1. A) An automobile company sells 2 tires for every one frame. Now the demand function for tire is t=189 - P and demand function for frame f-180 - Pr and firm's cost function is C=3t2 + 3f2 + 3tf + 570 now use the Lagrange Multiplier Method of constrained optimization to optimize the profit. b) Now use the Bordered Hessian method to show that all the optimal values that you find in (a) maximize the profit. c) Define the significance of Lagrange Multiplier in optimization using this context. What is the other name of Lagrange Multiplier? Please briefly discuss how it will affect a firm's decision in this context? (Hint: is there any constant in your constraint?)

1. A) An automobile company sells 2 tires for every one frame. Now the demand function for tire is t=189 - P and demand function for frame f-180 - Pr and firm's cost function is C=3t2 + 3f2 + 3tf + 570 now use the Lagrange Multiplier Method of constrained optimization to optimize the profit. b) Now use the Bordered Hessian method to show that all the optimal values that you find in (a) maximize the profit. c) Define the significance of Lagrange Multiplier in optimization using this context. What is the other name of Lagrange Multiplier? Please briefly discuss how it will affect a firm's decision in this context? (Hint: is there any constant in your constraint?)

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Green et al. (2005) estmate the supply and demand curves for Californa processod tomatoes. The supply function is: \[ \ln \left(Q_{s}\right)=0.200+0.550 \ln (p) \] whereQis the quantify of processing tomatoes in milions of tons per year andpis the price in dollars per ton. The demand function is: \[ \ln \left(Q_{d}\right)=2600-0.200 \ln (p)+0.150 \ln \left(p_{1}\right) . \] wherep1is the price of tornato paste (which is what processing tomatoes are used to produce) in dollars per ton. Supposept=$119Determine how the equilerium price and quantity of processing tomatees change if the price of tomato pasise tails by16%. If the price of tomato paste fals by18%, then the equaborium price will by 5 (Enter a numene response using a real number rounded to two decimal places)
An industrial firm makes two products, A and B. These products require water resources where they are very scarce. The products they make are unique, and hence they can set the unit price of each product at any value they want to. However, experience tells them that the higher the unit price for a product, the less amount of that product they will sell. The relationship between the unit price and quantity that can be sold is given by the following two demand functions: Assume for simplicity that the unit price for product A is (16 - A) and for product B is (18-2.5B). Suppose the total amount of A and B could not exceed the total amount of Tmax. Where Tmax = 10. Please use "Lagrange Multiplier" method to determine what are the amounts of A and B, and their unit prices, that maximize total revenue (Set the marginal increments at 1).
Note that the two terms in the Product Rule correspond to the separate effects of increasing the number of stores and the average revenue per store. dR (b) Calculate dt -0 (c) If Couture can implement only one leg (A or B) of its expansion at ! = 0, which choice will grow revenue most rapidly? %3D
A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as Price = 150 - 0.02 x Demand for an annual printing of this particular product. The fixed costs per year (ie., per printing) = $46,000 and the variable cost per unit=$40. What is the maximum profit that can be achieved? What is the unit price at this point of optimal demand? Demand is not expected to be more than 3,000 units per year. The maximum profit that can be achieved is $. (Round to the nearest dollar.) The unit price at the point of optimal demand is $ per unit. (Round to the nearest cent.) Enter your answer in each of the answer boxes.
1. It is 1908 and you are the CEO of Ford Motor Company. General Motors startedproducing cars this year and has quickly become your chief rival. Their recent entrance, as wellas your assembly line methods, allows you the advantage of producing cars faster and choosingyour output levels first. Assume the 1908 inverse demand function for cars is P = 3900 - Q(customers view cars as identical products at this point in time) and production costs are C(qi) =100qi. a. What is Ford’s profit-maximizing output level? GM's?b. What is the market equilibrium price?c. How much profit does each firm earn?d. As the assembly line is used by other firms, the first-mover advantage disappears (fast forward100 years to present day), and more firms have entered the market (e.g. FCA, Tesla, Hyundai,Toyota, Honda, etc.), what do you expect to happen to Ford’s profit (assume demand andcosts are the same)? Explain.e. From 1908 into the 1920s, Ford offered customers one car: the Model T. Further, Henry isfamous…
COURSE: MICROECONOMICS - Cournot Model:In the market for a given good there are only 2 firms satisfying the demand, and their respective total cost functions respond to the form: CTi = 10Qi + 5 and the demand is estimated to be: P = 31 - QIf the decision variable for both firms is that the quantity they will produce and realize will be decided simultaneously it is asked to:(a) calculate the profit and reaction function of each firmb) graph market equilibriumc) calculate the profits that both companies will obtain in equilibrium
No written by hand solution Suppose that the market for video games is competitive with demand function Qd = 170 – 4p + 2Y + 3pm – 2pc, where Qd is the quantity demanded, p is the market price, Y is the monthly budget that an average consumer has available for entertainment, pm is the average price of a movie, and pc is the price of a controller that is required to play these games. Given that Y = $100, pm = $30 and pc = $30, use Excel to calculate quantity demanded for p = $10 to p = $80 in $5 increments. Using Excel’s spreadsheet Find Qd = ________ when P=$30. Find Qd = ________ when P=$45. Now, Y increases to $120. Re-calculate the demand schedule and find Qd = ________ when P=$20. Let Y = $100 again, but pm increases to $40. Re-calculate the demand schedule and find Qd = ________ when P=$25. Let Y = $100, pm = $30, and pc increases to $40. Re-calculate the demand schedule and find Qd = ________ when P=$50.
