11.2 Universal Widget produces high-quality widgets at its plant in Gulch, Nevada, for sale throughout the world. The cost function for total widget production (q) is given by total cost = 0.25q. Widgets are demanded only in Australia (where the demand curve is given by qa = 100 – 2PA) and Lapland (where the demand curve is given by q1 = 100 – 4PL); thus, total demand equals q = qa + q1. If Universal Widget can control the quantities supplied to each market, how many should it sell in each location to maximize total profits? What price will be charged in each location?
11.2 Universal Widget produces high-quality widgets at its plant in Gulch, Nevada, for sale throughout the world. The cost function for total widget production (q) is given by total cost = 0.25q. Widgets are demanded only in Australia (where the demand curve is given by qa = 100 – 2PA) and Lapland (where the demand curve is given by q1 = 100 – 4PL); thus, total demand equals q = qa + q1. If Universal Widget can control the quantities supplied to each market, how many should it sell in each location to maximize total profits? What price will be charged in each location?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
Related questions
Question
11.2
![demand function for that input.
Short-run changes in market price result in changes to
the firm's short-run profitability. These can be mea-
sured graphically by changes in the size of producer
Increases in the price of an input will induce substitu-
tion and output effects that cause the firm to reduce
hiring of that input.
PROBLEMS
11.1
John's Lawn Mowing Service is a small business that acts as a price-taker (i.e., MR = P). The prevailing market price of lawn
mowing is $20 per acre. John's costs are given by
total cost = 0.1q² + 10g + 50,
where
q = the number of acres John chooses to cut a day.
a. How many acres should John choose to cut to maximize profit?
b. Calculate John's maximum daily profit.
c. Graph these results, and label John's supply curve.
11.2
Universal Widget produces high-quality widgets at its plant in Gulch, Nevada, for sale throughout the world. The cost function
for total widget production (q) is given by
total cost = 0.25q².
Widgets are demanded only in Australia (where the demand curve is given by qA = 100 – 2PA) and Lapland (where the
demand curve is given by q1 = 100 – 4PL); thus, total demand equals q = qA + qı. If Universal Widget can control the
quantities supplied to each market, how many should it sell in each location to maximize total profits? What price will be
charged in each location?
11.3
The production function for a firm in the business of calculator assembly is given by
q = 2Vi,
where q denotes finished calculator output and I denotes hours of labor input. The firm is a price-taker both for calculators
(which sell for P) and for workers (which can be hired at a wage rate of w per hour).
a. What is the total cost function for this firm?
b. What is the profit function for this firm?
c. What is the supply function for assembled calculators [q(P, w)]?
d. What is this firm's demand for labor function [I(P, w)]?
e. Describe intuitively why these functions have the form they do.
11.4
The market for high-quality caviar is dependent on the weather. If the weather is good, there are many fancy parties and caviar
sells for $30 per pound. In bad weather it sells for only $20 per pound. Caviar produced one week will not keep until the next
week. A small caviar producer has a cost function given by
Chapter 11: Prof it Maximization 39
C = 0.5q² + 59 + 100,
where q is weekly caviar production. Production decisions must be made before the weather (and the price of caviar) is know
but it is known that good weather and bad weather each occur with a probability of 0.5.
a. How much caviar should this firm produce if it wishes to maximize the expected value of its profits?
b. Suppose the owner of this firm has a utility function of the form
utility = VT,
where t is weekly profits. What is the expected utility associated with the output strategy defined in part (a)?
c. Can this firm owner obtain a higher utility of profits by producing some output other than that specified in parts (a) ar
(b)? Explain.
d. Suppose this firm could predict next week's price but could not influence that price. What strategy would maximi
expected profits in this case? What would expected profits be?
11.5
The Acme Heavy Equipment School teaches students how to drive construction machinery. The number of students that ti
school can educate per week is given by q = 10 min(k, 1)", where k is the number of backhoes the firm rents per week, I is t
number of instructors hired each week, and y is a parameter indicating the returns to scale in this production function.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb317bc60-e9ad-4b02-954e-b2233810850d%2F23ca6cd7-026b-4e1b-ae27-31b80ba94325%2Fvrcure7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:demand function for that input.
Short-run changes in market price result in changes to
the firm's short-run profitability. These can be mea-
sured graphically by changes in the size of producer
Increases in the price of an input will induce substitu-
tion and output effects that cause the firm to reduce
hiring of that input.
PROBLEMS
11.1
John's Lawn Mowing Service is a small business that acts as a price-taker (i.e., MR = P). The prevailing market price of lawn
mowing is $20 per acre. John's costs are given by
total cost = 0.1q² + 10g + 50,
where
q = the number of acres John chooses to cut a day.
a. How many acres should John choose to cut to maximize profit?
b. Calculate John's maximum daily profit.
c. Graph these results, and label John's supply curve.
11.2
Universal Widget produces high-quality widgets at its plant in Gulch, Nevada, for sale throughout the world. The cost function
for total widget production (q) is given by
total cost = 0.25q².
Widgets are demanded only in Australia (where the demand curve is given by qA = 100 – 2PA) and Lapland (where the
demand curve is given by q1 = 100 – 4PL); thus, total demand equals q = qA + qı. If Universal Widget can control the
quantities supplied to each market, how many should it sell in each location to maximize total profits? What price will be
charged in each location?
11.3
The production function for a firm in the business of calculator assembly is given by
q = 2Vi,
where q denotes finished calculator output and I denotes hours of labor input. The firm is a price-taker both for calculators
(which sell for P) and for workers (which can be hired at a wage rate of w per hour).
a. What is the total cost function for this firm?
b. What is the profit function for this firm?
c. What is the supply function for assembled calculators [q(P, w)]?
d. What is this firm's demand for labor function [I(P, w)]?
e. Describe intuitively why these functions have the form they do.
11.4
The market for high-quality caviar is dependent on the weather. If the weather is good, there are many fancy parties and caviar
sells for $30 per pound. In bad weather it sells for only $20 per pound. Caviar produced one week will not keep until the next
week. A small caviar producer has a cost function given by
Chapter 11: Prof it Maximization 39
C = 0.5q² + 59 + 100,
where q is weekly caviar production. Production decisions must be made before the weather (and the price of caviar) is know
but it is known that good weather and bad weather each occur with a probability of 0.5.
a. How much caviar should this firm produce if it wishes to maximize the expected value of its profits?
b. Suppose the owner of this firm has a utility function of the form
utility = VT,
where t is weekly profits. What is the expected utility associated with the output strategy defined in part (a)?
c. Can this firm owner obtain a higher utility of profits by producing some output other than that specified in parts (a) ar
(b)? Explain.
d. Suppose this firm could predict next week's price but could not influence that price. What strategy would maximi
expected profits in this case? What would expected profits be?
11.5
The Acme Heavy Equipment School teaches students how to drive construction machinery. The number of students that ti
school can educate per week is given by q = 10 min(k, 1)", where k is the number of backhoes the firm rents per week, I is t
number of instructors hired each week, and y is a parameter indicating the returns to scale in this production function.
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