Solve the following Cobb-Douglas Utility Maximization Problem. Show all your steps!

max UZ1 ,Z2 = Z 1 1 Z 2 2 , s.t.p1Z1 + p2Z2 = 100, 0 < 1<1; 0<2 < 1 where Z1 and Z2 are consumption levels of two products, p1,p2 are their prices, 100 is this individual consumer's income.

What are the exogenous parameters and endogenous variables in the model?

Solve for the optimal Z 1 , Z 2 such that the utility is maximized. (Show all your steps!)

Then write down the Lagrangian (L) and list all first order conditions. Explain the connections between the F.O.C.s you derieved in the gernal method and the two conditions in the "micky-mouse" method.