Managerial Economics

Please read the questions carefully.

Description

After coming up with an innovative idea for a new product, you paid $2000 to an industrial designer to draw the blueprints and found a factory in China that agreed to produce the product for you for $3.5 per unit (the price includes the shipping cost from China to you).

Since this is a totally new and unique product, you have no idea how the demand for it would be. Therefore, before you start pricing the product and ordering large amounts from the Chinese factory, you decide to run an experiment (or a pilot study): you talk to Target and they allow you to sell your product at 11 different Target stores for 11 different prices (a different price at each store). These stores are located in areas whose residents have similar average income, so you can be certain that price (and not income) is the only factor varying among these stores.

After 2 weeks, Target sends you the sale numbers for your product. (Find the data at the bottom of this file).

  1. On a graph (scatterplot), display the price-quantity pairs. (Use Excel.) (1pt)  Be careful what variable should be on the vertical axis and which one on the horizontal axis. (1pt)
  2. Using regression, find the demand line that is the best fit for the observed data points. (in other words, add a trend line to the graph you had in part (a)). (1pt)

    Write the demand function in the form of
    Q = a – bP          (1pt)

  3. What is the R-squared for the previous regression? (1pt)
    Given this R-squared, would you say the line is a good fit for the data points? (1pt)
  4. Given the demand equation found in part (b), what is the price elasticity of demand for your product at the price of $7.5? (1pt)

Does that mean your product is elastic or inelastic at that price? (1pt)
To increase your revenue, should you set the price above or below $7.5? (1pt)

  1. Given the information in the description part, how much are the total fixed cost (1pt) and the marginal cost (1pt) of production?
  2. Given the demand equation found in part (b), if you eventually decide to sell your product at $8 per unit for the first year, how many units do you expect to be sold (1pt) and how much will your revenue (1pt) and profits (1pt) be that year?
  3. Assume that your product is so unique that it doesn’t have any close substitutes. Which one best describes the market structure for your good? (competitive, monopoly, competitive fringe, oligopoly, monopolistic competition) (1pt)
  4. Let’s assume the market is a monopoly. Go back to part (b) where you used regression to find the best fit demand (or trend line). Add Marginal Revenue (MR) and Marginal Cost (MC) to the graph (1pt) and see what the profit maximizing quantity (1pt) and price (1pt) are in this scenario? (The numbers don’t need to be precise. Just use the graph and find the approximate price and quantity.)
  5. You forgot to file a patent, so after 2 years, many copycats make products that are somewhat (but not exactly) similar to yours. What kind of market structure would this be? (1pt)
  6. Now imagine another scenario in which your company has only 1 competitor. You and your competitor are both considering running TV ads to promote your own product. You estimate that you and your competitor profits will be as follows if you do or do not run the ads:
    Competitor
    Advertise Do not advertise
Your firm Advertise 1300, 1200 2700, 700
Do not advertise 900, 2000 2400, 1800

What is the Nash equilibrium of this game? (1pt)
If you and your competitor could talk on the phone (imagine it was legal to do so) to coordinate whether to advertise or not, what would the outcome be? (1pt)

 

Total Points: 21

 

 

 

Data:

Price    Quantity Demanded

4          406

5          379

6          355

7          322

8          306

9          283

10        257

11        236

12        205

13        176

14        149