2. Two goods, Boots (B) and Forestry products (F) are produced in a country. The production of Boots uses Labour (L) and Capital (K). Capital is a specific factor and the stock of Capital is fixed at KB. 10. The production of Forestry products uses Labour (L) and Land (T). Land is a specific factor and the stock of Capital is fixed at TF = 8. Production functions for the goods are as follows: L'B B KB(2LB 10 L} F = TF(3LF 8 Labour is mobile between the two industries. The total amount of labour is I = 10. LB + LE T. (a) Sketch a concave PPF with B on the horizontal and F on the vertical. Indicate the values on the horizontal and vertical axes and the output of the two goods when half the labour is allocated to each industry. (b) The marginal product of labour functions are as follows: MPLB = 2KB KgLB 5 TELF 4 MPLF 3TF Sketch the graph of the MPlb function. Use the MPlb to confirm the output of B when all the labour is allocated to the production of Boots. Sketch the graph of the MPlf function. Use the MPlf function to confirm the output of F when half of the labour is allocated to the production of F. (c) In autarky, the prices of goods at Home are PAut $2.50 and Paut = $3.00. Determine the autarky equilibrium allocation of labour and the wage at home and the output level of both goods. (d) When Home trades with Foreign the free-trade prices of goods are PB $3.50 and PF = $2.00. Determine the new allocation of labour when there is free-trade. Determine the wage in the home country. Determine the real wage measured with respect to each good. 2. Two goods, Boots (B) and Forestry products (F) are produced in a country. The production of Boots uses Labour (L) and Capital (K). Capital is a specific factor and the stock of Capital is fixed at KB. 10. The production of Forestry products uses Labour (L) and Land (T). Land is a specific factor and the stock of Capital is fixed at TF = 8. Production functions for the goods are as follows: L'B B KB(2LB 10 L} F = TF(3LF 8 Labour is mobile between the two industries. The total amount of labour is I = 10. LB + LE T. (a) Sketch a concave PPF with B on the horizontal and F on the vertical. Indicate the values on the horizontal and vertical axes and the output of the two goods when half the labour is allocated to each industry. (b) The marginal product of labour functions are as follows: MPLB = 2KB KgLB 5 TELF 4 MPLF 3TF Sketch the graph of the MPlb function. Use the MPlb to confirm the output of B when all the labour is allocated to the production of Boots. Sketch the graph of the MPlf function. Use the MPlf function to confirm the output of F when half of the labour is allocated to the production of F. (c) In autarky, the prices of goods at Home are PAut $2.50 and Paut = $3.00. Determine the autarky equilibrium allocation of labour and the wage at home and the output level of both goods. (d) When Home trades with Foreign the free-trade prices of goods are PB $3.50 and PF = $2.00. Determine the new allocation of labour when there is free-trade. Determine the wage in the home country. Determine the real wage measured with respect to each good