Consider the following specification of empirical demand and supply functions in the fresh market
segment of the carrot industry:
2
s
d
Q
Q a bP ct
d eP f W
= + +
= + +
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?
1 Since carrots are planted and harvested year-round, carrot prices are computed as average prices for each year.
2 Typically farmers make production decisions for the current year using the previous year's crop prices (or a weighted-average of several previous years of crop prices). Since carrots are planted year-round, it is not unreasonable to specify current annual production as a function of current average price of carrots.
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.
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.