a. Agricultural household models fenables policymakers to examine the consequences of an agricultural policy in three dimensions. Identify and briefly explain these dimensions. (3 marks) b. Below is the basic model of an agricultural household: U = x 5 x 5 x?; PmXme = Pace - X) - w(L – F); Xi+F = T; Q = AL0.5 where P = price of market-purchased commodity; Pa = price of agricultural staple; w= wage rate; F= family labour input; L= total labour demand; XA = agricultural staple; XM= market-purchased good; X = hours of leisure; T = total stock of household time; A = household's fixed quantity of land; Q = total output of agricultural staple Assuming the agricultural household is a price-taker in all markets, consumes 10 hours of leisure out of a total time stock of 24 hours, pays a wage rate of Gh c 2, receives a price of Gh c 2 for its agricultural staple, pays a price of Gh c 3 for market-purchased commodity and employs 10 units of land for the cultivation of its agricultural staple. Answer the following questions: i. ü. ii. Show that the household's production decision does not depend on it consumption and labour supply decisions (4 marks) Does this household hire labour? If so, how much? (1 mark) What is the total output of the agricultural staple produced by the household? martu) How mucı farm profit does this household make? (2 marks) i What are the levels of X, and Xm that maximizes the household's utility? (7 marks) What is quantity of the household's marketed surplus of X ? (1 marks) iv. V. vi.
