Question

7. An economy produces two goods, food (F) and manufacturing (M). Food is produced by the production function F = (Lp)? (T), where Ly is the labour employed, T is the amount of land used and F is the amount of food produced. Manufacturing is produced by the production function M = (Lx)2(K), where Ly is the labour employed, K is the amount of capital used and M is the amount of manufacturing production. Labour is perfectly mobile between the sectors (i.e. food and manufacturing production) and the total amount of labour in this economy is denoted by L. All the factors of production are fully employed. Land is owned by the landlords and capital is owned by the capitalists. You are also provided with the following data: K = 36, T = 49, and L = 100. Also assume that the price of food and that of manufacturing are the same and is equal to unity. (a) Find out the equilibrium levels of labour employment in the food sector and the manufacturing sector (i.e. Land L, respectively)

Answer 1

ATE K=36 , TE 49 L=100 - LM + LF = L =100 of - 2012 Tth Me Lime kila Pr = pm 1 putting in values of K&T F E JLF. Juq Me dlm 36 F = 7 Juf M = 6Jim (we have marginal products) ehtimal allocation of L into Lm Alf is achieved when the value of mp oh Lin each sector is some je. Pm dM - PF dF binupm=pfel dlm dar dm - df dem ALF ZULE 22m - Lm - GULF 49. Lm = 366f since 1m = 100-LF 49 (100 -LA) : 36LF. 4900 = 3644 +49LF LE 4900 4900 36+49 85 I 2 m = 160 - 4900 2360