Hello, in the solution on page 11 of chapter 2, can someone please explain how did we conclude U''(W) < 0 from U(w+1) - U(w)< U(w) - U(w-1)
Hi Aisha How about this: U'(w) = dU(w)/dw Working in increments of wealth of 1, this gives: U'(w) = [U(w+1) - U(w)] / [w+1 - w] U'(w) = U(w+1) - U(w) Similarly: U''(w) = dU'(w)/dw Again, working in increments of wealth of 1, this gives: U''(w) = [U'(w+1) - U'(w)] / [w+1 - w] U''(w) = U'(w+1) - U'(w) Substituting in from above for U'(w): U''(w) = [U(w+1) - U(w)] - [U(w) - U(w-1)] Therefore, if U''(w) < 0 then this means: [U(w+1) - U(w)] - [U(w) - U(w-1)] < 0 or U(w+1) - U(w) < U(w) - U(w-1)] Does this help? Anna
