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Homework answers / question archive / An economist estimated market demand for bottled water purchased in supermarkets in Chicago as: QW=400−200PW+70PT+0
An economist estimated market demand for bottled water purchased in supermarkets in Chicago as:
QW=400−200PW+70PT+0.01IQW=400−200PW+70PT+0.01I,
Where QWQW = gallons of bottled water purchased per week, PWPW = price of bottled water purchased in supermarkets ($/gallon), PTPT = price of bottled iced tea purchased in supermarkets ($/gallon), and I = income per year.
For simplicity, assume all bottles are the same size. Average values of the right hand variables in this equation in Chicago at the time were PWPW = $1.50, PTPT = $2.50, and I = $30,000.
a. Using this regression, calculate the cross-price elasticity of demand for bottled water with respect to iced tea (at the average values given above).
b. Given the above regression equation, could you estimate the cross-elasticity of demand for bottled iced tea with respect to the price of bottled water? Why or why not?
c. Suggest two variables you would add to this demand estimation model if you were re-estimating it. What sign would you expect on these two new variables (positive or negative), and why?
A) 0.304
The cross-price elasticity of demand here is the derivative of quantity demanded for bottled water over the price of iced tea multiplied by the average price of iced tea over the average quantity demanded of bottled water.
The average quantity demanded of bottled water is
QW=400−200×1.5+70×2.5+0.01×30,000=575QW=400−200×1.5+70×2.5+0.01×30,000=575.
Thus the cross price elasticity is ΔQWΔPT×PTQW=70×2.5575=0.304ΔQWΔPT×PTQW=70×2.5575=0.304.
B) No
To calculate cross-price elasticity of demand for bottled iced tea with respect to the price of bottled water we need a function of quantity demanded of iced tea with respect to the price of bottled water which we don't have.
C)
I would include both temperature and an indicator variable for the tourist season. Both should have positive coefficients as higher temperatures increased the utility of bottled water and tourists increase demand for bottled water.
