The country Arcadia produces two goods, cloth and food. Cloth production uses labour and capital as production factors, and food production uses labour and land. Labour is perfectly mobile between the two sectors, but capital and land are specific factors that are immobile across sectors. Arcadia is endowed with 84 units of labour, 125 units of land, and 1000 units of capital. All goods and factor markets are perfectly competitive. Assume that the aggregate production functions for cloth and food productio n are as follows: 푄푄 퐶퐶 = 퐿퐿 퐶퐶 2 / 3 퐾퐾 1 / 3 푄푄 퐹퐹 = 퐿퐿 퐹퐹 2 / 3 푇푇 1 / 3 where Q C and Q F denote the output of cloth and food in Home, respectively. L C denotes labour employed in the production of cloth, and L F denotes labour employed in the production of food. K denotes Arcadia’s capital stock ( K =1000) and T Arcadia’s endowment of land ( T =125). Derive the allocation of labour across the two sectors and Arcadia’s equilibrium wage rate ( w ). In doing so, assume that the price of cloth is P C =3 and the price of food is P F =2.