Consider the following intertemporal utility function of a consumer: U(c, cf) = u(c) + Bu(cf) where u(c) = log c. Let's give this consumer a financial profile: initial assets are a = $5,000, and the path for labor income is y = $10,000, and y/= $100,000. 5. Define the consumer's intertemporal optimization problem and derive the Euler equation. 6. Assume B = 1. How much does a consumer consume today and in the future? 7. By how much does consumption today rise if current labor income increases by $10,000? 8. By how much does a consumption today rise if future labor income increases by $10,000? Why does your answer differ from that in question #7