Mathematics for Economists

Dynamic programming

Calculating the derivatives

1

2

p

c

=

p

1 +k+k^2 +.. .+kt k

2

p

k(wc)

p

c=p^1

1 +k+k^2 +.. .+kt

p

wpc

k

kc=

1

1 +k+k^2 +.. .+kt(wc)

c



k+

1

1 +k+k^2 +.. .+kt



=

w

1 +k+k^2 +.. .+kt

c

k+.. .+kt+^1 + 1

1 +k+k^2 +.. .+kt =

w

1 +k+k^2 +.. .+kt

c= w

1 +k+k^2 +.. .+kt+kt+^1

.