8 Extra Exercises with Answers
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1 University of California Irvine ECON 100B Extra Exercises Exercise 1:
Ben and John are two individuals who one day discover a stream that flows wine cooler instead of water. Ben and John decide to bottle the wine cooler and sell it. The marginal cost of bottling wine cooler and the fixed cost to bottle wine cooler are both zero. The market demand for bottled wine cooler is given as: P = 90 - 0.25Q where Q is the total quantity of bottled wine cooler produced and P is the market price of bottled wine cooler. a. What is the economically efficient price of bottled wine cooler? b. What is the economically efficient quantity of bottled wine cooler produced? c. If Ben and John were to collude with one another and produce the profit-maximizing monopoly quantity of bottled wine cooler, how much bottled wine cooler will they produce? d. Given the output level in (c), what price will Ben and John charge for bottled wine cooler? e. At the output level in (c), what is the welfare loss? f. Suppose that Ben and John act as Cournot duopolists, what are the reaction functions for Ben and for John? g. In the long run, what level of output will Ben produce if Ben and John act as Cournot duopolists? h. In the long run, what will be the price of wine coolers be if Ben and John act as Cournot duopolists? Answer: a. zero b. 360 c. 180 d. 45
e. 4050 f. g. 120. h. 30.
2 Exercise 2:
Lambert-Rogers Company is a manufacturer of petrochemical products. The firm's research efforts have resulted in the development of a new auto fuel injector cleaner that is considerably more effective than other products on the market. Another firm, G.H. Squires Company, independently developed a very similar product that is as effective as the Lambert-Rogers formula. To avoid a lengthy court battle over conflicting patent claims, the two firms have decided to cross-license each other's patents and proceed with production. It is unlikely that other petrochemical companies will be able to duplicate the product, making the market a duopoly for the foreseeable future. Lambert-Rogers estimates the demand curve given below for the new cleaner. Marginal cost is estimated to be a constant $2 per bottle. Q = 300,000 - 25,000P. where P = dollars per bottle and a. Lambert-Rogers and G.H. Squires have very similar operating strategies. Consequently, the management of Lambert-Rogers believes that the Cournot model is appropriate for analyzing the market, provided that both firms enter at the same time. Calculate Lambert-
Rogers's profit-maximizing output and price according to this model. b. Lambert-Rogers's productive capacity and technical expertise could allow them to enter the market several months before Squires's. Choose an appropriate model and analyze the impact of Lambert Rogers being first into the market. Should Lambert-Rogers hurry to enter first? Answer: a. Q = 83,333 + 83,333 = 166,666 and P = $5.33 per bottle b. Q = 125,000 + 62,500 = 187,500 and P = $4.50
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Related Questions
Exercise 4.6
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a) If you could distinguish between regular and casual players, what price would be set for each type? How many games would each type of player play? How much profit could the golf course generate? Represent graphically.
b) As an alternative to the discrimination of third degree prices, those in charge consider a double tranche rate according to which the members can play as many games as they wish at a price of € 20 per game. How much profit will the golf course generate if it charges all players the same annual fee for becoming a member of the club? What if you…
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Exercise 3.1
A publisher must take a decision on the pricing of a new book based on the following demand
estimates:
Price
100
90
80
70
60
50
40
30
20
10
0
Number of copies demanded
0
100 000
200 000
300 000
400 000
500 000
600 000
700 000
800 000
900 000
1 000 000
According to his contract, the writer gets two million euros for writing the book and the
marginal cost of publishing the book is constant at €10 per book.
a) Calculate the total income, total cost and profit corresponding to each amount. How many
books would a profit-maximizing publisher print? What price would she charge?
(b) Calculate the marginal revenue. What is the difference between marginal revenue and
price? Explain your answer.
c) Draw the curves of marginal revenue, marginal cost and demand. For what output level does
the marginal revenue curve cut the marginal cost curves? What does that mean?
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After analazing the graph, answer the following question:
Great Brew threatens Little Kona by telling her, "If you go in, we're going to set a low price, so the best thing you can do is not get in." Do you think Little Kona should believe the threat? Why yes or why not?
