COMPUTE THE FIRST BEST CONTRACT FOR THE MONOPOLY INSURER (I.E. SUPPOSING IT CAN OBSERVE THE INDIVIDUAL’S DOMINANT HAND)

COMPUTE THE FIRST BEST CONTRACT FOR THE MONOPOLY INSURER (I.E. SUPPOSING IT CAN OBSERVE THE INDIVIDUAL’S DOMINANT HAND)
Suppose that the left-handed people are more prone to injury than right-handed people. Lefties have an 80 percent chance of suffering an injury leading to a $1,000 loss (in terms of medical expenses and the monetary equivalent of pain and suffering) but righties have only a 20 percent chance of suffering such an injury. The population contains equal numbers of lefties and righties. Individuals all have logarithmic utility-of-wealth functions and initial wealth of $10,000. Insurance is provided by a monopoly company.
a. Compute the first best contract for the monopoly insurer (i.e. supposing it can observe the individual’s dominant hand). (20 points)
b. Set up the constrained profit maximization problem that would solve for the payouts and the insurance prices for both types in the second-best contract. Construct the necessary constraints and indicate the choice variables that would solve the optimization problem

 
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