Consider a consumer with the Cobb-Douglas utility function U(q1,q2)=(q1q2), where q1 and q2 are the quantities of goods q and 2 consumed, respectively. This consumer derives a level of utility denoted by U0. The prices of goods 1 and 2 are denoted p1 and p2.

a. Write out the Lagrangian for the consumer's expenditure minimization problem.

b. Using the Lagrangian method, derive the consumer 's (expenditure minimizing) quantity of good 1 as functions of variables p1, p2, and U0

c. Derive the consumer's expenditure function, E(p1,p2,U0)