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Suppose that managers at Honda are deciding how to price the new Honda Accord. The managers estimate that their total costs
increase by $20,000 for each car they produce. They also estimate the demand curve they face; it is described by the equation:
Q = -0.4 P + 16,000,
where Q represents the quantity of Honda Accords they will sell and P represents the price they charge in US dollars.
We can re-write that demand curve as:
P = 40,000 - 2.5 Q.
Take every possibly quantity that the managers might choose between
and 7,000 in units of 100. For each possible quantity,
calculate the associated price the managers would need to charge, the revenue they would earn, and the total costs. You can then
calculate profits for each level of quantity. Highlight the cell that contains the highest value of profit.
Finally, you can also approximate marginal revenue here as the change in total revenue after the next 100 cars are produced. At what
quantity does marginal revenue roughly equal marginal cost?…
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Suppose that managers at Honda are deciding how to price the new Honda Accord. The managers estimate that their total costs increase by $20,000 for each car they produce. They also estimate the demand curve they face; it is described by the equation:
Q = -0.4 P + 16,000,
where Q represents the quantity of Honda Accords they will sell and P represents the price they charge in US dollars.
We can re-write that demand curve as:
P = 40,000 - 2.5 Q.
Take every possibly quantity that the managers might choose between 0 and 7,000 in units of 100. For each possible quantity, calculate the associated price the managers would need to charge, the revenue they would earn, and the total costs. You can then calculate profits for each level of quantity. Highlight the cell that contains the highest value of profit.
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Exercise A.9
In a market only two firms produce a homogeneous good. You work on one of them and are tasked with drawing up the production strategy for the coming year.
The two companies in the market have the same information and the objective of both is the maximization of their profit.
You know:
the inverse market demand curve of the good: P(Q)=200-2Q where Q = q₁ + q₂ ,
the function that represents the costs of your company and the rival company: C(qᵢ) = 20qᵢ (for i=1, 2), and
the data in the following table, with the optimal decisions according to the different types of competition:C(qᵢ) = 20qᵢ and the data in the following table, with the optimal decisions according to the different types of competition:
q1
q2
P
Bertrand
45
45
20
Cournot
30
30
80
Collusion
22,5
22,5
110
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production budget is set at $50,000.How many units of A & B should the firm make in order to
maximize profit.
Conduct sensitivity analysis and answer the following questions:
1. State the optimal solution.
2. What is the objective function value?
3. Find out the range of profit for A in the objective function for which the above solution
remains optimal.
4. Which constraint/s is/are binding?
5. Interpret the shadow price for production budget.
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the price of corn and the consumption of corn as food?
1.) Use the line drawing tool to draw either a new demand curve (D₂) or a new supply curve (S₂) that shows how the increased use of corn
for producing ethanol affects the market for corn as food. Properly label this line.
2.) Use the point drawing tool to indicate the new market equilibrium. Label this point 'e₂'.
Carefully follow the instructions above, and only draw the required objects.
$, price of corn
Q₁
Q, quantity of corn as food
S₁
D₁
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QOregon = 120-2P (or P = 60 -0.5QOregon)
QNevada = 60 - 4P (or P = 15 -0.25QNevada)
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How much should it charge in each state? (Assume that resale between the
states is not possible.)
P = $10 (price = marginal cost) in both Oregon and Nevada.
P = $35 in Oregon and P = $10 in Nevada.
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None of the above choices are correct.
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the questions that follow.
Price ($)
50
45
Critical mass
Equilibrium
40
40
35
30
25
20
15
10
5
Marginal cost
Demand
0
0
10
20 30 40 50
60
70
80 90 100
Quantity of users (in thousands)
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Green et al. (2005) estimate the supply and demand curves for California processed tomatoes. The supply function is
In(Q) = 0.250 +0.450 In(p),
Question Viewer
where Q is the quantity of processing tomatoes in millions of tons per year and p is the price in dollars per ton. The demand function is
In(Q)=2.600 -0.200 In(p) + 0.150 In(pt),
where pt is the price of tomato paste (which is what processing tomatoes are used to produce) in dollars per ton.
How does the quantity of processing tomatoes supplied vary with the price?
