Question

Ann, owner of Terrific Burgers in Weatherford, Texas decides to estimate the empirical demand function for her firm’s burgers. She collects data on the last 24 months of Burger sales from her own firm records. She knows the price she charged for her Burgers during that time period, and she also has kept a record of the prices charged by one of her close competitor, Stormy Burgers.

Ann is able to obtain average household income figures from the Small Business Development Center in Weatherford. The only other competitor in the neighborhood is the local branch of Burger King selling their Whoppers. Ann is able to find the price of their Whoppers for the last 24 months from advertisements in old newspapers. She adjusts her price and income data for the effects of inflation by deflating the dollar figures, using a deflator she obtained from the Survey of Current Business. To measure the number of buyers in the market area (N), Ann collected data on the number of residents in Weatherford. As it turned out, the number of residents had not changed during the last 24 months, so Ann dropped N from her specification of demand equation.

Since the price of burgers at Terrific Burgers in Weatherford set by Ann- she possesses a degree of market power- she can estimate the empirical demand equation using linear regression.

Ann first estimates the following linear specification of demand using the 24 monthly observations she collected:

Q= a + b (P) +c (M) + d (P_SB) + e P(_W)

Where:

Q= sales price of a Burger at Terrific Burgers

P= price of a burger at Terrific Burgers

M= average annual household income in Weatherford, TX

P_SB= price of a burger at Stormy Burgers

P_W= price of a Whopper at Burger King

The following computer printout shows the results of her least-squares regression:

Dependent Variable	Q	R-Square	F-Ratio	P-Value On F
Observations	24	0.9555	101.90	0.0001

Variable	Parameter Estimate	Standard Error	T-Ratio	P-Value
Intercept	183.80	506.298	2.34	0.0305
P	-21.42	13.4863	-15.83	0.0001
M	4.09109	0.0241	7.34	0.0001
PSB	10.30	38.7478	2.61	0.0171
PW	7.84	27.0997	2.65	0.0158

Ann decides to calculate estimated demand elasticities at values of P, M, P_SB, and P_W that she feels “typify” the Burgers market in Weatherford for the past 24 months.

These values are:

P= $7.50, M= 25 (in thousands),  P_SB= $8.25, and P_W = $4.50       

Using this information, answer the following questions:

1. Estimate the total number of sales using the equation specified above with the empirical results
2. Calculate own-price elasticity, income elasticity and cross-price elasticities with Stormy Burgers and BK Whopper.   Besides statistical skills, Ann also comprehends economic s and is relying on you to make interpretations of these results.
3. Using economic rationale and terminology, make recommendation to Ann :

• If she should raise or lower the price she is selling? Explain why or why not
• The impact of the economy heading into a recession on Ann’s sales. Explain.
• Who is her main competitor – Stormy Burgers or Burger King? Hint: Use the magnitude of the cross-price elasticities

Answer 1

Estimated regression equation: Q = 183.8 - 21.42 x P + 4.09109 x M + 10.3 x PSB + 7.84 x PW

(1)

Q = 183.8 - 21.42 x 7.5 + 4.09109 x 25 + 10.3 x 8.25 + 7.84 x 4.5 = 183.8 - 160.65 + 102.27725 + 84.975 + 35.28

= 245.68225

(2)

Own-price elasticity = (Q/P) x (P/Q) = - 21.42 x (7.5 / 245.68225) = - 0.75

Cross-price elasticity_{Stormy_Burgers} = (Q/PSB) x (PSB/Q) = 10.3 x (8.25 / 245.68225) = 0.35

Cross-price elasticity_{BK_Whopper} = (Q/PW) x (PW/Q) = 7.84 x (4.5 / 245.68225) = 0.14

(3)

Since absolute value of own-price elasticity is less than 1, demand is inelastic. With inelastic demand, if she lowers price, revenue will increase.

(4)

Since coefficient of income > 0, the good is a normal good. Therefore, a fall in consumer income caused by recession will decrease demand. Specifically, a $1,000 decrease in income will decrease demand by 4.09109 units.

(5)

Since Cross-price elasticity_{Stormy_Burgers} > Cross-price elasticity_{BK_Whopper}, Stormy Burgers is the main competitor.