A sales employee generates sales revenue of either $1250 or $750, each with equal probability. A...

A sales employee generates sales revenue of either $1250 or $750, each with equal probability. A manager is paying the sales employee 25% of sales revenue, and the sales person has a utility function u(x) = x0.5. What is the lowest fixed salary (ie., independent of sales outcome) the manager can pay the employee instead, so that the sales person is not worse off? (a.)$887 (b.)$667.7 (c.)$453.5 (d.)$246.1

Expert Solution

The correct answer is (d.) $246.1.

The manager will pay the employee that fixed salary (so that Sales employee is not worse off) where Expected utility sales employee will get if A manager is paying the sales employee 25% of sales revenue is equal to utility he get if manager gives him a fixed salary F.

Utility If manager gives him fixed salary F is u(F) = F^0.5

Expected utility= P₁u(x₁) + P₂u(x₂)

where P₁ = Probability that he will generate 1250 = 0.5, x₁ = he will get if he generate 1250 = 25% of 1250 = 312.5, P₂ = Probability that he will generate 750 = 0.5, x₂ = he will get if he generate 750 = 25% of 750 = 187.5

Hence, Expected utility= P₁u(x₁) + P₂u(x₂) = 0.5u(312.5) + 0.5u(187.5)

=> Expected utility(EU)= 0.5*312.5^0.5 + 0.5*187.5^0.5 = 15.685

We want this EU to be equal to Utility If manager gives him fixed salary F = u(F)

=> EU = u(F) => F^0.5 = 15.685 => F = 246.1

So, the manager can pay the employee instead, so that the sales person is not worse off is $246.1

Hence, the correct answer is (d.) $246.1.

Rahul Sunny answered 6 months ago

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