W with Consider a facing prices Consumer P₁ =2 an income. P₂=4 for and Commodities I and 2 respectively. (a) Write down the budget set of the consumer. (call it (b) Is the set 1 Compact 3 Why or why not? If your answer will not is yes, then indicate when the best set D be compact ? set (0) Is the budget budget set convex 3 Explain in detail. (d) Suppose the price for commodity 2 to decreases from P₂ > P2 =3. Write down the new budget for the consumer (call it D') D'CD 3 Explain in detail. set (e) Is (2) For each of the following functions, (i) compute the first derivative, ciis compute the second derivative, cili Indicate Whether the function is Concave, Couvex or neither at X =2. + Inx-x+x² 6x²-3x³ (b) (a) g(x) g(x (0 900) доо (d) goo 3²-1+3 √4x-x³ = of M<[infinity]