Problem 3: A startup firm must maximize profit over a two-year horizon. They must decide between machinery that runs on coal (C) or machinery that runs on natural gas (N). Once the investment in machinery has been made, all production will occur with the selected technology. Assume that the price of the output stays constant over the two years at p= $60 and wage rate stays constant at the rate w = $50. The one year discount factor is .96, so that a dollar in one year is worth only .96 dollars today. The technology options are: Option 1: Coal Based Production 5 f(CL) 5 [1/202/3 16 Input contract for 2 years: C = 64 units of coal each year at a cost of r = $3 per unit. Option 2: Natural Gas Based Production f(N, L) = (1/31/2 Input contract for 2 years: N = 100 units of natural gas each year at a cost of r = $6 in the first year and r = $3.5 in the second year. Since for both options the contracts fix the level of the energy input C or N, there is only one variable that can be chosen to maximize profit i.e. labor input L. a) Determine the profit maximizing amount of labor and output for each of the two options for each of the time periods. b) Based on your calculations which option should the firm select? The firm should maximize the present value of their profits, i.e. discount future profits using the interest rate. c) So far we have not explicitly considered set up costs. If the set up cost for the chosen technology is $1000 what is the optimal amount of output that should be produced? (Part (C) should not require much calculation). Problem 3: A startup firm must maximize profit over a two-year horizon. They must decide between machinery that runs on coal (C) or machinery that runs on natural gas (N). Once the investment in machinery has been made, all production will occur with the selected technology. Assume that the price of the output stays constant over the two years at p= $60 and wage rate stays constant at the rate w = $50. The one year discount factor is .96, so that a dollar in one year is worth only .96 dollars today. The technology options are: Option 1: Coal Based Production 5 f(CL) 5 [1/202/3 16 Input contract for 2 years: C = 64 units of coal each year at a cost of r = $3 per unit. Option 2: Natural Gas Based Production f(N, L) = (1/31/2 Input contract for 2 years: N = 100 units of natural gas each year at a cost of r = $6 in the first year and r = $3.5 in the second year. Since for both options the contracts fix the level of the energy input C or N, there is only one variable that can be chosen to maximize profit i.e. labor input L. a) Determine the profit maximizing amount of labor and output for each of the two options for each of the time periods. b) Based on your calculations which option should the firm select? The firm should maximize the present value of their profits, i.e. discount future profits using the interest rate. c) So far we have not explicitly considered set up costs. If the set up cost for the chosen technology is $1000 what is the optimal amount of output that should be produced? (Part (C) should not require much calculation)
