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Managerial Economics Unit 2
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An economist estimated that the cost function of a single-product firm is:
C(Q) = 90 + 35Q + 25Q^2 + 10Q^3.
Based on this information, determine the following:
a. The fixed cost of producing 10 units of output.
b. The variable cost of producing 10 units of output.
c. The total cost of producing 10 units of output.
d. The average fixed cost of producing 10 units of output.
e. The average variable cost of producing 10 units of output.
f. The average total cost of producing 10 units of output.
g. The marginal cost when Q = 10.
a. answer is 90 as
b. Replace Q with 10. 90+35(10)+25(10)^2+10(10)^3-90
= 12,850
c. Variable cost - fixed cost, or 12,850-90 = 12,760
d. fixed cost / quantity, or 90/10 = 9
e. variable cost / quantity, or 12,850/10 = 1285
f. average fixed cost + average variable cost, or 1285+9 = 1294
g. Take part of the original equation, take the power number and multiply by the number it effects, then reduce the power number by 1. 35Q + 25Q^2 + 10Q^3 becomes
35 + 50Q + 30Q^2. Since Q = 10, solve for answer: 3535
A manager hires labor and rents capital equipment in a very competitive market. Currently the wage rate is $8 per hour and capital is rented at $12 per hour. If the marginal product of labor is 60 units of output per hour and the marginal product of capital is 50 units of output per hour, should the firm increase, decrease, or leave unchanged the amount of capital used in its production process?
Labor = 60/8 = 7.5, Capital = 50/12 = 4.167, The firm should decrease capital.
A firm's product sells for $4 per unit in a highly competitive market. The firm produces output using capital (which it rents at $25 per hour) and labor (which is paid a wage of $30 per hour under a contract for 20 hours of labor services). Complete the following table and use that information to answer the questions that follow.
Working notes:
(1) MPK = Change in output (Q) / Change in K
(2) APK = Q / K and APL = Q / L
(3) VMPK = MPK x Price = 4 x MPK
(4) Total cost = wL + rK
When Q = 0, TC = Fixed cost (FC)
So, FC = 20 x $30 = $600
(5) Profit = (P x Q) - TC = 4Q - (wL + rK) = 4Q - 600 - 25K
A firm can manufacture a product according to the production function:
Q = F(K,L) = K^3/4 L^1/4.
a. Calculate the average product of labor, APL, when the level of capital is fixed at 81 units and the firm uses 16 units of labor.
b. Find an expression for the marginal product of labor, MPL, when the amount of capital is fixed at 81 units.
Then, illustrate that the marginal product of labor depends on the amount of labor hired by calculating the marginal product of labor for 16 and 81 units of labor.
c. Suppose capital is fixed at 81 units. If the firm can sell its output at a price of $200 per unit and can hire labor at $50 per unit, how many units of labor should the firm hire in order to maximize profits?
a) When K = 81 &
(1) L = 16.
Q = (81)3/4 x (16)1/4 = 27 x 2 = 54
APL = Q / L = 54 / 16 = 3.375
(ii) L = 256
Q = (81)3/4 x (256)1/4 = 27 x 4 = 108
APL = Q / L = 108 / 256 = 0.422
(b) MPL = dQ / dL = (1/4) x K3/4L-3/4
(i) When K = 81, MPL = (1/4) x (81)3/4L-3/4 = (1/4) x 3 x L-3/4 = 0.75 x L-3/4
(ii)
When L = 16, MPL = 0.75 x (1/8) = 0.0938
When L = 81, MPL = 0.75 x (1/27) = 0.028
As L increases, MPL decreases. So MPL depends on L.
