Preview

Problem Set 6 Answers

Satisfactory Essays
Open Document
Open Document
475 Words
Grammar
Grammar
Plagiarism
Plagiarism
Writing
Writing
Score
Score
Problem Set 6 Answers
Microeconomics (Fall 2014)
Simon Bowmaker
Problem Set 6
Submit at lecture (Monday, November 10)

Write your answers on separate sheets of paper. Please include: your name your recitation teacher’s name day and time of the recitation
NB: if your recitation takes place on Monday morning, you must submit your assignment to your teacher at the beginning of the recitation. 1. Assume a monopolist faces the following market demand: Q = 100 - 2P. The monopolist’s total cost function is TC = 5+8Q2. What is the monopolist’s profit-maximizing level of output and price?
Answer

Step 1. Derive the MR and MC functions.

Since Q = 100 - 2P, P = 50 – (Q/2)
TR=P*Q=(50-1/2Q)Q=50Q-1/2Q2
MR=dTR/dQ=50-Q

MC=dTC/dQ=16Q

Step 2. Set MR=MC and solve for P*, Q*
MR=MC
50-Q=16Q
Q*=2.94 or 3 (rounded)
P*=50-1/2Q*=50-1/2*3=48.5

2. Assume a monopolist faces a market demand curve P = 130 – 2Q, and has the short-run total cost function TC = 350 + 10Q.

(a) What is the profit-maximizing level of output and price? What are profits?

(b) Graph the marginal revenue, marginal cost, and demand curves.

(a) Step 1. Derive the MR and MC functions.
P  130 – 2Q
TR=P*Q=(130 – 2Q)Q=130Q – 2Q2
MR=dTR/dQ=130 – 4Q
MC= dTC/dQ=10
Step 2. Set MR=MC and solve for P*, Q*, and π.
MR=MC
130 – 4Q=10
4Q=120
Q*=30
P*=130 – 2Q=130 – 2*30=130-60=70
Π=TR-TC=P*Q-TC=70*30-(350  10*30)=2100-650=1450

(b) Deadweight loss is equal to area abc.

3. If a monopoly firm sells a product with price $100, and marginal cost of $20, what is the Lerner Index? Interpret the Lerner Index here. What is the demand elasticity?
The price/marginal cost ratio will be 100/20  5. Its Lerner Index is (100-20)/100  80/100=0.8. As the number is close to 1, this indicates significant market power. For every dollar given to the firm by the consumer, 80 cents is mark-up. The firm believes it faces a demand elasticity of –1.25 (the Lerner Index is the inverse of the price elasticity of demand).

4. When the iPod was

You May Also Find These Documents Helpful

  • Satisfactory Essays

    week 2

    • 594 Words
    • 3 Pages

    • Relating to the simulation, explain how the price elasticity of demand affects a consumer’s purchasing and the firm’s pricing strategy.…

    • 594 Words
    • 3 Pages
    Satisfactory Essays
  • Good Essays

    BUS 640 Week 4 Problems

    • 718 Words
    • 3 Pages

    A small business which produces plastic vacuum-suction covers for round household dishes has a monopoly that is protected by a utility patent. The market demand curve for this product is estimated to be: – 25P where Q is the number of plate covers per year and P is in dollars. Cost estimation processes have determined that the firm’s cost function is represented by + 2500Q -0.25*Q2.…

    • 718 Words
    • 3 Pages
    Good Essays
  • Satisfactory Essays

    Problem Set 3

    • 294 Words
    • 2 Pages

    Assume the competitive market shown below faces a short run price of $10. Using the graph below, identify the following:…

    • 294 Words
    • 2 Pages
    Satisfactory Essays
  • Satisfactory Essays

    Problem Set 3

    • 706 Words
    • 4 Pages

    2. Assume the competitive market shown below faces a short run price of $10. Using the graph below, identify the following:…

    • 706 Words
    • 4 Pages
    Satisfactory Essays
  • Powerful Essays

    7) Refer to the graph on the left for a firm in pure competition. Line A represents:…

