Consider a monopolist facing linear demand P(Q) = 16 – Q. Find the monopolist’s profit-maximizing choice...

Consider a monopolist facing linear demand P(Q) = 16 – Q.
1. Find the monopolist’s profit-maximizing choice of price and quantity if the total cost function is C(Q) = 8Q.
2. Find the monopolist’s profit-maximizing choice of price and quantity if instead C(Q) = 2Q². Note that this cost function yields exactly the same total cost as the original cost function C(Q) = 8Q for the monopolist’s optimal quantity in 2.1. Explain why the monopolist’s optimum quantity, however, is not the same in 2.1 and 2.2

Expert Solution

Rahul Sunny answered 7 months ago

Monopoly with linear inverse demand. Consider a monopolist facing a linear inverse demand curve p(q)= a-...

Monopoly with linear inverse demand. Consider a monopolist facing a linear inverse demand curve p(q)= a- bq, and cost function C(q)= F + cq, where F denotes its fixed costs and c represents the monopolist's (constant) magical cost a>c 1. Graph demand, marginal revenue and marginal cost. Label your graph carefully, including intercepts 2. Solve the profit maximizing output q^m. To do this, first write down the expression for MR=MC and solve for the optimal quantity. Next find the price...

if a profit maximizing firm facing a linear demand curve is operating where |?| = 1,...

if a profit maximizing firm facing a linear demand curve is operating where |?| = 1, i.e. the unit elastic portion of the demand curve, what must marginal cost be? Draw this on a graph (recall from your answer to #1 that MR is twice as steeply sloped as demand). ( 2 pts)

A monopolist faces a market demand curve of q=100-p. The monopolist’s cost function is given by...

A monopolist faces a market demand curve of q=100-p. The monopolist’s cost function is given by (q) = 3000 + 20q. a) If the monopolist can perfectly price discriminate, how many units will be sold? b) If the monopolist can perfectly price discriminate, how much consumer surplus will there be? c) If the monopolist cannot price discriminate, how much consumer surplus will there be? (For this question, think long run.)

A profit-maximizing monopolist operates in market with an inverse demand curve given by P = 20...

A profit-maximizing monopolist operates in market with an inverse demand curve given by P = 20 − Q and an associated marginal revenue MR = 20 − 2Q. Their marginal cost of production is constant at MC = 4. Assume for now that they have to sell each unit of output for the same price. a) Find the monopolist’s optimal choice of output and the socially efficient output. b) Sketch demand, marginal revenue, and marginal cost. Indicate on your diagram...

A profit-maximizing monopolist operates with an inverse demand curve P = 20 − Q and an associated marginal revenue MR = 20 − 2Q.

A profit-maximizing monopolist operates with an inverse demand curve P = 20 − Q and an associated marginal revenue MR = 20 − 2Q. Marginal cost of production is constant at MC = 4. Assume they have to sell each unit of output for the same price. a) Find the monopolist’s optimal choice of output and the socially efficient output. b) Sketch demand, marginal revenue, and marginal cost. Indicate on your diagram the points you found in part a)....

A monopolist faces a demand of P = -3Q + 400. The monopolist’s marginal cost is...

A monopolist faces a demand of P = -3Q + 400. The monopolist’s marginal cost is MC = 2Q + 80. The total cost for the monopolist is TC = Q2 + 80Q + 6000 a) Find the profit-maximizing quantity, price, and profit of the monopolist. b) A regulatory agency tries to force the monopoly to produce the same quantity as a competitive firm. Show what this price and quantity is and why the firm will eventually shut down rather...

A monopolist is facing the following demand schedule P=24-3Q. That is, Q=0 implies P=24, then Q=1...

A monopolist is facing the following demand schedule P=24-3Q. That is, Q=0 implies P=24, then Q=1 implies P=21, and Q=2 implies P=18, and so one. Fixed costs will be neglected in this analysis. The marginal cost is constant and equal to 6 for every unit produced. How do I find the quantity produced and the amount of maximum profits? How do I find the Price and quantity to yield the efficient solution? How do I find what happens if a...

Suppose a monopolist facing a downward sloping inverse demand curve p(q) sets prices and quantity (p...

Suppose a monopolist facing a downward sloping inverse demand curve p(q) sets prices and quantity (p ∗ , q∗ ). Show that the area between the demand curve and the marginal revenue curve equals the consumer surplus.

A monopolist is facing the following demand curve P = 50 − 5Q. The monopolist has...

A monopolist is facing the following demand curve P = 50 − 5Q. The monopolist has the following marginal cost MC = 10. The monopolist knows exactly the willingness to pay of each individual consumer and charge consumers individual prices. Calculate the monopolist’s profit (assuming FC=0). (a) π=40 (b) π=80 (c) π = 160 (d) None of the above.

You are a monopolist facing inverse demand for your product given by p=40-Q and you have...

You are a monopolist facing inverse demand for your product given by p=40-Q and you have constant marginal cost given MC=10 A) Assume you can charge 2 different prices based on quantity purchased. What are the producer’s surplus-maximizing levels of these prices? B) How much more producer’s surplus do you make by doing this instead of charging a single monopoly price for all your output? (The best answer is a quantitative one.)

Question