MBA 504 – Consider the following Cobb-Dougla

Subject: Economics / General Economics

Problem Set #4:
Production & Costs
Consider the following Cobb-Douglas production function for your company, which provides bus service
in Nanaimo.
Q AL K F Where Q =output in millions of passenger miles, L= labour input in worker hours, K=capital input in bus
transit hours and F= Fuel input in gallons
Each of the parameters of this model was estimated by regression analysis using monthly data over a
recent 3 year period. Results obtained were as follows
A= 1.2, ?=0.285 ?=0.638 ?=0.126
The standard error estimates for each coefficient are
SA = 0.4 S? = 0.15 S?= 0.12 S?= 0.07
a) Estimate the effect on output of a 4% decline in workers hours (holding K and F constant)
b) Estimate the effect on output of a 3% reduction in Fuel availability accompanied by a 4% decline
in bus transit hours (holding L constant)
c) Which input is significant in determining the output? How do you know?
d) Estimate the returns to scale for this production system
e) Determine the expression for Marginal product of labour input
Your firm produces output that can be sold at a price of $10. The production function is givenby
Q L1 / 2 K 1 / 2 If K is fixed at 1 unit in the short run, how much labour should the firm employ to maximize profits if
the wage rate=2.
You recently replace Yen, the manager of the Roller Division at a major conveyor-manufacturing firm,
despite her strong external sales record. Roller manufacturing is relatively simple, requiring only
labour and a machine that cuts and crimps rollers. As you begin reviewing the company’s production
information, you learn that labour is paid $16 per hour and the last worker produced 200 rollers per
hour. The company rents roller cutters and crimping machines for $30 per hour and the marginal
product of capital is 240 rollers per hour. What do you think Yen could have done to keep her job?

Q.4 Which of the following news items involve a short run decision and which involve a long run decision?
Assume that factors of production include Land, Labour, Capital, Entrepreneurship and other capital
inputs). Explain
(a) January 31, 2017: Toyota will open 75 more plant abroad than originally predicted, for a total of
(b) February 25, 2016: For three hours on Tuesday, Cactus Club will shut down every single one of
its 80 restaurants so that servers (waiters and waitresses) can receive a refresher course.
(c) June 2, 2010: Starbucks to replace baristas (men and women who serve the coffee) with
vending machines
(i) Sonia’s Surfboards rents a factory building. If the rent is increased by $200 a week and other
things remain constant, how do Sonia’s Surfboards short run average cost curves, average
variable costs and marginal cost curves change? Explain
If other things remain the same, the average fixed cost curve shifts upward, the average variable
cost curve does not change, the average total cost curve shifts upward, and the marginal cost
curve does not change (ii)
Jusu Coffee House is raising its prices because the wholesale price of milk has risen 70% and
there’s a lot of milk in the coffee house’s lattes. Describe how the price of milk changes Jusu’s Coffee
House short-run cost curves
The management of Chisom Industries is considering a plan to terminate a new employee Stu. The
action stemmed from documented evidence supplied by the firm’s accounting department manager,
Ayo, that Stu did not add as much to the firm’s overall output as did Maji, a worker hired two weeks
earlier. Based on this evidence, do you agree that the Stu should be fired? Explain
While looking into your firm’s books you noted that the TC = 250,000+40Q+0,01Q 2. Determine the
output level at which your firm’s average cost is minimized. (hint: remember the cost curves)
The Sudheer Winery plans to open a new production facility in India. Based information provided by
the accounting department, the company estimates fixed costs of $200,000 per year and average
variable costs of AVC = 100 + 0.5Q
a. Estimate total cost and average total cost functions
b. Find the MC function

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