Assume the inverse demand function in a market is given byP(Q) = 500 - Qwhereis the total industry output, that is the sum of the output of all firms in the market.There are two firms (indexed by i = 1,2) who both have a cost of producing the goodgiven byc(qi) = 10 * qiThe two firms are competing in the Cournot manner, that is they choose theirquantities simultaneously in order to maximize profits.What is the best response of firm 1 if firm 2 chooses an output level of 200? (input awhole number:)The best response function of firm 1 with respect to firm 2's quantity choice takesthe form:91 (92) = w * (x − y * q2 z)where (w,x,y,z) are parameters of the problem. Solve for this best response functionand provide the product (w*x*y*z) in the next blank:What is the Nash Equilibrium quantity produced by firm 1?(round to the nearest whole number)

Market Demand function : P = 500 - Q => P = 500 - (q1 + q2 ) Where , Q = Total Quantity for two…

Answered: Assume the inverse demand function in a…

Assume the inverse demand function in a market is given by P(Q) = 500 – Q where Q is the total industry output, that is the sum of the output of all firms in the market.

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

A toy manufacturing from has demand for the product is given by the demand function Q= 500 - 3p. Where P is the price in dollars and q is the quantity sold per year. What quantity will the firm sell at price $100.
A firm’s demand function is P= 60 − 0.5Q If fixed costs are 10 and variable costs are Q + 12 per unit, find the value of output to maximize the profit.
There are 100 consumers on the market for product X. The individual demand function is the same and has the form: p = 2200 -5q. And assume that only one enterprise produce product X has a production cost function of TC = 1/10Q2 + 400Q + 3,000,000. Determine: 1. The market demand function 2. Marginal Cost fuction 3. Marginal Revenue fuction 4. Price and Quantity to maximize profit 5. The price If the company wants to maximize the output without losses
The following table gives information about a firm’s short-run cost function in a perfectly competitive industry – candy manufacturing. a) What quantity will the firm supply when price of candy is $2? When price is $5? When price is $8? b) Consider the case where price = $2. Suppose that you have been renting capital (a candy-making machine) for a long time under a long-run capital rental agreement, but now the rental contract is about to expire. Should you renew your capital rental contract or not? Explain why or why not. How would your answer change if price is $5? How would your answer change if price is $8? Quantity Total Cost Average Variable Cost Average Total Cost Marginal Cost 0 10 1 15 5 15 5 2 17 3.5 8.5 2 3 18 2.66667 6 1 4 20 2.5 5 2 5 25 3 5 5 6 33 3.83333 5.5 8
Consider a firm's profit function, II(x) = R(2) -C(2), where R(x) is total revenue as a function of output (2), and C(x) is total cost as a function of output (a) Under perfect competition, each firm is a price taker. Assuming a competitive market price, p* = 10 and a cost function, C(x) = (x – 5), express the firm's profit as a function of x. (b) Find the competitive firm's profit maximizing level of output, r* (Hint: maximize the firm's profit by taking the first derivative of the profit function, setting it equal to zero, and solving for the level of output, r*). (c) If the firm were only interested in minimizing costs, what level of output would it choose?
A firm has a cost function of C = 1000 + 20Q + 1/10Q2a) Estimate the firm’s demand function. You may assume that the slope is a wholenumber, and the intercept is a multiple of 10. b) Find the firm’s revenue function. You do not need to draw it. c) Find the marginal revenue function, and draw it on a copy of the graph. d) Find and draw the marginal cost function.e) Use your results from parts (c) and (d) to find the profit-maximising level of output.(3 marks)f) Find the market price at this level of output.
Firm A and Firm B sell identical goods The total market demand is:Q(P) = 1,000-1.0P The inverse demand function is therefore: P(QM) = 10,000-10QM QM is total market production (i.e., combined production of firm’s A and B). That is: QM = QA + QB As a result, the inverse demand curve for each firm is: P(QA,QB) = 10,000-10QA-10QB The difference between this example and the example in class is that the two firms have different costs. Firm A has the same cost as in class, but firm B has a different cost function: TCA(QA) = 5000QA TCB(QB) = 5000QB Using the demand function and the cost functions above, what is firm A’s profit function? Using the profit function above and assuming that firm B produces QB, calculate what firm A’s best response is to firm B’s decision to produce QB. (Note: Firm A’s best response should be a function of QB) Using the demand function and the cost functions above, what is firm B’s profit function? Using the profit function above and assuming that firm A…
A firm faces the inverse demand function: P = 900-2Q+0.24⁰.5 The firms TC of production is given as: TC = 5Q² +12Q + A What level of Q. A, and P maximize the firm's profits?
Imagine that the cell-phone market is made up of one large firm that leads the industry and sets its own price first, while smaller firms in the industry follow. There are 20 such smaller firms, each with a supply function of q; = 67.50 + for i = 1,2, ..., 20 firms, while pis the per-unit price. Total market demand for cell phones is given by the function Q = 6, 700.00 – p. If the cost function for the leading firm is CL(qL) = 109L, calculate the following values: %3D Leading firm's production: q1 = (Round to two decimals if necessary.) Total follower firm production: qF = (Round to two decimals if necessary.) Equilibrium price: p = $ (Round to two decimals if necessary.)
A competitive firm's production function is given by y = f(K, L) = 8K 1/2 + L 1/4 Assume that the price of the good produced is p = $100, the price of capital is r = $4, and the price of labor is w = $5. Find the profit- maximizing levels of capital and labor (K * and L * ). Find the profit-maximizing level of output (y * ). What is the maximum profit of the firm (π * )?
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).
On the graph input tool, change the number found in the Quantity Demanded field to determine the prices that correspond to the production of 0, 6, 12, 15, 18, 24, and 30 units of output. Calculate the total revenue for each of these production levels. Then, on the following graph, use the green points (triangle symbol) to plot the results. Calculate the total revenue if the firm produces 6 versus 5 units. Then, calculate the marginal revenue of the sixth unit produced. The marginal revenue of the sixth unit produced is________. Calculate the total revenue if the firm produces 12 versus 11 units. Then, calculate the marginal revenue of the 12th unit produced. The marginal revenue of the 12th unit produced is_________.