Problem:
q(x1,x2) = x1^a(x2^b)
a) What kind of returns to scale does this technology exhibit?
b) Calculate the Conditional Input Demand for good 1, and good 2,
c) Find the cost function, as well as the marginal cost function.
d) Using the Sheppard's Lemma, find once again the conditional demand for inputs
e) Solve the profit maximization problem to find the Unconditional Input Demands,, in which P is the price the producer gets for the final good q.
f) Find the profit functionfor this technology.
g) Using the Envelop Theorem, find again the Unconditional Input Demand
h) Use Hotelling's Lemma to find the supply function
i) Use the perfect competition condition P = MC to once again find the supply function