! L " 1. Suppose that the price r of capital services is equal to 1, and let w denote the price of labor services. If the firm is required to produce 5 units of ?
7.18. A researcher claims to have estimated input demand curves in an industry in which the production technology involves two inputs, capital and labor. The input demand curves he claims to have estimated are L ! wr 2 Qand K ! w2 rQ. Are these valid input demand curves? In other words, could they
7.17. A paint manufacturing company has a production function For this production function MPK ! 1 and The firm faces a price of labor w that equals $1 per unit and a price of capital services r that equals $50 per unit.a) Verify that the firm’s cost-minimizing input combination to produce Q ! 10
7.16. A construction company has two types of employees: skilled and unskilled. A skilled employee can build 1 yard of a brick wall in one hour. An unskilled employee needs twice as much time to build the same wall. The hourly wage of a skilled employee is $15. The hourly wage of an unskilled
7.15. Ajax, Inc., assembles gadgets. It can make each gadget either by hand or with a special gadget-making machine. Each gadget can be assembled in 15 minutes by a worker or in 5 minutes by the machine. The firm can also assemble some of the gadgets by hand and some with machines. Both types of
7.14. A cost-minimizing firm’s production function is given by Q ! LK, where MPL ! K and MPK ! L. The price of labor services is w and the price of capital services is r. Suppose you know that when w ! $4 and r ! $2, the firm’s total cost is $160. You are also told that when input prices change
7.13. Consider the production function Q ! LK, with marginal products MPL ! K and MPK ! L. Suppose that the price of labor equals w and the price of capital equals r.Derive expressions for the input demand curves.
7.12. A firm operates with the production function Q ! K2 L. Q is the number of units of output per day when the firm rents K units of capital and employs L workers each day. The marginal product of capital is 2KL, and the marginal product of labor is K2. The manager has been given a production
7.11. A firm produces an output with the production function Q ! KL, where Q is the number of units of output per hour when the firm uses K machines and hires L workers each hour. The marginal products for this production function are MPK ! L and MPL ! K. The factor price of K is 4 and the factor
7.10. The processing of payroll for the 10,000 workers in a large firm can either be done using 1 hour of computer time (denoted by K) and no clerks or with 10 hours of clerical time (denoted by L) and no computer time.Computers and clerks are perfect substitutes; for example, the firm could also
7.9. Suppose the production of airframes is characterized by a Cobb–Douglas production function: Q ! LK.The marginal products for this production function are MPL ! K and MPK ! L. Suppose the price of labor is$10 per unit and the price of capital is $1 per unit. Find the cost-minimizing
7.8. Suppose the production of airframes is characterized by a CES production function:The marginal products for this production function are and Suppose that the price of labor is $10 per unit and the price of capital is $1 per unit. Find the cost-minimizing combination of labor and capital for an
7.7. The text discussed the expansion path as a graph that shows the cost-minimizing input quantities as output changes, holding fixed the prices of inputs. What the text didn’t say is that there is a different expansion path for each pair of input prices the firm might face. In other words, how
7.6. A farmer uses three inputs to produce vegetables:land, capital, and labor. The production function for the farm exhibits diminishing marginal rate of technical substitution.a) In the short run the amount of land is fixed. Suppose the prices of capital and labor both increase by 5 percent.What
7.5. A firm uses two inputs, capital and labor, to produce output. Its production function exhibits a diminishing marginal rate of technical substitution.a) If the price of capital and labor services both increase by the same percentage amount (e.g., 20 percent), what will happen to the
7.4. A consulting firm has just finished a study for a manufacturer of wine. It has determined that an additional man-hour of labor would increase wine output by 1,000 gallons per day. Adding another machine-hour of fermentation capacity would increase output by 200 gallons per day. The price of a
7.3. Last year the accounting ledger for an owner of a small drug store showed the following information about ?
7.2. A grocery shop is owned by Mr. Moore and has the following statement of revenues and costs:Revenues $250,000 Supplies $25,000 Electricity $6,000 Employee salaries $75,000 Mr. Moore’s salary $80,000 Mr. Moore always has the option of closing down his shop and renting out the land for

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