Famous Econ 100A Optimization Problems Optimization Problem Objective Function Constraint Control Variables Parameters Solution Functions Optimal Value Function Consumer’s Problem Max U Subject to Budget Constriant U(X1, X2) utility function P1X1+P2X2=I budget constraint x1, x2 commodity levels p1, p2, I prices and incomes !!∗!!,!!,!ordinary demand functions !!!,!!,!indirect utility functionExpenditure Minimization Subject to Utility Constraint (Mumsie’s Problem) P1X1+P2X2 expenditure level U(X1, X2)=!desired utility level x1, x2 commodity levels p1, p2, !prices and utility level !!!!!,!!,!compensated demand functions!!!,!!,!expenditure functionGeneral Properties of the Solution Functions A. Utility max: !!∗!!,!!,!!"#!!∗!!,!!,!: Ordinary/Marshalllian/Uncompensated Demand functions a. Ordinary demand curves are scale invariant in prices and income b. Budget shares sum to one. c. Whatever the values of the prices and incomes, the optimal values of the commodities will satisfy the budget constraint.