1. Consider a monopolist that faces a linear inverse demand of:
P(q) = 304 ???? 4q
The rm has the cost function:
C(q) = 100 + 4q + 2q2
What are the monopolistic market price (pM), quantity(qM), and pro ts (M)? Show deriva-
tions (neatly!) below. (30 points)
2. Imagine a textbook company has a monopoly over a textbook in both the U.S. and India.
If they can price discriminate by charging a separate price in each of the two markets (each
country prohibits importation from the other market), nd the optimal quantities and prices
they would charge in those markets.
The rm’s cost function is C(q1+q2) = C(q) = 2q2+30. In the U.S. (which we’ll call Market
1), the inverse demand function is p(q1) = 1296 ???? 30q1 and in India it is p(q2) = 400 ???? 38q2
(a) What quantity does the rm sell in each market? What is the total quantity sold? (10
q(total for rm) =
(b) What price does the monopolist charge in each market? (8 points)
(c) What is the total pro t for the monopolist? (2 points)
(d) In equilibrium, what is the monopolist’s elasticity of demand in each of the two markets?
(e) Circle the correct choice:
Comparing your answers to (b) and (d), this rm charges a higher price in the market
in which its demand curve is more (elastic / inelastic). (4 points)
3. Consider a Cournot duopoly with both rms producing a homogeneous good and facing linear
demand of the form: P(Q) = 124 ???? 30Q, where Q = q1 + q2. Assume both rms have the
same costs: C(q) = 4q.
(a) For each rm, derive the best response function below. Show all work. (8 points)
(b) Graph the best response functions for both rms on the axes below. As in class, q1
should be on the y ???? axis and q2 should be on the x ???? axis. (4 points)
(c) Solve for the Nash Equilibrium output of each rm. (6 points)
(d) Solve for the equilibrium market price. (4 points)
(e) Solve for the equilibrium pro ts of each rm. (4 points)
4. Stackelberg Duopoly with Heterogeneous Costs.
Now consider a Stackelberg duopoly with both rms producing a homogeneous good and
facing a linear demand of the form P(Q) = 138 ???? 6Q where Q = q1 + q2. Assume the rms
have di erent costs. Firm 1 has costs C1(q) = 3q+3 and Firm 2 has costs of C2(q) = 6q+12.
Firm 1 will be the rst mover in this case.
(a) What is the Equilibrium output of each rm under Stackelberg Competition? (10 points)
(b) What are the equilibrium pro ts of each rm? (4 points)
At 111papers.com, we value all our customers, and for that, always strive to ensure that we deliver the best top-quality content that we can. All the processes, from writing, formatting, editing, and submission is 100% original and detail-oriented. With us, you are, therefore, always guaranteed quality work by certified and experienced writing professionals. We take pride in the university homework help services that we provide our customers.
As the best homework help service in the world, 111 Papers ensures that all customers are completely satisfied with the finished product before disbursing payment. You are not obligated to pay for the final product if you aren’t 100% satisfied with the paper. We also provide a money-back guarantee if you don’t feel that your paper was written to your satisfaction. This guarantee is totally transparent and follows all the terms and conditions set by the company.Read more
All products that we deliver are guaranteed to be 100% original. We check for unoriginality on all orders delivered by our writers using the most advanced anti-plagiarism programs in the market. We, therefore, guarantee that all products that we submit to you are 100% original. We have a zero-tolerance policy for copied content. Thanks to our strict no plagiarized work rule, you can submit your homework to your professor without worrying.Read more
TThis is one of the most cherished courtesy services that we provide to help ensure that our customers are completely satisfied with our finished products. Delivering the best final product to our customers takes multiple inputs. 111papers.com prides itself on delivering the best university homework help services in the writing industry. And, in part, our free revision policy is how we do it. What’s more, all our revisions are 100% free without any strings attached.Read more
Client privacy is important to use. We know and understand just how important customers value their privacy and always want to safeguard their personal information. Thus, all the information that you share with us will always remain in safe custody. We will never disclose your personal information to any third party or sell your details to anyone. 111 Papers uses the most sophisticated, top-of-the-line security programs to ensure that our customers’ information is safe and secured.Read more
Placing your order with us means that you agree with the homework help service we provide. We, in turn, will endear to ensure that we do everything we can to deliver the most comprehensive finished product as per your requirements. We will also count on your cooperation to help us deliver on this mandate. Yes, we also need you to ensure that you have the highest-quality paper.Read more