It might be easier for you to exponentiate both sides of the equation first. Exponentiating both sides of the supply equation,
Q = e(0.250+ 0.450ln(p))
The effect of a change in price on quantity supplied is
=
(Properly format your expression using the tools in the palette. Hover over tools to see keyboard shortcuts. E.g., a fraction can be created with the / character.)
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Distinguish between technical efficiency and economic efficiency
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Green et al. (2005) estimate the supply and demand curves for California processed tomatoes. The supply function is:
In(Q) = 0.200 + 0.550 In(p).
where Q is the quantity of processing tomatoes in millions of tons per year and p is the price in dollars per ton. The demand function is:
In(Qa) = 2.600 - 0.200 In(p) + 0.150 In(p;).
where p, is the price of tomato paste (which is what processing tomatoes are used to produce) in dollars per ton.
Suppose pt = $109.
Determine how the equilibrium price and quantity of processing tomatoes change if the price of tomato paste falls by 7%.
If the price of tomato paste falls by 7%, then the equilibrium price will
by S . (Enter a numeric response using a real number rounded to two decimal places.)
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Given that the demand and supply functions must be linear:
Find the linear equations representing both demand and supply
Find the point of market equilibrium (number of TVs: q) and the price per unit (p) at that point.
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??= 45−QT/60
a. Find the profit-maximizing price and quantity of movie tickets, and indicate them on the graph above. How much would the theater make in profits?
b. Suppose the local government implements a property tax, so that each month the theater now must pay a lump sum tax of $700. What will be the price and quantity of movie tickets under this tax?
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(1) You can pay $T1 up front and drink as much as you want; or (2) Pay $T2 up front and the price per ounce of whiskey will be $p.
1.a If p = 4, what is the maximal T2 that Jack can charge so that Burt is willing to come to the bar?
1.b What is the maximal T1 that Jack can charge so that Adam will choose the first pricing option?
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Jack is the owner of the only local bar in a small town.He sells whiskey in one-ounce glasses. For simplicity, let’s assume it doesn’t cost Jack anything to run his business. There are two customers, Adam and Burt who are twin brothers. Adam’s demand function is yA = 16 – 2p, and Burt’s demand function is yB = 8 – p (price is measured in dollars and quantity is measured by ounces). Jack knows their demand functions, but the problem is that he cannot tell them apart since they look exactly the same to him. To increase his profits, Jack offers the following two options that his customers can choose from:
(1) You can pay $T1 up front and drink as much as you want; or (2) Pay $T2 up front and the price per ounce of whiskey will be $p.
1.a If p = 4, what is the maximal T2 that Jack can charge so that Burt is willing to come to the bar?
1.b What is the maximal T1 that Jack can charge so that Adam will choose the first pricing option?
Answer Key that was given. I seems not to understand…
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As more and more people bought home computers during the 1990s, the demand for access to the World Wide Web and the Internet increased sharply. At same time, new companies like Earl’s began to enter the internet-access market competing with older, more established services such as American Online. Despite a massive increase in demand, the price of access to the Web actually declined.
Change in Demand
Increase
Decrease
Did not Change
Indeterminate
Change in Supply
Increase
Decrease
Did not Change
Indeterminate
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The food and feed demand curves used in the Application "Summing the Corn Demand Curves," were estimated by McPhail and Babcock (2012) to be
Qfood = 1,487-22.1p
and
Qfeed = 6,247.5-226.7p,
respectively, where Q is measured in billions of bushels of corn per year. Mathematically derive the total demand curve, which the application's figure illustrates. (Hint:
Remember that the demand curve for feed is zero at prices above about $27.56 per bushel.)
The total demand curve is (enter your responses rounded to one decimal place):
Q=-p for p≥ $27.56 per bushel and Q =
-p for p <$27.56 per bushel.
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On average, the price of a patented pharmaceutical drops between 30 and 50 percent after the patent expires. Explain why this occurs. (Do not use AI).
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Consider the following scenario and select the best answer:
A company is trying to determine how to allocate its $145,000 advertising budget for a new product. The company is considering newspaper ads and television commercials as its primary means for advertising. The
following table summarizes the costs of advertising in these different media and the number of new customers reached by increasing amounts of advertising.