In 1990, the town of Ham Harbour had a more-or-less free market in taxi services. Any respectable firm could provide taxi services as long as the drivers and cabs satisfied certain safety standards. Let us suppose that the marginal cost per trip of a taxi ride is $18, and that the average taxi has a capacity of 10 trips per day. There are no other costs. Let the demand function for taxi rides be given by D(p) = 2100 10p, where demand is measured in rides per day, and price is measured in dollars. Assume that the industry is perfectly competitive. Part 1: a) What is the competitive equilibrium price per ride? (Hint: in competitive equilibrium, price must be equal to marginal cost. b) What is the equilibrium number of rides per day? c) How many taxi cabs will there be in equilibrium?
Uver is a ride-sharing service that has become very popular in large cities. In one of these large cities, Uver is trying a new model: selling a bundle of 10 rides per week (instead of charging for each ride). Let y stand for the number of bundles, and suppose the weekly cost of providing a bundle of 10 rides is given by the following function: c(y) -10y²+200y+ 500. Assume all Uver drivers have the same cost function. 4th attempt See Hint The market for Uver rides in this city is competitive. Suppose there are 158 Uver drivers in the city. If the price of a bundle of rides is $164, the number of bundles of rides that will be provided is bundles.
Problem Set: A х —3 (1) For the function f(x)= evaluate and simplify the following: 4- 2x? (i) f(-1) (ii) f(2a–b) (2) The length of a rectangular floor is two metres more than twice its width. If a diagonal of the rectangle is 13 meters, find the area of the floor. (3) The demand function for a tablet is given by the model p= 200 – 16x where p is measured in dollars per tablet and x is measured in millions of tablets. If it costs $50 to produce each tablet and a profit of $125 million was derive when 2.5 million tablets were produced. Derive the number of tablets that the company could sell to make the same amount of profit?
Respond to the question with a concise and accurate answer, along with a clear explanation and step-by-step solution, or risk receiving a downvote. n the table below are the marginal abatement costs of two firms. Note that an entry in the table indicates the cost of reducing emissions by one unit from the previous level. For example, $104 is the additional abatement cost for Firm 1 to reduce its emissions from 3 tons to 2 tons, and $40 is the cost for Firm 2 to reduce its emissions from 7 tons to 6 tons. 1.In an unregulated environment each firm produces 10 tons of emissions (20 tons total). Using the table above, what emissions levels (i.e., emissions standards) would you assign if you wanted to limit aggregate emissions to 7 tons in a cost-effective manner? Firm 1’s emissions level ________________ Firm 2’s emissions level ________________ 2.Given the emissions levels from Question 1, calculate the total abatement cost for each firm? Firm 1’s total abatement cost ________________…
When the admission price for a baseball game was $4 per ticket, 50,000 tickets were sold. When the price was raised to $5, only 45,000 tickets were sold. Assume that the demand function is linear and that the variable and fixed costs for the ball park owners are $0.10 and $95,000 respectively. (a) Find the profit P as a function of x, the number of tickets sold. P(x) = (b) Select the graph of P. y 150000 y 150000 150 000 100 000 100 000 100 000 50 000 50 000 50 000 20000 40 000 60 00p 20000 40 000 60 000 20000 40 000 60 000 - 50 000 -50 000 -50 000 -100 000 100000 100000 The xy-coordinate plane is given. The curve starts at the approximate point (0, 3,000), goes up and right becoming less steep, and exits the window at the approximate point o-150000 O o-150000L O O (70,000, 69,000). 150000 100 000. 50 000- 20000 40 000 60 do0 - 50 000 100 000- o 150 000