Question 6. Suppose that Dave has 100 dollars as initial wealth. He faces two types of financial loss. The risk of a large financial loss of 30 dollars occurs with the probability 0.2. The risk of a small financial loss of 10 dollars occurs with the probability 0.4. The probability of no loss is 0.4. An insurance company offers to sell the products that cover 10x whenever the loss occurs (regardless of the type of loss), where x is the number of product units that Dave purchases. The price of each unit of the product is 2 and Dave's budget constraint for the products is 02x ≤ 100. Suppose that Dave has a logarithmic utility U(z) = ln x. Compute the optimal choice of a to maximize Dave's expected utility. ==

ENGR.ECONOMIC ANALYSIS
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Chapter1: Making Economics Decisions
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Question 6. Suppose that Dave has 100 dollars as initial wealth. He faces two types of
financial loss. The risk of a large financial loss of 30 dollars occurs with the probability
0.2. The risk of a small financial loss of 10 dollars occurs with the probability 0.4. The
probability of no loss is 0.4. An insurance company offers to sell the products that cover
10r whenever the loss occurs (regardless of the type of loss), where r is the number of
product units that Dave purchases. The price of each unit of the product is 2 and Dave's
budget constraint for the products is 0 < 2r < 100. Suppose that Dave has a logarithmic
utility U(z) = In z. Compute the optimal choice of a to maximize Dave's expected utility.
%3D
Transcribed Image Text:Question 6. Suppose that Dave has 100 dollars as initial wealth. He faces two types of financial loss. The risk of a large financial loss of 30 dollars occurs with the probability 0.2. The risk of a small financial loss of 10 dollars occurs with the probability 0.4. The probability of no loss is 0.4. An insurance company offers to sell the products that cover 10r whenever the loss occurs (regardless of the type of loss), where r is the number of product units that Dave purchases. The price of each unit of the product is 2 and Dave's budget constraint for the products is 0 < 2r < 100. Suppose that Dave has a logarithmic utility U(z) = In z. Compute the optimal choice of a to maximize Dave's expected utility. %3D
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