Boston University

EC 201

There are three exercises. The exercises have a different number of questions each and the number of points that each question is worth is detailed (total points are 100). Take these numbers as a guide to how long you should spend on a question. Be sure that you write everything (diagrams, calculations and explanations) in the allocated space. A solution without the corresponding calculations will not be given any credit. Graphs without the associated explanations will only be given partial credit. Answers should be precise and concise. Clarity of exposition will be taken into account. 1 1. (32 pts) 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  is half than the rental cost of capital . Show that the isocost corresponding to the cost minimizing equilibrium has equation  = 30 − 1 2 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 equilibrium 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  =  =  that holds at all minimization points, can you deduce the form of the cost function for given  and ?