A firm can produce cardboard boxes using capital (machines) and workers. Technology is such that you have to combine one worker and one machine to produce one unit of boxes. Putting more machines at the disposal of the worker doesn't increase production, and putting more workers than one to operate a machine doesn't increase production as well. Production can be however doubled by using two machines and two workers and so on. a. (4 pts) How do we call this production technology and how we say that the inputs labor and capital are among them?
b. (4 pts) Draw the isoquants corresponding to the production of 10, 20 and 30 units of boxes.
c. (8 pts) Suppose that the firm needs to produce 20 units of boxes, and wage w is half than the rental cost of capital r. Show that the isocost corresponding to the cost minimizing equilibrium has equation K 30 - L and explain intercepts and slope.
d. (8 pts) The wage suddenly rises at the same level than the rental cost of capital. Draw the new isocost corresponding to the cost minimization equilib- rium for the same production of 20 units of boxes. Since wage has increased, do we have a substitution effect of capital for labor)?
e. (8 pts) Taking into account the relationship L = K = Q, that holds at all minimization points, can you deduce the form of the cost function for given w and r?