Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
14th Edition
ISBN: 9781305506381
Author: James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris
Publisher: Cengage Learning
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Chapter 9, Problem 1.2CE
To determine
To evaluate the kind of mathematical relationship that would to appear to exist between enrollment and operating expenditures per students.
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A study of the costs of electricity generation for a sample of 56 British firms in 1946-1947 yielded the following long-run cost function: (Source:
Johnston, "Chapter 4," in Statistical Cost Analysis)
AVC = 1.24 + 0.0033Q + 0.00000290²
Q
= output; measured in millions of kWh per year
Z = plant size; measured in thousands of kilowatts
where AVC = average variable cost (i.e., working costs of generation), measured in pence per kilowatt-hour (kWh). (A pence was a British monetary
unit equal, at that time, to 2 cents U.S.)
What is the long-run total variable cost function for electricity generation?
1.24 +0.0033 +0.0000029Q -0.000046Z 0.026Z 0.000182²
Q
Q
Q
○ 0.0033 +20.0000029Q -0.000046 Z
O 0.0033Q +20.00000290² - 0.000046 QZ
O 1.24Q +0.0033Q² +0.0000029Q³ – 0.000046Q²Z – 0.026ZQ+0.00018Z²Q
What is the long-run marginal cost function for electricity generation?
0.000046 QZ
O 0.0033Q +20.0000029Q² +0.000046 QZ
O 1.24 +0.0066Q+0.0000087Q² - 0.000092QZ – 0.026Z+0.00018Z2
O +0.0033…
Derive the average cost function from :TC = 20 + 10Q + Q2/2
A study of 86 savings and loan associations in six northwestern states yielded the following cost function.
C�
=
3.69
-
0.007999Q�
+
0.000005359Q2�2
+
25.0X1�1
(3.69)
(3.08)
(3.42)
(3.50)
where C� = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent.
Q� = output; measured by total assets ($ million)
X1�1 = ratio of the number of branches to total assets ($ million)
Note: The number in parentheses below each coefficient is its respective t-statistic.
Holding constant the effects of bank branching (X1�1), what is the level of total assets that minimizes the average operating expense ratio?
$746.31 million
$1,562.70 million
$1,492.63 million
$461.31 million
What is the average operating expense ratio for a savings and loan association with the level of total assets determined in the previous part and 1 branch?…
Chapter 9 Solutions
Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)
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- Given the following cost functions: TC=100+60Q-3Q2+0.1Q3 TC=100+ 60Q+3Q2 TC=100 + 60Q In each case, indicate the point at which diminishing returns occurs. Also, indicate the point of maximum cost efficiency (i.e., the point of minimum average cost).arrow_forwardConsider the following cost function: C(Q)=9,300+44Q+0.025Q 2 Calculate total costs when Q=180arrow_forwardThe estimated cost to produce x items is given by the function: C(x) = 0.004x² + 5x + 6000 Determine the average cost and marginal cost of producing 2,000 items and calculate the level of output for which the average cost is the lowest and what that cost is.arrow_forward
- Here is the production cost function, in $ of producing q units of a product: 2200 C(q) = 300 +0.8q2 + %3D and the demand function of the product is: p(x) = 200 - 0.05q a. Determine the marginal cost, marginal revenue and marginal profit when q=50 and q=150? b. Interpret the results of the calculation in part (a) if it is related to cost, revenue and profit?arrow_forwardConsider the following function: Ĉ = 0.03q + 6 + 200/q - determine the approximate cost to increase production from 200 units to 201 units - determine the function of marginal costarrow_forwardA study of 86 savings and loan associations in six northwestern states yielded the following cost function. C� = 2.38 - 0.006153Q� + 0.000005359Q2�2 + 19.2X1�1 (2.86) (3.08) (3.68) (2.96) where C� = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent. Q� = output; measured by total assets ($ million) X1�1 = ratio of the number of branches to total assets ($ million) Note: The number in parentheses below each coefficient is its respective t-statistic. Which of the variable(s) is (are) statistically significant in explaining variations in the average operating expense ratio? (Hint: t0.025,70=1.99�0.025,70=1.99.) Check all that apply. Q� Q2�2 X1�1 What type of average cost-output relationship is suggested by these statistical results? Quadratic Cubic Linear Based on these results, what can we…arrow_forward
- A study of 86 savings and loan associations in six northwestern states yielded the following cost function. C = 3.12 - 0.006768Q + 0.000005359Q2 +21.1X1 (3.12) (2.61) (2.89) (2.96) where C = average operating expense ratio, expressed as a percentage and defined as total operating expense ($ million) divided by total assets ($ million) times 100 percent. Q = output; measured by total assets ($ million) X1 = ratio of the number of branches to total assets ($ million) Note: The number in parentheses below each coefficient is its respective t-statistic. Holding constant the effects of bank branching (X1), what is the level of total assets that minimizes the average operating expense ratio? $1,262.92 million $1,558.81 million $631.46 million $460.99 million What is the average operating expense ratio for a savings and loan association with the level of total assets determined in the previous part and 1 branch? 1.17% 3.15% 1.02% 5.63% What is the ratio with 10 branches instead? 5.93% 1.47%…arrow_forwardThe monthly demand equation for an electric utility company is estimated to be p=55- (105)x, where p is measured in dollars and x is measured in thousands of killowatt-hours. The utility has fixed costs of $1,000,000 per month and variable costs of $27 per 1000 kilowatt-hours of electricity generated, so the cost function is C(x)=1-10° +27x. (a) Find the value of x and the corresponding price for 1000 kilowatt-hours that maximize the utility's profit. (b) Suppose that the rising fuel costs increase the utility's variable costs from $27 to $39, so its new cost function is C₁(x)=1.10° +39x. Should the utility pass all this increase of $12 per thousand kilowatt-hours on to the consumers?arrow_forwardFor the given cost function C(x) = 40000 + 700x + x² find: a) The cost at the production level 1700 b) The average cost at the production level 1700 c) The marginal cost at the production level 1700 d) The production level that will minimize the average cost e) The minimal average costarrow_forward
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