Question 1 (15 points) Do farmers in poor countries respond to economic incentives? A well-known argument...

Question 1 (15 points) Do farmers in poor countries respond to economic incentives? A well-known argument is that farmers might be poor but they are efficient and do respond to incentives in a normal way. An investigator, interested in this question, examines the supply response of Bangladeshi farmers in the cultivation of sugar-cane to the price of sugar-cane as well as to the price of jute. Both sugarcane and jute are crops that compete for the same land (that is, are substitutes in production), which is a relatively scarce resource in the country. The researcher's model is: where AREA- area planted to sugar-cane (thousands of hectares) and PS price of sugar-cane ($ per ton) and Pj-price of jute (S per ton). The prices are in Canadian dollars converted from the local currency (Taka) what would you expect β2 and β3 to be if farmers did not respond to price incentives? what would you expect the signs of these parameters to be if they responded to such incentives in a normal way? (2 points) A. Using annual time series data, the researcher obtained the following regression: B. AREAA 134.425.19PS 6.97PJ se (46.2) (3.59) (2.66) N 34, R-squared 0.62 Sample means: AREA 125.53, PS 4.98, PJ -19.00 1. Use t tests to determine whether Bangladeshi farmers respond to incentives? Set α to 0.05. (3 points) 2. Suppose PS and PJ were to rise simultaneously by $1 per ton and $3 per ton respectively a. write down the expression for the change in area planted ΔΕ(AREA), using the population regression (the first b. Obtain a point estimate of λ using the estimated model. Construct a 95% confidence interval for λ, given that c. Test the hypothesis that these simultaneous price changes have no impact on the area planted to sugarcane equation). This is a linear combination of parameters. Call this linear combination A. (2 points) cov(b2,b3)-4.1201. (4 points) Use the 5 percent significance level. (4 points)