Question

1. A customer service call center uses customer service representatives (L) and rents computer software technology (K) to serve customer calls. Servicing each customer call requires exactly 1 hour of the representative's time and exactly 30 minutes (or half hour), of running the software application. Let Q represent the number of customers served in a day. The hourly wage and rental rate for L and K are w = $10, r = $40. a) Draw the isoquant that represents this production technology. b) Write down the corresponding production function Q = f(L,K). c) What is the cost-minimizing input combination, L* and K* for serving Q consumers? d) What is the cost function, C(Q)? e) What is the Marginal Cost, MC? Manufacturers outsource customer service calls to call centers. Let p be the price charged by the call center from manufacturers for servicing the manufacturers' customers. Suppose there is a perfectly competitive market for call centers. The daily market demand for customer service from manufacturers is Q = 300 - 2p. f) What is the equilibrium price? g) How many customers are served daily?

Answer 1

1) Preferences are perfectly complements ( Leontieff )

Then, Q(L,K) = Min ( .5L, K)

bcoz at eqm, .5L = K

So at eqm, K/L = .5 , the ratio between K & L

Isoquants are L shaped

( Blue colored )

20 -10 K = 5L line along which IC kink 10 20 30

.

B) Q = Min ( .5L, K)

.

c) at eqm, .5L = K = Q

So, L* = 2Q, K* = Q

Cost minimizing combination,

L* = 2Q, K*= Q

.

D)Then cost function C* = wL* + rK*

C* =10*2Q + 40Q

C* = 20Q + 40Q

C* = 60Q

.

e) MC = dC*/dQ = 60

.

f) at eqm in perfect Competition

P* = MC = 60

.

G) Q = 300-2*60 = 180