(b)5. When T=P, in Example 3.4, we have shown that the solution must be on the 45 line. When T>p, the budget line is Hatter, and the tangent point must be below the 45 line. That is the individual is under-insured slope=t slope P gure 5.1. Insurance in a non-competitive market Answer 1.12. Individual A's utility function is equivalent to ua(aA, xa) (=A)(al-a. Let p= P1 and P2= 1. Then the income is IA=P0+1.1=1 and the demands are (1-a) For individual B, by its utility function, we know that the demands must satisfy aB=x3 Then by budget constraint pzB +aa=IB=p 1+1.0=p, the demands are IB P 1+p1+p In equilibrium, the total supply of good 1 must be equal to the total demand for good 1 p I+p Therefore, p and the allocation is 9(b) [5]. When π = p, in Example 3.4, we have shown that the solution must be on the 45◦ line. When π > p, the budget line is flatter, and the tangent point must be below the 45◦ line. That is, the individual is under-insured. I I 1 2 w w-l slope= slope= 1-p p 45o . . 1-π π . Figure 5.1. Insurance in a non-competitive market Answer 1.12. Individual A’s utility function is equivalent to uA(x1 A, x2 A) = (x1 A)a(x2 A)1−a. Let p = p1 and p2 = 1. Then the income is IA = p · 0+1 · 1=1, and the demands are: x1 A = aIA p = a p , x2 A = (1 − a)IA 1 = 1 − a. For individual B, by its utility function, we know that the demands must satisfy x1 B = x2 B. Then by budget constraint px1 B + x2 B = IB = p · 1+1 · 0 = p, the demands are: x1 B = x2 B = IB 1 + p = p 1 + p . In equilibrium, the total supply of good 1 must be equal to the total demand for good 1: a p + p 1 + p = 1. Therefore, p∗ = a 1−a and the allocation is (x1 A) ∗ = (x2 A) ∗ = 1 − a, (x1 B) ∗ = (x2 B) ∗ = a. 9