Question

The demand for beer for heavy drinkers is given by the following demand function: Qd=190-3P. The demand for beer for light drinkers is given by the following demand function Qd=60-4P. Suppose the current price for beer is, on average, $12 per case.
a. What is the price elasticity of demand for heavy drinkers?
b. How does this compare to the price elasticity of demand for light drinkers?
c. Are the differences in the price elasticity between the two groups what you expected? Why or why not?

Suppose you are doing a research project analyzing health care spending of individuals. You decide that health spending is a function of several variables: the age of the person, the person’s income, whether a person smokes, and whether the person is obese. You estimate the relationship between health spending and these variables using a multivariate regression. The dependent variable is the total amount spent on healthcare in a given year. Age and Income are continuous variables, while Smoker and Obese are dummy variables – taking the value of 1 if the person is a smoker or is obese, respectively. From your estimation, you obtain the following results:

VARIABLE (1) Age 50.33*** (3.45) Income -4.56*** (0.45) Smoker 515.35*** (30.42) Obese 624.22*** (33.44)
a. Interpret the coefficient for each variable.
b. Assuming that the average amount spent on healthcare was $12,000 and the average income was $59,000, calculate the income elasticity of health expenditures according to the results above. Interpret the elasticity. What type of good is healthcare?
c. This is a very simplified example and health spending is likely a function of several other variables. Suggest three other factors that should impact health spending that is not included above. What is the expected impact of your added variables?

Answer 1

Ed = (dQ/dP)*(P/Q)

For heavy drinkers, Qd = 190-3P

at P= 12, Q= 190-36= 154

and differentiating Qd w.r.t P, we get dQ/dP = -3

Hence, Ed = -3*(12/154)

b) Similarly proceeding for light drinkers, one can compare the elasticity of demand.

Note - Elasticity is always compared in absolute terms i.e ignoring the negative sign. Hence, -3 would be considered less than say -5, because 3<5, in absolute terms.

c) one would expect the elasticity for heavy drinkers to be lower than that of light drinkers. This is because heavy drinkers are less likely to change their consumption in response to price change as they are habitual of more consumption as compares to light drinkers.

Note - actual result may differ from the above reasoning based on the calculation.

(Which question has to be answered is not mentioned in the question, hence I will try to provide some help with second question too)

a) interpretation of covariates : one unit change in the independent variable will lead to a coefficient time change in the health spending. If cofficient is positive, spending will increase, decrease if negative.

interpretation of dummy : person being smoker increases the health spending by 515.35 units as compared to being non smoker. Obesity dummy can be interpreted in the same fashion.

b) income elasticity : dHExp/dIncome = -4.56

Elasticity = (dHexp/dincome)*(income/Hexp)

= -4.56*(59000/12000)

c) Insurance cover dummy, Past disease index, Extent of availability of healthcare services

If these factors are correlated with the already included variables and as well as the dependent variable, then we might observe ommited variable bias, which will make the estimated coefficients of the given model biased.

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