Integrated Sessions - Mod II

Session 1: Nov 2, 2011

Assignment
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Use the model for beef demand estimated in DMD 4 to answer the following questions:

1. The data set contains economic variables that explain to varying degrees the quantity of beef demanded.  List three non-economic variables that you believe influence the quantity demanded for beef.
Ans: Consumer preference for beef as food, health benefits of eating beef, Madcow disease, 


2. Use the model estimated to calculate the point elasticity of demand, income elasticity of demand and cross price elasticity. Note: Use the average values for prices, income and consumption in the point elasticity formulae. Describe the market for beef in terms of these calculated elasticities.  Is your computed price elasticity consistent with our discussion of the optimal pricing rule?
Ans: 
Using the model: BeefConsump=97.80–0.15*RealBeefPrice+0.36*RealChickenPrice+0.0003*RealDPI

(BeefConsum = Q or Qb ; RealBeefPrice = Pb; RealChickenPrice = Pc and RealDPI = I)


so, Q=97.80–0.15*Pb+0.36*Pc+0.0003*I
Pb (avg) = 185.36; Pc(avg) = 85; I(avg)= 11061
Q = 97.8 - 0.15*185.36 + 0.36*85 + 0.0003*11061 = 103.9 ~ 104


Point elasticity of demand, Q = dQ/dPb * Pb/Q
dQ/dPb =  -0.15 
PED = -0.15 * 185.36/104 = -0.26735 (relatively inelastic)


Cross price elasticity, % change in Q / % change in Pc
elasticity (b,c) = dQ/dPc * Pc/Q
dQ/dPc = 0.36 
elasticity (b,c) = 0.36* 85/104 = 0.294231 -> the goods are substitutes


Income elasticity of demand, %change in Q / %change in I
elasticity(b,I) = dQ/dI * I/Q
elasticity(b,I) = 0.0003 * 11061/104 = 0.031907 => normal good 

3. Using the average chicken price and average real disposable income, calculate the revenue maximizing price in the market for beef using the model estimated.

Ans: With Pc=85; I=11061;

Q = (97.8 + 0.36*85 + 0.0003*11061) - 0.15Pb

Q = 131.7 - 0.15Pb

P = 878.12 - 6.67Q

TR = P*Q

TR = 878.12 - 6.67Q^2

TR(max) is attained when MR=0 => dTR/dQ = 0

dTR/dQ = 878.12 - 2*6.67Q
(solving for =0)
Q = 65.82
P = 439

4. Compute the level of per capita beef consumption at the price calculated in Question 3.

1. What is the range of sales volume at that price that can be expected at the 95% prediction interval?
2. What are some strategic implications of this information for the beef industry?
3. What are some of operating implications of the 95% prediction interval for large food supermarkets? For example, how might the ordering activities or inventory forecasts be affected?
4. Are there any operating implications for the sales of different cuts of beef (e.g., chuck, sirloin and tenderloin)?

Ans: Q = 65.82
a) For the range of sales in the 95% prediction interval I can say that the beef consumption will be between 54 - 77
which is 65.82 +- 2(5.85)  {coming from the regression model}
confidence interval 66 +- (5.85/sqrt(36))
b)

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Class Notes:

Discussion on the regression model that was discussed in the DMD class
R-square of

Robert Ng comes in :P
Marketing perspectives about demand forecasting

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Case: Cambridge Software company