Grossman Model of Healthcare Demand and Regression Equations:

Part 1: Suppose you manage a vet office and are considering offering a sale on dental cleanings (10% off) for December. Use the Grossman model diagram to predict the effect of this program on the quantity of dental cleanings demanded.Provide a textual explanation to accompany the diagram submitted.

Part 2: Sticking with the theme, I found a study that examines factors that affect the demand for "canine wellness visits". Using data from the 2012 Pet Demographic Survey, the authors estimated the following demand equation

ln(V) = -0.65 - 1.04ln(P) + 0.31ln(Y) + 0.362(ln(Y)NI) + 0.02(YRS)

t= -8.82 t= -21.7 t= 11.7 t= 6.97 t=1.786

where V is the number of preventive visits made in a year, P is the price per visit (average $95), Y is income (average $50,000), NI is an indicator that the respondent did not think preventive visits were important (=1 means not important, =0 means important; average 0.4), and YRS is the age of the dog (average 6). The analysis was based on data from 3300 completed questionnaires.

a. Evaluate the equation against the appropriate model covered in class. Explain the role of each variable in the equation in terms of that model.

b. Given the average values above, estimate the average number of preventative visits made per dog. No R² was reported, but I doubt there is much precision in this estimate. What other variables might you want to have included in this equation (consider both likely importance and feasibility of measurement) to improve its predictive power?

c. Interpret the coefficient on the YRS variable. How confident are you that the age of the dog affects the number of preventive visits? Based on my own experience, I believe age is a stronger predictor of wellness visits than this equation would suggest. Provide a possible explanation for this discrepancy in how preventive visits varies with age.

d. Calculate the elasticity with respect to price, using the average values of the other variables. What managerial implications can you infer from the value obtained? Note: given the variables are logged, you cannot assume that the coefficient on price reflects the change in V for a unit increase in price, so you cannot use the formula from class. Instead, you can calculate elasticity using the formula

;

it works best to vary price by a small amount, e.g., a dollar up or down).

e. Calculate the income elasticity, using the average values for the other variables. What does this suggest about the nature of demand for wellness visits? Do you think this result is reasonable? Why or why not? Suppose you were to undertake an ad campaign that reduced the proportion of dog owners who thought wellness visits were unimportant. What effect would it have on income elasticity? Explain why this pattern might be observed.