In Section 4.6, we considered the demand for edible chicken, which the U.S. Department of Agriculture calls "broilers." The data for this exercise are in the file newbroiler.

a. Using the 52 annual observations, 1950-2001, estimate the reciprocal model \(Q=\alpha_{1}+\) \(\alpha_{2}(1 / P)+e\). Plot the fitted value of \(Q=\) per capita consumption of chicken, in pounds, versus \(P=\) real price of chicken. How well does the estimated relation fit the data?

b. Using the estimated relation in part (a), compute the elasticity of per capita consumption with respect to real price when the real price is its median, \(\$ 1.31\), and quantity is taken to be the corresponding value on the fitted curve.

Compare this estimated elasticity to the estimate found in Section 4.6 where the \(\log\)-log functional form was used.

c. Estimate the poultry consumption using the linear-log functional form \(Q=\gamma_{1}+\gamma_{2} \ln (P)+e\). Plot the fitted values of \(Q=\) per capita consumption of chicken, in pounds, versus \(P=\) real price of chicken. How well does the estimated relation fit the data?

d. Using the estimated relation in part (c), compute the elasticity of per capita consumption with respect to real price when the real price is its median, \$1.31. Compare this estimated elasticity to the estimate from the log-log model and from the reciprocal model in part (b).

e. Estimate the poultry consumption using a log-linear model \(\ln (Q)=\phi_{1}+\phi_{2} P+e\). Plot the fitted values of \(Q=\) per capita consumption of chicken, in pounds, versus \(P=\) real price of chicken. How well does the estimated relation fit the data?

f. Using the estimated relation in part (e), compute the elasticity of per capita consumption with respect to real price when the real price is its median, \$1.31. Compare this estimated elasticity to the estimate from the previous models.

g. Evaluate the suitability of the alternative models for fitting the poultry consumption data, including the log-log model. Which of them would you select as best, and why?