Consider an individual's savings decision when there are two periods. Her utility depends on the consumption...

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Consider an individual's savings decision when there are two periods. Her utility depends on the consumption levels c and c according to the following function: U(C, C) = f(c) +0.95 * E[f(c)] where f(c) = 0.2 * c is the utility function in consumption and E[] means expectations. The individual has income Y=100 in period 1. The amount saved is invested in a portfolio of one risk-free and one risky asset with equal weights. The risk-free interest rate is 0.05. The risky return is 0.02 with probability 0.4 or 0.1 with probability 0.6. A. Mathematically formulate the individual's utility maximization problem. (10 marks) B. Compute the optimal amount saved. (10 marks) C. Assume now that the saving is invested into a different portfolio: 30% of the saving is invested in the risk- free asset and 70% in the risky asset. Compute the optimal amount saved in this case. Theoretically, how does the optimal amount saved depend on the riskiness of the investment? (10 marks) Consider an individual's savings decision when there are two periods. Her utility depends on the consumption levels c and c according to the following function: U(C, C) = f(c) +0.95 * E[f(c)] where f(c) = 0.2 * c is the utility function in consumption and E[] means expectations. The individual has income Y=100 in period 1. The amount saved is invested in a portfolio of one risk-free and one risky asset with equal weights. The risk-free interest rate is 0.05. The risky return is 0.02 with probability 0.4 or 0.1 with probability 0.6. A. Mathematically formulate the individual's utility maximization problem. (10 marks) B. Compute the optimal amount saved. (10 marks) C. Assume now that the saving is invested into a different portfolio: 30% of the saving is invested in the risk- free asset and 70% in the risky asset. Compute the optimal amount saved in this case. Theoretically, how does the optimal amount saved depend on the riskiness of the investment? (10 marks)

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A Mathematically formulate the individuals utility maximization problem The individuals utility maximization problem can be formulated as follows Maxi... View the full answer