Suppose that Gloucester Old Bank's customers can complete their transactions at a teller's window (involving labor) or at an ATM (involving capital). The production function for the bank's services is given as follows: Q = 4K + 6L, where Q is the number of customers served, K is the number of ATMs the bank has installed in town, and L is the number of tellers the bank has hired.
a. Suppose that Gloucester currently has 20 ATMs and 20 tellers. If 3 ATMs suddenly fail, how many additional tellers must the bank hire to maintain their original level of service?
b. Does your answer to (a) change if Gloucester originally only uses 17 ATMs? 30 ATMs?
c. What do production isoquants look like for Gloucester Old Bank?
d. How would you verbally describe the relationship between tellers and ATMs?
e. Suppose that installing and maintaining an ATM costs $20, and hiring a teller costs $32. What will happen to Gloucester's total number of customers served if it lays off 2 workers and installs 3 ATMs? What will happen to the bank's costs?
f. Using the idea developed in (e), if Gloucester Old Bank is interested in minimizing its costs, what strategy should it employ regarding its input mix?