Media & No. of Ads
No. of New Customers
Cost per Ad
Reached
Newspaper: 1–10
900
$1,000
Newspaper: 11–20
700
$900
Newspaper: 21–30
400
$800
Television: 1-5
10,000
$12,000
Television: 6–10
7,500
$10,000
Television: 11–15
5,000
$8,000
For instance, each of the first 10 ads the company places in newspapers will cost $1,000 and is expected to reach 900 new customers. Each of the next 10 newspaper ads will cost $900 and is expected to reach 700 new customers.
Note that the number of new customers reached by increasing amounts of advertising decreases as the advertising…
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Take this hypothetical situation: Suppose that the supply side of the market for for electric energy is comprised of two sellers: Seller 1 and Seller 2. Let P be the price of one unit of electric energy, and Q be the quantity of electric energy.
Seller 1 owns a hydropower factory with a constant marginal cost of $3 and can produce a maximum of 10 units of electric energy. In addition, the hydropower plant has a requirement of a minimum of 3 units of electric energy.
Seller 2 owns a solar factory to produce electric energy. This factory has a constant marginal cost of $5 and can produce a maximum of 5 units of electric energy.
A) With this given information, please sketch the market supply by aggregating the two individual supplies. Please label the graph clearly for slopes, kinks, intercepts, etc.
B) Suppose that the price of geothermal increases. On the graph drawn in part A, show precisely how the supply curve changes.
C) Suppose that the price of geothermal increases. In a market…
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Take this hypothetical situation: Suppose that the supply side of the market for for electric energy is comprised of two sellers: Seller 1 and Seller 2. Let P be the price of one unit of electric energy, and Q be the quantity of electric energy.
Seller 1 owns a hydropower factory with a constant marginal cost of $3 and can produce a maximum of 10 units of electric energy. In addition, the hydropower plant has a requirement of a minimum of 3 units of electric energy.
Seller 2 owns a solar factory to produce electric energy. This factory has a constant marginal cost of $5 and can produce a maximum of 5 units of electric energy.
With this given information, please sketch the market supply by aggregating the two individual supplies. Please label the graph clearly for slopes, kinks, intercepts, etc.
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(Problem 3.4 in Chapter 2 of Perloff)
The estimated Canadian processed pork demand function (Moschini and Meilke, 1992) is
Q = 171 - 20p + 20pp + 3pc + 2Y, and the supply function is Q = 178 +40p - 60pn.
If Ph=1.5 (dollars per kg), p₁= 4 (dollars per kg), p= 3 (dollars per kg), and Y= 12.5 (thousands
of dollars), what are the equilibrium price and quantity?
Given the estimated demand and supply functions above, what is the equilibrium price of
Canadian processed pork?
Round your answer to two decimal places.
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A large share of the world supply of diamonds comes from Russia and South Africa. Suppose that the marginal cost of mining diamonds is constant at $1,000 per diamond, and the demand for diamonds is described by the following schedule:
Price ($)
Quantity (diamonds)
8000
5000
7000
6000
6000
7000
5000
8000
4000
9000
3000
10000
2000
11000
1000
12000
a) If there were many suppliers of diamonds, what would be the price and quantity?
b) If there were only one supplier of diamonds, what would be the price and quantity?
c) If Russia and South Africa formed a cartel, what would be the price and quantity? If the countries split the market evenly, what would be South Africa’s production and profit? What would happen to South Africa’s profit if it increased its production by 1,000 while Russia stuck to the cartel agreement?
d) Use your answers to part (c) to explain why cartel agreements are often not successful.
