(24 marks) Consider two goods that are produced in Home after trade: coffee (C) and doughnuts (D). Home starts with 120 units of labour and 1200 units of capital. To begin, capital is immobile between sectors (due to contractual requirements), such that half of it is in the coffee sector and half of it in the doughnut sector, respectively. The marginal products of labour in each industry are given by MPLC = 60 Lc and MPLD = 60 - LD , respectively. Both markets are perfectly competitive, all labour is employed and the world prices of coffee and doughnuts are $1 and $2, respectively. a. (2 marks) Derive equations for the value of marginal product of labour in coffee, VMPLC and the value of marginal product of labour in doughnuts, VMPLD. b. (2 marks) Use part (a) and the fact that all labour is employed to calculate the optimal amounts of labour employed in each of the coffee and doughnut sectors