Suppose individuals consume two goods, baked beans q1 and apples q2. Total budget is y and prices are 0 ≤ p1 < y/A and p

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Suppose individuals consume two goods, baked beans q1 and apples q2. Total budget is y and prices are 0 ≤ p1 < y/A and p2 ≥ 0. Preferences are represented by the indirect utility function
B.II.1 Suppose individuals consume two goods, baked beans ₁ and apples 92. Total budget is y and prices are 0 ≤ P₁ <y/A and p2 ≥ 0. Preferences are represented by the indirect utility function 1 v (y, P1, P2) = ln (y-p₁A). In [ap₁-3 + (1-a)p²-³] 1-8 - 1-8 where • A ≥ 0 is a parameter reflecting baked bean needs, • 0 < a < 1 is a parameter reflecting taste for baked beans and apples, and • B20 is a parameter reflecting substitutability between baked beans and apples. (a) Find the uncompensated demand functions for the two goods. (b) Which, if either, good is a necessity? Suppose that in a base period p₁=p2 = 1 and in a later period p₁ = 1 +8 >1 and p2 = 1. (c) Explain what a true (or Konüs) cost of living index is and show that a true (or Konüs) cost of living index at base-period utility can be expressed for an individual with total expenditure y as 1/(1-3) A [a(1+5)¹-³ + (1− a)]'¹/(¹-²) + (¹+5 − [a(1+6)¹¬³ + (1 − a)]¹/(¹-²) 4. (d) Find an expression for the Laspeyres cost of living index as a function of preference parameters, y and 8.