(c)
Firm should hire labor upto that point where Price x MPL = wage rate
When K = 81, MPL = 0.75 x L-3/4
$200 x 0.75 x L-3/4 = $50
L3/4 = 3
Raising each side to (4/3)rd power,
L = 4
The World of Videos operates a retail store that rents movie videos. For each of the last 10 years, World of Videos has consistently earned profits exceeding $36,000 per year. The store is located on prime real estate in a college town. World of Videos pays $2,300 per month in rent for its building, but it uses only 50 percent of the square footage rented for video rental purposes. The other portion of rented space is essentially vacant. Noticing that World of Videos only occupies a portion of the building, a real estate agent told the owner of World of Videos that she could add $1,650 per month to her firm's profits by renting out the unused portion of the store. While the prospect of adding an additional $1,650 to World of Videos's bottom line was enticing, the owner was also contemplating using the additional space to rent video games. What is the opportunity cost of using the unused portion of the building for video game rentals?
$1,650
You were recently hired to replace the manager of the Roller Division at a major conveyor-manufacturing firm, despite the manager's strong external sales record. Roller manufacturing is relatively simple, requiring only labor and a machine that cuts and crimps rollers. As you begin reviewing the company's production information, you learn that labor is paid $13 per hour and the last worker hired produced 100 rollers per hour. The company rents roller cutters and crimping machines for $16 per hour, and the marginal product of capital is 120 rollers per hour.
Should you change the mix of capital and labor, and if so, how should it change?
L = 100/13 = 7.69 > Capital = 120/16 = 7.5
Since labor exceeds capital, You should increase labor and decrease capital.
Suppose the marginal benefit of writing a contract is $100, independent of its length. Find the optimal contract length when the marginal cost of writing a contract of length L is:
a. MC(L) = 35 + 5L.
b. MC(L) = 55 + 3L.
a. MC(L) = MB (L)
35 + 5L = 100
5L = 65
L = 13
b. MC(L) = MB(L)
55 + 3L = 100
3L = 45
L = 15
Identify whether each of the following transactions involves spot exchange, contract, or vertical integration.
a. Barnacle, Inc., has a legal obligation to purchase 2 tons of structural steel per week to manufacture conveyor frames.
b. Exxon-Mobil uses the oil extracted from its wells to produce raw polypropylene, a type of plastic.
c. Boat Lifts R Us purchases generic AC motors from a local distributor.
d. Kaspar Construction—a home-building contractor—purchases 50 pounds of nails from the local Home Depot.
a. contract
b. vertical integration
c. spot exchange
d. spot exchange
Refer to the figure below. Suppose that the marginal benefit of writing a contract is $100 and the marginal cost of that contract is $50. Based on this information, the optimal contract length should:
Be increased
When cost is less than benefit, increase contract length. When cost is the same as benefit, contract length should be constant. When cost is more than benefit, contract should be decreased
Describe how a manager who derives satisfaction from both income and shirking allocates a 10-hour day between these activities when paid an annual, fixed salary of $120,000.
When this same manager is given an annual, fixed salary of $120,000 and 3 percent of the firm's profits—amounting to a total salary of $155,000 per year—the manager chooses to work 8 hours and shirks for 2 hours. Given this information, which of the compensation schemes does the manager prefer?
Time working: 0 hours
Time shirking: 10 hours
The scheme with fixed payment of $120,000 and a percentage of profits.
Recently, the owner of a Trader Joe's franchise decided to change how she compensated her top manager. Last year, she paid him a fixed salary of $55,000 and her store made $120,000 in profits (not counting payment to her top manager). She suspected the store could do much better and feared the fixed salary was causing her top manager to shirk on the job. Therefore, this year she decided to offer him a fixed salary of $28,000 plus 15% of the store's profits. Since the change, the store is performing much better, and she forecasts profits this year to be $260,000 (again, not counting the payment to her top manager). Assuming the change in compensation is the reason for the increased profits, and that the forecast is accurate, how much more money will the owner make (net of payment to her top manager) because of this change?
Does the manager make more money under the new payment scheme?
0.15*260,000 = 39,000
39,000+28,000 = 67,000
260,000-67,000 = 193,000
120,000-55,000 = 65,000
193,000-65,000 = 128,000 = answer 1
Yes = answer 2. 67,000>55,000
The manager of your company's pension fund is compensated based entirely on fund performance; he earned over $1.2 million last year. As a result, the fund is contemplating a proposal to cap the compensation of fund managers at $100,000. Which of the following is a likely consequence of this proposed change in compensation?
