(Answered) 1. A logging operation needs 4 worker-hours (L) per 2 crane-hours (K) to move one batch of a…

1. A logging operation needs 4 worker-hours (L) per 2 crane-hours (K) to move one batch of a hundred logs in an hour.
1.1. Write down the total cost function for the firm (as a function of K and L), given that the hourly wage (w) is $12 and the lease on the crane (r) is $48 an hour. The firm paid $5000 to have the right to log the area.
1.2. Graph one isocost line with (K) in the vertical axis. Identify which is more expensive.
1.3. What is the slope of the isocost line? (be aware of which input is in the vertical axis)
1.4. Write down the production function for the logging company, where the output is the number of batches of hundred logs moved per hour.
1.5. Graph one isoquant for this production function.
1.6. What is the (numeric value) Marginal Rate of Technical Substitution? (again, be aware of which input is asked to be in the vertical axis)
1.7. Does this firm’s production function display increasing, constant or decreasing returns to scale?
1.8. Suppose that the firm wants to minimize their total cost while being able to move θ (where θ is some generic number) batches of one hundred logs an hour: how many cranes and how many workers would it use?
1.9. Write down the firm’s total cost (TC), variable cost (VC) and fixed cost (FC) functions, as a function of θ.
1.10. In one plot graph the firm’s TC, VC and FC.
1.11. Write down the firm’s average total cost (ATC), average variable cost (AVC), average fixed cost (AFC), and marginal cost (MC) functions, as a function of γ̂.
1.12. In one plot, graph the ATC, AVC, AFC and MC.
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