The market for carrots is comprised
of two segments: fresh market carrots, which have excellent, uniform color and
a small core, and processing carrots, which are larger than fresh market
carrots but still have good flavor, color, and sweetness. Annual data for the
years 1983–2000 in the fresh market segment of the carrot industry are
presented below. Q is total annual fresh market carrot production (measured in
thousands of hundred weight units, which are 100,000 pound units), P is average
annual real price per hundred weight of fresh market carrots (in constant 1991
dollars),1 and W is a weather index based on temperature and rainfall (W varies
directly with conduciveness of weather for growing carrots). To account for the
increasing popularity of carrots during the sample period, the time variable t
is added to the demand equation to reflect growing popularity of carrots. The
production data do not account for imports and exports of carrots. During the
period of this sample, however, net exports of carrots (exports minus imports)
were quite small in every year
t Q P W
1983 7242 10.03 100.0
1984 8220 6.62 108.3
1985 8886 10.47 109.5
1986 9300 12.59 96.3
1987 9593 11.54 98.3
1988 10758 10.56 101.2
1989 10356 13.88 101.5
1990 11322 10.01 100.6
1991 11741 14.71 111.8
1992 12486 13.15 109.0
1993 13927 13.16 112.31
1994 15072 16.14 115.4
1995 14969 18.06 107.2
1996 14163 19.45 90.5
1997 15589 19.65 92.5
1998 16192 17.29 95.6
1999 15479 19.22 94.8
2000 17.992 19.24 98.7C
Consider the following specification of empirical demand and
supply functions in the fresh market segment of the carrot industry:
Q_d=a+bP+ct
Q_s=d+eP+fW
a. Should the ordinary least-squares (OLS) method or the
two-stage least-squares method (2SLS) method be employed to estimate market
demand for carrots? Explain briefly.
b. Which variables are endogenous variables in the system?
Which variables are exogenous? For the model specified above, is the demand for
fresh market carrots identified? Explain why or why not?
c. Using statistical software, estimate the parameters of
the empirical demand function specified in part a. Write the estimated industry
demand equation for carrots.
d. Are the estimated slope parameters of demand
statistically significant at the 15 percent level of significance? Are the
algebraic signs of the parameter estimates and reasonable? Explain. ˆbˆc
e. Would you expect the demand for carrots to be elastic or
inelastic when measured at the average price over the period of the sample?
(Hint: Consider the discussion in Chapter 3 concerning the factors that
influence demand elasticity.)
f. Compute the price elasticity of demand for carrots
measured at the sample mean values of price (P), quantity (Q), and time (t). Is
the demand for fresh market carrots elastic, inelastic, or unitary elastic when
measured at the sample mean values of P, Q, and t?
g. By approximately what percentage amount would the price
of carrots have to fall in order for quantity demanded to increase by 10
percent?
h. Explain, in quantitative terms, the meaning of the
estimate of the slope parameter on t.T