    • 3065 Words
    • 14 Pages
    Powerful Essays
  • Satisfactory Essays

    Problem Set 3 Econ 213

    • 452 Words
    • 3 Pages

    2. Assume the competitive market shown below faces a short run price of $10. Using the graph below, identify the following:…

    • 452 Words
    • 3 Pages
    Satisfactory Essays
  • Good Essays

    Economics of the environment

    • 8415 Words
    • 29 Pages

    1.Research on the admission fees to national parks has found that the price elasticity of demand for annual visits to Glacier National Park is 0.2. The National Park Service is now considering a 10-percent increase in the admission fee.…

    • 8415 Words
    • 29 Pages
    Good Essays
  • Satisfactory Essays

    problem set 3

    • 386 Words
    • 2 Pages

    2. Assume the competitive market shown below faces a short run price of $10. Using the graph below, identify the following:…

    • 386 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    Mt 445 Unit 4 Assignment

    • 407 Words
    • 2 Pages

    3. How does the demand curve faced by a monopoly differ from the demand curve faced by a perfectly competitive firm? Explain.…

    • 407 Words
    • 2 Pages
    Good Essays
  • Good Essays

    Economic Eqilibriums

    • 1183 Words
    • 5 Pages

    2.Suppose P = 20 - 2Q is the market demand function for a local monopoly. The marginal cost is 2Q. If fixed costs are zero and the firm engages in two-part pricing, the most profits the firm will earn is:…

    • 1183 Words
    • 5 Pages
    Good Essays
  • Satisfactory Essays

    Textile Industry

    • 584 Words
    • 3 Pages

    Now, finding the elasticity of demand of raglan with respect to the above mentioned factors, we have:…

    • 584 Words
    • 3 Pages
    Satisfactory Essays
  • Powerful Essays

    This report was authorized by the request of ECO5005 Economic of the Business Environment course leader, Heng Kiat Sing. This is to enable student to have a clear understanding on Externality, and Price Elastic, thus, enable to analyze price elasticity of demand of problem.…

    • 3793 Words
    • 16 Pages
    Powerful Essays
  • Satisfactory Essays

    The …rm “Mono” is a …rm operating on a market with the following inverse demand function: P (Q) = a bQ: The total cost function of Mono is T C (q) = 10 + cq where q is Mono’ output. s Assume that a > c > 0 and b > 0: 1. Compute Mono’ pro…t. (5 points; if you do not like letters, you can replace s them by the following numbers, but then you can score 4 points maximum only: a = 140; b = 2 and c = 20); 2. Suppose another …rm, “Duo” with the same cost function, enters this market , and competes in quantites with Mono. Compute Mono’ pro…t in this Cournot s competition game (5 points; 4 points if you replace the letters with the above numbers)…

    • 264 Words
    • 2 Pages
    Satisfactory Essays
  • Good Essays

    Problem Set 8 Solutions

    • 1329 Words
    • 6 Pages

    Problem 1. Exchange Rates and International Transmission a. Suppose that the US engages in a monetary expansion. Since exchange rate is pegged to the US dollar, country X’s monetary authorities are forced to expand their money supply as well (recall that i = i* under FixER). Interest rates fall in country X, output expands, and of course the exchange rate remains unchanged. On the AA-DD diagram, both the AA and the DD schedules shift to the right. The shift in DD can be explained by the increase in US output which causes an increase in net exports of country X. In addition, smaller interest rates are known to increase investment, which can also explain the shift in DD. The case of monetary contraction is similar. Thus with fixed exchange rates, monetary shocks transmit positively from the US to country X.…

    • 1329 Words
    • 6 Pages
    Good Essays
  • Satisfactory Essays

    Problem Set Week 1 6

    • 333 Words
    • 2 Pages

    Use the three indicators of question (a) to describe the pattern of globalization over the last century.…

    • 333 Words
    • 2 Pages
    Satisfactory Essays