First-order Condition for Expected Utility Maximization

---

• For every state s
  • expected marginal utility of wealth = k*price

• If every state is equally probable
  • mu(w_s ) = k*P_s

• for CRRA utility
  • mu(w_s ) = w_s^-l

• Thus
  • P_s = K*(w_s^-l )
  • ln(P_s) = ln(K) - l*ln(w_s)