The fund manager will have lower incentives to maximize the value of the fund, resulting in a lower return for the participants.
Jim's diner is just about to open in Memphis, Tennessee. However, Jim is trying to decide whether he wants to offer Coke or Pepsi soda products. He determines that, to offer either product, he will have to spend $1,800 in sunk costs to purchase and install the appropriate paraphernalia, e.g., a large Coca-Cola or Pepsi sign out front. Ultimately, he chooses to offer Coke products and agrees to pay Coke 5 cents per ounce of Coke sold for the right to use its product. After Jim makes the investments specific to his soda choice, Coke returns and asks for a fixed (one-time) fee in addition to the 5 cents per ounce. What is the most Jim should be willing to pay?
1,800 Because of this being sung cost amount. And reasons.
Ten firms compete in a market to sell product X. The total sales of all firms selling the product are $2,500,000. Ranking the firms' sales from highest to lowest, we find the top four firms' sales to be $415,000, $350,000, $280,000, and $195,000, respectively. Calculate the four-firm concentration ratio in the market for product X.
Total Sales=$2500000
Market Share 1= 415000/2500000 = 17%
Market Share 2= 350000/2500000 = 14%
Market Share 3= 280000/2500000 = 11%
Market Share 4= 195000/2500000 = 8%
Four Firm Concentartion Ratio=.17+.14+.11+.08=.50=50%
An industry consists of three firms with sales of $250,000, $825,000, and $315,000.
a. Calculate the Herfindahl-Hirschman index (HHI).
b. Calculate the four-firm concentration ratio (C4).
c. Based on the FTC and DOJ Horizontal Merger Guidelines described in the text, is the Department of Justice likely to attempt to block a horizontal merger between two firms with sales of $250,000 and $315,000?
a. First, sum of the three sales = 1,390,000
HHI = 10,000[(250,000/1,390,000)^2 + (825,000/1,390,000)^2 + (315,000/1,390,000)^2] = 4360 rounded up
b. sum of the sales / sale total, or 1,390,000/1,390,000 = 1
c. 250,000 + 315,000 = 565,000
10,000[(250,000/565,000)^2 + (315,000/565,000)^2]= 312,789 This is more than 100-200 difference, so it will be challenged.
The industry elasticity of demand for gadgets is −2, while the elasticity of demand for an individual gadget manufacturer's product is −10. Based on the Rothschild approach to measuring market power, we conclude that:
In this problem, elasticity of firm and industry are -2. So index is 1. It indicates presence of sufficient degree of monopoly power in the market.
A firm has $1,600,000 in sales, a Lerner index of 0.55, and a marginal cost of $45, and competes against 1000 other firms in its relevant market.
a. What price does this firm charge its customers?
b. By what factor does this firm mark up its price over marginal cost?
a. P= 1/(1-L)
MC or 1/(1-0.55)
45 = 100
b. 1/(1-L) or 1/(1-0.55) = 2.22
(a) Suppose Fiat recently entered into an Agreement and Plan of Merger with Case for $4.3 billion. Prior to the merger, the market for four-wheel-drive tractors consisted of five firms. The market was highly concentrated, with a Herfindahl-Hirschman index of 2,685. Case's share of that market was 9 percent, while Fiat comprised just 5 percent of the market. If approved, by how much would the postmerger Herfindahl-Hirschman index increase?
(b) Based only on this information, is the Justice Department likely to challenge the merger according to the Horizontal Merger Guidelines?
a. 2
10,000
0.09*0.05 = 90
90+2685 = 2775
b. Possibly due to 2775 being above 2500 post merger, but the amount of the index increase is only 90, which is below the 100-200 amount in which a challenge typically takes place
(a) Several years ago, Pfizer and Warner-Lambert agreed to a $90 billion merger, thus creating one of the world's largest pharmaceutical companies. Pharmaceutical companies tend to spend a greater percentage of sales on R&D activities than other industries. The government encourages these R&D activities by granting companies patents for drugs approved by the Food and Drug Administration. For instance, Pfizer-Warner-Lambert spent large sums of money developing its popular cholesterol-lowering drug, Lipitor, which is currently protected under a patent. Lipitor sells for about $3 per pill. Calculate the Lerner index if the marginal cost of producing Lipitor is $0.30 per pill.
