Find the partial derivative of this function with respect to c.
mathematics
Description
1. Consider the utility function u(c, l) = c 1−γ−1 1−γ + l.
(a) Find the partial derivative of this function with respect to c.
(b) Find the limit of this function as γ → 1.
2. Consider a firm aiming to maximising total profits from time 0 through infinity. The
firm’s production function is f(kt) where kt
is the capital stock at time t. New investment
is it
, and costs wt
.
max X∞
t=0
1
1 + r
t
[f(kt) − wtit
]
s.t. kt+1 = (1 − δ)kt + it
.
Solve for the condition that determines the firm’s optimal investment decision given kt
.
