Let yp(y) be the C(2) inverse demand function facing a monopoly, where y++ is its rate of output, and let yC(y) be the C(2) total cost function of the monopoly. Assume that p(y)>0, p'(y)<0, and C'(y)>0 for all y++, and that a profit maximizing rate of output exists. Total revenue is therefore given by R(y)=p(y)y. Given that question uses an inverse demand function, the elasticity of demand, namely (y), is defined as (y)= 1/p'y p(y)/y.
Why is (y)<0?
Prove that price is greater than marginal cost at the profit maximizing rate of output. Use the product rule when differentiating R(y)=p(y)y
Prove that the monopoly sets price in the elastic portion of its demand curve at the profit maximizing rate of output.
Let yp(y) be the C(2) inverse demand function facing a monopoly, where y++ is its rate...
Suppose that a monopoly faces inverse market demand function as P = 70−2Q, and its marginal cost function is MC = 40 – Q. Please answer the following two questions: a. What should be the monopoly’s profit-maximizing output? b. What is the monopoly’s price?
MC Qu. 084 Consider a monopoly where the inverse demand for i... Consider a monopoly where the inverse demand for its product is given by P = 50 - 20. Total costs for this monopolist are estimated to be C(q) = 100 + 2Q+Q2. At the profit- maximizing combination of output and price, deadweight loss is: Multiple Choice $32. $64. $128. cannot be determined with the given information.
Take a monopolist facing the inverse demand function p(y) = 100 – y. Suppose his total cost function is C(y) = 20 + y^2. Compute the monopoly equilibrium and the deadweight losses.
A monopolist has a cost function given by c(y) = y and faces an inverse demand curve given by P(y) = 156.00 - y, where P is the per-unit price and y is the quantity of output sold. Assume this monopolist cannot discriminate and charges a single price. What is the profit-maximizing level of output? What is its profit-maximizing price? $ Part 2 (2 points) See Hint Assume you want to choose a price ceiling for this monopolist so as...
Consider a monopolist facing the following inverse demand function: P = 200 - Q The total cost function is given by C = 100 + 50Q + 0.5Q^2 What is the monopolist's uniform profit-maximizing price? a. 130 b. 140 c. 150 d. 160
A competitive firm has a cost function given by c(y)=2y2+98 and marginal cost of MC(y)=4y. What is the firm's supply function? Choose one: A. p(y)=4y B. y(p)=(p)/4 C. p(y)=2y2+98 D. p(y)= (p-98)/(4) How many units will the firm supply if the price is $32? What if the price is $12? What is the firm's profit when the price is $32? $ What is profit when the price is $12? $ At what price and quantity will the firm break even?...
Let ⊂ be a rectangle and let f be a function which is integrable on R. Prove that the graph of f, G(f) := {(x, f(x)) ∈ : x ∈ }, is a Jordan region and that it has volume 0 (as a subset of ). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
The monopoly’s cost is a function of its output, which is C(Q)=Q2+12, and the monopoly faces the linear inverse demand function: P=24—Q (1) Calculate the following items: marginal cost, average fixed cost, average variable cost, average total cost, and marginal revenue (2) Calculate profit-maximizing output and profit-maximizing price, determine its economic profit
1. A monopoly is facing an inverse demand curve that is p=200-5q. There is no fixed cost and the marginal cost of production is given and it is equal to 50. Find the total revenue function. Find marginal revenue (MR). Draw a graph showing inverse demand, MR, and marginal cost (MC). Find the quantity (q) that maximizes the profit. Find price (p) that maximizes the profit. Find total cost (TC), total revenue (TR), and profit made by this firm. Find...
*2.2 If a monopoly faces an inverse demand function of p = 90 − Q , p=90−Q, has a constant marginal and average cost of 30, and can perfectly price discriminate, what is its profit? What are the consumer surplus, total surplus, and deadweight loss? How would these results change if the firm were a single-price monopoly?