Exam 19: A: Cost Minimization

Two firms, Wickedly Efficient Widgets (WEW) and Wildly Nepotistic Widgets (WNW), both produce widgets with the same production function , where K is the input of capital and L is the input of labor. Each company can hire labor at $1 per unit and capital at $1 per unit. WEW produces 10 widgets per week, choosing its input combination so as to produce these 10 widgets in the cheapest way possible. WNW also produces 10 widgets per week, but its dotty CEO requires it to use twice as much labor as WEW uses. Given that it must use twice as many laborers as WEW does and must produce the same output, how much larger are WNW's total costs than WEW's?

In Problem 3, the production function is f(L, M) , where L is the number of units of labor and M is the number of machines used. If the cost of labor is $25 per unit and the cost of machines is $64 per unit, then the total cost of producing 6 units of output will be

Suppose that in the short run, the firm in Problem 3 which has production function F(L, M) must use 9 machines. If the cost of labor is $5 per unit and the cost of machines is $6 per unit, the short-run total cost of producing 84 units of output is

In Problem 3, the production function is f(L, M) = , where L is the number of units of labor and M is the number of machines used. If the cost of labor is $49 per unit and the cost of machines is $25 per unit, then the total cost of producing 7 units of output will be

Suppose that in the short run, the firm in Problem 3 which has production function F(L, M) must use 9 machines. If the cost of labor is $5 per unit and the cost of machines is $5 per unit, the short-run total cost of producing 108 units of output is

Suppose that Nadine in Problem 1 has a production function 3x₁ + x₂. If the factor prices are $3 for factor 1 and $3 for factor 2, how much will it cost her to produce 80 units of output?