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.

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: 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

Solution:

Part(a)

The scatter plot is given below:

The X-axis is the price and the Y-axis is the Quantity Demanded. We find that as price increases the Quantity Demanded decreases.

Part(b)
We perform the regression analysis and we have the following output:

	Coefficients
Intercept	157.0909
Price	-10.3636

So, the regression equation is,

Q = 157.0909 - 10.3636*P

where, Q = Quantity Demanded and P = Price.

Part(c)

We have the following results from regression analysis:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.997509
R Square	0.995023
Adjusted R Square	0.99447
Standard Error	2.562354
Observations	11

The value of R-squared is = 0.995023.

The value of R-squared is = 0.995023 which very high. We conclude that 99.5023% variability in Quantity Demand is explained by Price. So, the line fit is good for the data set.

Part(d)

The price elasticity is given by,

So, we have,

when P= $ 7.5 we have Q is given by,

Q = 157.0909 - 10.3636*P

Q = 157.0909 - 10.3636*7.5

Q = 79.3639

Also,

So, the elasticity is given by,

So, the price elasticity e = -0.979375 < 1. Hence, the product is inelastic.

So, to increase my revenue, I should set the price below $7.5.