What does the law of diminishing marginal returns state?
a) When all inputs to production are increased in equal proportions, output will
eventually decrease.
b) When one input is increased, with all other inputs unchanged, the marginal product
of the input will eventually decline.
c) When one input is held constant, and all other inputs are increased, output will
eventually decrease.
d) When one input is increased, and all other inputs are held constant, output will
increase at an increasing rate.
e) When all inputs to production are increased in equal proportions, the addition to
output will increase at an increasing rate.
You have taken over your parents’ small dry-cleaning shop, and are interested in
forecasting demand for your services. Your parents never quite got around to trying to
measure demand, but they have kept extensive price and sales records. Using this data,
you employ multiple regression techniques and estimate the following logarithmic
equation:
Log(Q) = .95 − .6Log(P) + .9Log(Y) + .25Log(Pc),
where Q is the number of shirts laundered per week, P is the price in dollars of a
laundered shirt, Y is the per capita income in the local area, and Pc is the price charged
by another dry cleaner two blocks away. The number of observations is 39 (i.e., nine
months of weekly data). The equation’s R2is 0.85, the standard error of the estimate is
200, and the standard errors for the rightside variables are .45, .15, .39, and .18
respectively.
(a) Interpret the demand equation and discuss the associated regression statistics.
(b) If you were to raise the price per shirt, what would happen to total revenue?
(c) Evaluate the impact of the other dry cleaner’s price on your sales. (At the 95%
confidence level, the relevant t-statistic is about 2.04 for 35 degrees of freedom).
(d) Were your parents maximizing profit? If not, suggest an appropriate course of action
to
increase profitability.