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Related Questions
- Exercise 4.6 An econometrician hired to analyse a local golf course has determined that there are two types of golfers, the regular and the occasional. The annual demand for games from regular players is given by QH = 24 – 0.3P, where P is the price of a round of golf. On the other hand, the annual demand for occasional items is given by QO = 10 – 0.1P. The marginal cost and the average total cost per item are equal to €20. a) If you could distinguish between regular and casual players, what price would be set for each type? How many games would each type of player play? How much profit could the golf course generate? Represent graphically. b) As an alternative to the discrimination of third degree prices, those in charge consider a double tranche rate according to which the members can play as many games as they wish at a price of € 20 per game. How much profit will the golf course generate if it charges all players the same annual fee for becoming a member of the club? What if you…arrow_forwardTHE OCOBEE RIVER RAFTING COMPANY Vicki Smith, Penny Miller, and Darryl Davis are students at State University. In the summer they often go rafting with other students down the Ocobee River in the nearby Blue Ridge Mountain foothills. The river has a number of minor rapids but is not generally dangerous. The students' rafts basically consist of large rubber tubes, sometimes joined together with ski rope. They have noticed that a number of students who come to the river don't have rubber rafts and often ask to borrow theirs, which can be very annoying. In discussing this nuisance, it occurred to Vicki, Penny, and Darryl that the problem might provide an opportunity to make some extra money. They considered starting a new enterprise, the Ocobee River Rafting Company, to sell rubber rafts at the river. They determined that their initial investment would be about $3,000 to rent a small parcel of land next to the river on which to make and sell the rafts; to purchase a tent to operate out…arrow_forwardExercise 3.1 A publisher must take a decision on the pricing of a new book based on the following demand estimates: Price 100 90 80 70 60 50 40 30 20 10 0 Number of copies demanded 0 100 000 200 000 300 000 400 000 500 000 600 000 700 000 800 000 900 000 1 000 000 According to his contract, the writer gets two million euros for writing the book and the marginal cost of publishing the book is constant at €10 per book. a) Calculate the total income, total cost and profit corresponding to each amount. How many books would a profit-maximizing publisher print? What price would she charge? (b) Calculate the marginal revenue. What is the difference between marginal revenue and price? Explain your answer. c) Draw the curves of marginal revenue, marginal cost and demand. For what output level does the marginal revenue curve cut the marginal cost curves? What does that mean?arrow_forward
- Exercise 6.3.Little Kona is a small coffee company considering entering a market dominated by Big Brewer. The benefits of each of them depend on whether or not the first enters and whether the second sets a high or low price: After analazing the graph, answer the following question: Great Brew threatens Little Kona by telling her, "If you go in, we're going to set a low price, so the best thing you can do is not get in." Do you think Little Kona should believe the threat? Why yes or why not?arrow_forwardSuppose that managers at Honda are deciding how to price the new Honda Accord. The managers estimate that their total costs increase by $20,000 for each car they produce. They also estimate the demand curve they face; it is described by the equation: Q = -0.4 P + 16,000, where Q represents the quantity of Honda Accords they will sell and P represents the price they charge in US dollars. We can re-write that demand curve as: P = 40,000 - 2.5 Q. Take every possibly quantity that the managers might choose between and 7,000 in units of 100. For each possible quantity, calculate the associated price the managers would need to charge, the revenue they would earn, and the total costs. You can then calculate profits for each level of quantity. Highlight the cell that contains the highest value of profit. Finally, you can also approximate marginal revenue here as the change in total revenue after the next 100 cars are produced. At what quantity does marginal revenue roughly equal marginal cost?…arrow_forwardSuppose that managers at Honda are deciding how to price the new Honda Accord. The managers estimate that their total costs increase by $20,000 for each car they produce. They also estimate the demand curve they face; it is described by the equation: Q = -0.4 P + 16,000, where Q represents the quantity of Honda Accords they will sell and P represents the price they charge in US dollars. We can re-write that demand curve as: P = 40,000 - 2.5 Q. Take every possibly quantity that the managers might choose between 0 and 7,000 in units of 100. For each possible quantity, calculate the associated price the managers would need to charge, the revenue they would earn, and the total costs. You can then calculate profits for each level of quantity. Highlight the cell that contains the highest value of profit.arrow_forward
