To dig a trench, each worker needs a shovel. Workers can only use one

To dig a trench, each worker needs a shovel. Workers can only use one shovel at a time. Workers without shovels do nothing, and shovels cannot operate on their own.

What kind of production technology is this? Graphically (with isocost and isoquant lines) determine the optimal number of shovels and workers used by a firm to dig two trenches when w = r = 10. What will be the (long-run) total cost of the two trenches? What will happen if the rental rate drops to $5 while the wage remains at $10? Add the relevant lines to your graph and compute the new optimal quantity of inputs and total cost.

ANSWER

This is the fixed-proportion production technology. In order to dig two trenches, it must be that L = 2 and K = 2, so the total cost will be $40. If the rental rate drops, the optimal K and L remain unchanged and the cost falls to $30.