show full stpes
3. Producer theory (4%) Suppose a lumber mill uses labor (L) and equipment (K). Their production function is Q=3000K0.6L0.4 in board.feet per day. The workers earn an average wage of $240 per worker per day but the firm's cost of labor (w) is double that, taking into account sick time, benefits, workers' comp, El, etc. The equipment for the mill was financed through bonds, which the mill owners pay interest on. This interest cost (r) amounts to $600 per machine per day. The mill currently employs 60 workers, and has 80 machines. The mill also has fixed costs of $1.2M per month for management and overhead, and operates 360 days per year. (a) Find the current output Q. Include units. Express this production rate in terms of the number of pieces of 8ft24 studs per day. (Hint: a board foot is 1 foot 1 foot 1 inch or 144 in 3; the studs are 81224 in 3 ) (b) Calculate the mill's variable costs per day for labor (VCL) and machinery (VCK). Also find their fixed costs per day. Add variable and fixed costs per day to arrive at their total cost (TC) of operations, and then express this as average cost (AC=TC/Q) in $ per board. ft. (c) Calculate the total average cost (TAC) per board.foot if distribution costs an additional $0.25 per board foot. (d) If the market price (wholesale) is $0.90 per board foot, calculate the firm's markup (markup =(PTAC)/TAC) and gross profit per day, and per year. (e) The firm pays taxes to the provincial and federal governments on gross profits at a rate of 15%. Calculate their taxes paid, and net profit after taxes, per year. (f) In class, we said the required condition for efficient production was that the marginal cost for each factor of production should be equal. Find the equation of their marginal product for each factor of production (ie, MPL=Q/L and MPK=Q/K ) include units. (g) Calculate their current marginal cost of labor MCL=w/MPL and compare it to their current marginal cost of capital MCK=r/MPK). Have they chosen an efficient level of machines and workers? If not, if they want to increase production slightly, would you recommend they hire more workers or install more equipment? 3. Producer theory (4%) Suppose a lumber mill uses labor (L) and equipment (K). Their production function is Q=3000K0.6L0.4 in board.feet per day. The workers earn an average wage of $240 per worker per day but the firm's cost of labor (w) is double that, taking into account sick time, benefits, workers' comp, El, etc. The equipment for the mill was financed through bonds, which the mill owners pay interest on. This interest cost (r) amounts to $600 per machine per day. The mill currently employs 60 workers, and has 80 machines. The mill also has fixed costs of $1.2M per month for management and overhead, and operates 360 days per year. (a) Find the current output Q. Include units. Express this production rate in terms of the number of pieces of 8ft24 studs per day. (Hint: a board foot is 1 foot 1 foot 1 inch or 144 in 3; the studs are 81224 in 3 ) (b) Calculate the mill's variable costs per day for labor (VCL) and machinery (VCK). Also find their fixed costs per day. Add variable and fixed costs per day to arrive at their total cost (TC) of operations, and then express this as average cost (AC=TC/Q) in $ per board. ft. (c) Calculate the total average cost (TAC) per board.foot if distribution costs an additional $0.25 per board foot. (d) If the market price (wholesale) is $0.90 per board foot, calculate the firm's markup (markup =(PTAC)/TAC) and gross profit per day, and per year. (e) The firm pays taxes to the provincial and federal governments on gross profits at a rate of 15%. Calculate their taxes paid, and net profit after taxes, per year. (f) In class, we said the required condition for efficient production was that the marginal cost for each factor of production should be equal. Find the equation of their marginal product for each factor of production (ie, MPL=Q/L and MPK=Q/K ) include units. (g) Calculate their current marginal cost of labor MCL=w/MPL and compare it to their current marginal cost of capital MCK=r/MPK). Have they chosen an efficient level of machines and workers? If not, if they want to increase production slightly, would you recommend they hire more workers or install more equipment
