The State of West Bengal is one of India's largest rice producers, accounting for about 20% of rice production. Rice occupies three-quarters of the entire agricultural area in the lower Ganga Plains. The Rice.xlsx data file includes data from 352 observations of 44 paddy farmers in West Bengal, India, between 2000 and 2007. The data file contains the following variables. Ar: hectares planted (land) Fe: kilograms of fertilizer Lb: person-days of hired and family labour Pd: tonnes of freshly threshed rice Treat the data set as one sample with N= 352 and answer the following questions. (a) Estimate the following production function and report the results, interpret the estimates, and comment on the statistical significance of the estimates. In (Pd) = 1 + 2 ln(Ar) + 3 ln(Lb) + 4 ln(Fe) + e Page 3 of 3 (b) Using 5% level of significance, test the hypothesis that the elasticity of substitution with respect to land is equal to the elasticity of production with respect to labour. (c) Using 10% level of significance, test the hypothesis that the production function exhibits constant returns to scale. That is, H0: 2 + 3 + 4 =1. (d) Using a 5% level of significance, jointly test the two hypotheses in parts (b) and (c). (e) Re-estimate the model in part (a) with (i) Fe omitted, (ii) Lb omitted, and (iii) Ar omitted. In each case discuss the effect of omitting a variable on the estimates of the remaining two elasticities. (f) In each case given in part (e), check to see if the RESET test has picked up the