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. (Find the data that matches your last name initial at the bottom of this file).

a. 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)

b. 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)

c. What is the R-squared for the previous regression? (2pt) Given this R-squared, would you say the line is a good fit for the data points? (2pt)

d. 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? (2pt) To increase your revenue, should you set the price above or below $7.5? (2pt)

Data:

Price 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14

Quantity Demanded 118, 107, 90, 85, 74, 65, 51,41 36, 24, 11

Answer 1

a. The scatter plot is shown as follows:

The above graph shows the inverse demand where Price is shown along Y-axis and Quantity Demanded is shown along X-axis

The Demand graph is shown as follows:

b.

The regression model is given by:

Thus, the regression model is: Q = 126 - 10.36363636 P

c. The R-Square is given as 0.995023352 as shown.

Yes, the line is a good fit for the data as the regression line explains 99.50% variation in quantity demanded with the help of the model that uses Price as the only explanatory variable.

d.

When P= $7.5, Q= 126-10.36363636*7.5 = 48.27272727

The slope of regression line is -10.36363636

Thus, price elasticity is: (-10.36363636)*(7.5/48.27272727) = -1.61

Since, the absolute value of price elasticity is 1.61 which is greater than 1 , hence, the price is elastic

To increase revenue, the price should be set below $7.5 as increase in price would cause total revenue to decrease when there is elastic demand.