# Help Finding Restrictions on Cobb-douglas function to meet certain requirements

• Jun 27th 2010, 04:53 PM
seanP
Help Finding Restrictions on Cobb-douglas function to meet certain requirements
For a) i suppose k>0 and a+b =/= 0
i'm not really sure how to derive the average and marginal cost funtions. If someone could help me with that It would help a lot!!

The Generalized Cobb-Douglas technology has a cost function of the form c(y) = ky^1/(a+b), where k is a function of prices and parameters. Find restrictions on k, a, and b that would make:

a) The cost function c(y)>0

b) Average cost AC(y) and marginal cost MC(y) positive

c)Under what conditions will average cost AC(y) and marginal cost MC(y) are increasing? OR AC(y) and MC(y) are constant?

d) If average cost AC(y) and marginal cost MC(y) are both increasing, show which one is greater. If AC(Y) and MC(Y) are constant, show which one is greater.
• Jun 28th 2010, 12:19 PM
SpringFan25
b)
You know from elementary economics that Average cost = $\displaystyle \frac{Total~Cost}{Quantity}$

Continuous cost functions are no different
$\displaystyle AC(y) = \frac{c(y)}{y}$

The marginal cost is defined as
$\displaystyle MC(y) = \frac{d(c(y))}{dy}$

Can you finish from there?