Maggie must decide if she wants to open a start-up or work as an economics tutor. The business she is considering is risky because with 60% probability she earns $300 and with 40% probability she earns nothing. As an economics tutor she earns $160 with certainty. She has an initial wealth of $100 and her utility function is

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Explanation:

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Maggie must decide if she wants to open a start-up or work as an economics tutor. The business she is considering is risky because with 60% probability she earns $300 and with 40% probability she earns nothing. As an economics tutor she earns $160 with certainty. She has an initial wealth of $100 and her utility function is

U(C) = ✓C

a. What is Maggie's expected income from her start up?

b. What is Maggie's expected utility for opening the start up?

c. What is Maggie's certainty equivalent associated with opening the start up?

a. Expected income = 60% of ($100 + $300) + (40% of $100)

= (0.6 × 400) + (0.4 × 100)

= $240 + $40

= $280

Maggie's expected income from her start up is $280.

b. Expected utility

= (60% × ✓100 + ✓300) + (40% × ✓100)

= (0.6 × ✓400) + (0.4 × 10)

= (0.6 × 20) + (0.4 × 10)

= 12 + 4

= 16

Maggie's expected utility for opening the start up is 16

c. Certainty equivalent

U(C) = ✓C

Since expected utility= 16

✓C = 16

C = 16²

C = 16 × 16

= 256

Maggie's certainty equivalent associated with opening the start up is 256.

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