Solving constrained optimisation

1. Jamal has utility function UB(X1,X2)=(X1+2)(X2+3). He also has income m, and faces prices P1and P2 for goods 1 and 2 respectively.

What is Jamal's budget constraint?

2. What is Jamal's MRS of good 1 for good 2?

3. What is Jamal's optimal choice of goods 1 and 2 as functions of his income and prices? (Assume an interior solution.)

4. Korra has utility function UA(X1,X2)=[(X1+2)(X2+3)]². She has the same income as Jamal, and faces the same prices. Find her optimal consumption bundle. (Assume an interior solution.)

5. A third consumer, Larry has preferences UC(X1,X2))=(X1+2)²(X2+3) and the same income as Jamal and Korra. Find his optimal consumption bundle. (Assume an interior solution.)6

6. How does Larry's consumption differ from Korra's? (Assume interior solutions.)