Question

After coming up with an innovative idea for a new product, you paid $4000 to an industrial designer to draw the blueprints and found a factory in China that agreed to produce the product for you for $3 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. (use the following data).

Price    Quantity Demanded

4          221

5          210

6          185

7          162

8          144

9          122

10        102

11        81

12        61

13        46

14        25

1. On a graph (scatterplot), display the price-quantity pairs. Be careful what variable should be on the vertical axis and which one on the horizontal axis. (3pts) (Use Excel.)
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)). (2pts)
   Write the demand equation in the form of
   (3pts)
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? (2pt)
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? (3pts)

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? (2pt)

5. Given the information in the description part, how much are the total fixed cost (2pts) and the marginal cost (2pts) of production?
6. 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 (2pts) and how much will your revenue (2pts) and profits (2pts) be that year?
7. 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) (2pts)
8. 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 and see where the profit maximizing quantity (3pts) and price (3pts) are in this scenario? (The numbers don’t need to be precise. Just use the graph and find the approximate price and quantity. Don’t need to actually include the grap)
1. 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? (2pts)

Answer 1

a) The required graph is below: Quantity Demanded 16 14 10 S0 100 150 200 250 Price is on the y-axis and quantity on x-axis b) The trend line found using regression in Excel is drawn below: Price Line Fit Plot 250 200 E 150 O 100 E 50 Quantity Demanded Predicted Quantity Demanded 10 15 Price

c) The obtained regression results are: earession Statistics MultipleR R Square Adjusted R Square Standard Error Observations 0.999130902 0.998262559 0.998069509 2.932920081 ANOVA MS Significance F Regression Residual Total 1 44481.30909 44481.31 5171.031 9.83296E-14 9 77.418181828.60202 10 44558.72727 Cofficients Standard Error tStat P-value Lower 95% Intercept Price 304.5272727 2.667623795 114.1568 1.54E-15 298.4926885 20.10909091 0.279642957719099 9.83E-14 20.74168723 Regression equation: Q- 304.527-20.109P c) R-squared 0.9982 This means the variable P explains 99.82% variation in the value of Q This means the model is a very good fit. d) Q- 304.527-20.11P Elasticity (do/dPP/)20.11P/Q When P 7.5, Q 153.7 Thus, elasticity--20.11(7.5/153.7)- 0.98 This means the product is inelastic In order to increase revenue, price must be increased above $7.35