Question

George is a loan officer at a small bank, and he must make 25 loans per month. As a loan officer, George must choose capital (K) and labor (L) to minimize his costs while achieving his loan target. Loans (Q) are made using capital and labor via the relationship Q(K,L)=K*L. Labor and capital are paid w wages and r in rent, respectively. a) What is George’s objective function b) What is George’s constraint? c) Which variables are endogenous, and which variables are exogenous? d) What is George’s constrained optimization problem?

Answer 1

a) George’s objective function is

wL + rK

b)  George’s constraint is

K*L=25

c) capital and labour are endogenous variables and wage and rent are exogenous variable.

d) George’s constrained optimization is

by langrangian multiplier

$L= wL + rK + \lambda(25/KL)$

optimisation problem is

mrts= W/l

MP_L / MP_L = w/r

K/L= w/r

K= wL/r