(b) Does the Lerner index make sense in this situation?
PART-1
Solution: 0.9
Explanation: The Lerner index is L = (P - MC) / P = ($3 - $0.30) / $3 = 0.9
PART-2
Solution: Yes, Lipitor has a patent-protected monopoly
Explanation: The Lerner index is 0.9, which indicates the firm has considerable market power. This makes sense because the product that the firm sells is currently under patent protection, which essentially makes the firm a legal monopoly.
In the 1990s five firms supplied amateur color film in the United States: Kodak, Fuji, Konica, Agfa, and 3M. From a technical viewpoint, there was little difference in the quality of color film produced by these firms, yet Kodak's market share was 67 percent. The own price elasticity of demand for Kodak film was - 2.0 and the market elasticity of demand was - 1.75. Suppose that in the 1990s, the average retail price of a roll of Kodak film was $6.95 and that Kodak's marginal cost was $3.475 per roll. Based on this information, calculate the Rothschild index and Kodak's Lerner index.
Which type of market structure best describes the film industry in the 1990s?
Rothschild index -1.75/-2 = 0.88
Kodak's Lerner index L=P-MC/P or
(6.95-3.475)/6.95 = 0.5
The manager of a local monopoly estimates that the elasticity of demand for its product is constant and equal to -3. The firm's marginal cost is constant at $25 per unit.
a. Express the firm's marginal revenue as a function of its price.
b. Determine the profit-maximizing price.
a. Marginal Cost is constant at $25
b. P = (25*-3/-3+1)
The CEO of a major automaker overheard one of its division managers make the following statement regarding the firm's production plans: "In order to maximize profits, it is essential that we operate at the minimum point of our average total cost curve." If you were the CEO of the automaker, would you praise or chastise the manager?
Chastise the manager. Profit maximization requires producing where MR = MC.
A firm sells its product in a perfectly competitive market where other firms charge a price of $120 per unit. The firm's total costs are C(Q) = 60 + 8Q + 2Q2.
a. How much output should the firm produce in the short run?
b. What price should the firm charge in the short run?
c. What are the firm's short-run profits?
d. What adjustments should be anticipated in the long run?
a. How much output should the firm produce in the short run?
Where MC = Price.
MC = 8 + 4Q = 120
4Q = 120 - 8 = 112
Q = 112/4 = 28
b. What price should the firm charge in the short run?
Prices are given as $120 (all firms have the same price)
c. What are the firm's short-run profits?
Profit = Total Revenue - Total Cost
Profit = Price * Quantity - TC
Profit = 120*28 - (60 + 8(28) + 2(28)(28))
Profit = 3360 - (60 + 224 + 1568)
Profit = 3360 - 1852 = 1508
d. What adjustments should be anticipated in the long run?
In long run, Entry will occur until economic profits shrink to zero
The elasticity of demand for a firm's product is -2.5 and its advertising elasticity of demand is 0.25.
a. Determine the firm's optimal advertising-to-sales ratio.
b. If the firm's revenues are $60,000, what is its profit-maximizing level of advertising?
a. 0.25/2.5 = 0.10
b. 0.10*60,000 = 6,000
You are the manager of a small pharmaceutical company that received a patent on a new drug three years ago. Despite strong sales ($175 million last year) and a low marginal cost of producing the product ($0.75 per pill), your company has yet to show a profit from selling the drug. This is, in part, due to the fact that the company spent $1.8 billion developing the drug and obtaining FDA approval. An economist has estimated that, at the current price of $1.75 per pill, the own price elasticity of demand for the drug is -3.
Based on this information, what can you do to boost profits?
Decrease price to improve profit.
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