- Based on market research, a film production company in Ectenian obtains the following information about the demand and production costs of its new DVD:Demand: P = 1,000 – 10QTotal Revenue: TR = 1,000Q – 10Q2Marginal Revenue: MR = 1,000 – 20QMarginal Cost: MC = 100 + 10Qwhere Q indicates the number of copies sold and P is the price in Ectenian dollars.d. Suppose, in addition to the costs above, the director of the film has to be paid. The company is considering four options:i. A flat fee of 2,000 Ectenian dollarsii. 50 percent of the profitsiii. 150 Ectenian dollars per unit soldiv. 50 percent of the revenueFor each option, calculate the profit-maximizing price and quantity. Which, if any, of these compensation schemes would alter the deadweight loss from monopoly? Explainarrow_forwardBased on Zangwill (1992). Murray Manufacturing runs a day shift and a night shift. Regardless of the number of units produced, the only production cost during a shift is a setup cost. It costs $8000 to run the day shift and $4500 to run the night shift. Demand for the next two days is as follows: day 1, 2000; night 1, 3000; day 2, 2000; night 2, 3000. It costs $1 per unit to hold a unit in inventory for a shift. a. Determine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. (Note: Not all shifts have to be run.) b. After listening to a seminar on the virtues of the Japanese theory of production, Murray has cut the setup cost of its day shift to $1000 per shift and the setup cost of its night shift to $3500 per shift. Now determine a production schedule that minimizes the sum of setup and inventory costs. All demand must be met on time. Show that the decrease in setup costs has actually raised the average inventory level. Is this…arrow_forwardExercise A.9 In a market only two firms produce a homogeneous good. You work on one of them and are tasked with drawing up the production strategy for the coming year. The two companies in the market have the same information and the objective of both is the maximization of their profit. You know: the inverse market demand curve of the good: P(Q)=200-2Q where Q = q₁ + q₂ , the function that represents the costs of your company and the rival company: C(qᵢ) = 20qᵢ (for i=1, 2), and the data in the following table, with the optimal decisions according to the different types of competition:C(qᵢ) = 20qᵢ and the data in the following table, with the optimal decisions according to the different types of competition: q1 q2 P Bertrand 45 45 20 Cournot 30 30 80 Collusion 22,5 22,5 110 a) What is more in your company's interest to compete or cooperate with the rival company? Keep in mind that explicit collusion agreements are illegal, so each…arrow_forward
- Q.5 A firm is making two products A & B. Each unit of A incurs a cost of production to the tune of $150 and that of B incurs a cost of $200. Product A earns a profit of $15/unit and B gets $20/unit. The estimated monthly demand of both A & B is at maximum 500 units. Monthly production budget is set at $50,000.How many units of A & B should the firm make in order to maximize profit. Conduct sensitivity analysis and answer the following questions: 1. State the optimal solution. 2. What is the objective function value? 3. Find out the range of profit for A in the objective function for which the above solution remains optimal. 4. Which constraint/s is/are binding? 5. Interpret the shadow price for production budget.arrow_forwardEthanol, a fuel, is made from corn. Ethanol production increased 9.1 times from 2000 to 2019 (https://ethanolrfa.org/statistics/annual-ethanolproduction/). What effect did this increased use of corn for producing ethanol have on the price of corn and the consumption of corn as food? 1.) Use the line drawing tool to draw either a new demand curve (D₂) or a new supply curve (S₂) that shows how the increased use of corn for producing ethanol affects the market for corn as food. Properly label this line. 2.) Use the point drawing tool to indicate the new market equilibrium. Label this point 'e₂'. Carefully follow the instructions above, and only draw the required objects. $, price of corn Q₁ Q, quantity of corn as food S₁ D₁arrow_forwardAn umbrella manufacturer sells its product in Nevada and Oregon. Due to different climates, each state has different demands for umbrellas. The marginal cost of production is the same in each state and is a constant $10. The demand curve for raincoats in each state is: QOregon = 120-2P (or P = 60 -0.5QOregon) QNevada = 60 - 4P (or P = 15 -0.25QNevada) The umbrella manufacturer wants to practice third-degree price discrimination. How much should it charge in each state? (Assume that resale between the states is not possible.) P = $10 (price = marginal cost) in both Oregon and Nevada. P = $35 in Oregon and P = $10 in Nevada. P = $35 in Oregon and P = $12.5 in Nevada. It should only sell in Oregon, and charge P = $35 there. None of the above choices are correct.arrow_forward
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