EWU – ECON 437 – Econometrics – Briand
Homework assignment #5 (20 points total)
1. In the file Econ437hmk5DATA.xls, worksheet "cocaine" you will find 56 observations on variables
related to the sales of cocaine powder in northeastern California over the period 1984-1991.
(http://www.ewu.edu/econ/briand) The data are a subset of those used in the study Caulkins, J.P. and
R. Padman (1993), "Quantity Discounts and Quality Premia for Illicit Drugs," Journal of American
Statistical Association, 88, 748-757. The variables are
price = price per gram in $ for a cocaine sale
quant = number of grams of cocaine in a given sale
qual = quality of the cocaine expressed as percentage purity
trend = a time variable with 1984 = 1 up to 1991 = 8
Consider the regression model:
pricet = 1 + 2quantt + 3qualt + 4trendt + et
a) What sign would you expect for 2 and why? (0.5 point)
What sign would you expect for 3 and why? (0.5 point)
What sign would you expect for 4 and why? (0.5 point) (Do this before the estimation.)
b) Estimate the model with the regression routine in Excel (0.5 point). Report the results (0.5 point).
Interpret coefficient estimate for 2 and discuss whether its sign has turned out the way you
expected. (0.5 point) Interpret coefficient estimate for 3 and discuss whether its sign has turned
out the way you expected. (0.5 point) Interpret coefficient estimate for 4 and discuss whether its
sign has turned out the way you expected. (0.5 point)
c) What proportion of variation in cocaine price is explained by variation in quantity, quality, and
time? (1 point).
d) It is claimed that the greater the number of sales, the higher the risk of getting caught; and, thus,
sellers are willing to accept a lower price if they can make sales in larger quantities. Set up H0 and
H1 that would be appropriate to test this hypothesis. Carry out the hypothesis test. (2 points)
e) Test the hypothesis that the quality of cocaine has no influence on price against the alternative that
a premium is paid for better quality cocaine. (2 points)
2. Consider the following total cost function where yt represents total cost for the t-th firm and xt
represents the quantity of output. Data on a sample of 28 firms in the clothing industry are in the
"clothes" worksheet of the Econ437hmk5DATA.xls file.
y t  1   2 x t   3 x 2t   4 x 3t  e t
a) List the desired properties that a total cost function should have (1 point).
b) Consider the relationship between Y (total cost) and X (output) above and determine if this
functional form would have the flexibility to illustrate the desirable properties you listed in a. (1
point)
c) Estimate the "cubic" total cost function with the least squares routine in Excel (1 point). Report
the results (0.5 point).
d) Derive the marginal cost function (0.5 point) and average cost function (0.5 point) based on the
estimation results.
e) Graph the estimated total, marginal and average cost functions. Use the range from 0 to 10 for x.
(1 point)
EWU – ECON 437 – Econometrics – Briand
f) What hypothesis test can be done based on the F-value given in the computer output (0.5 point)
What is the H0-hypothesis (0.5 point) and what do you conclude (0.5 point)?
g) Test the H0 hypothesis that the total cost function is linear in output quantity. (Hint: What is (are)
the implied restriction(s) on the coefficients of the cubic cost function?) (2 points)
h) Test the hypothesis that the marginal cost function is linear in output quantity. (Hint: What is (are)
the implied restriction(s) on the coefficients of the cubic cost function?) (2 points)