3. An individual lives for one period with certainty and may live into a second period with probability \( \rho \), where \( 0 \leq \rho \leq 1 \). He knows the value of \( \rho \). He does not find out whether he lives in the second period until after he has done his first period consumption. He has labor income \( w_1 = 2 \) in the first period of life, and no labor income in the second period of life. His first period utility is \( \ln(c_1) \). The time discount rate and interest rate are both zero.