1) Suppose your utility function is U = ln(2C), where C is the amount of consumption you have in any given period. Your income is $40,000 per year and there is a 2% chance that you will be involved in a catastrophic event that will cost you $30,000 next year.
a) what is your expected utility?
b) What is the actuarially fair insurance premium for full insurance coverage?
c) What would your expected utility be were you to purchase the actuarially fair premium?
d) What is the most that you would be willing to pay for insurance, given your utility function?
2) Janice (J) and Kelly (k) like firework displays. The marginal benefit curve for Janice is MB(j) = 9-q. Kelly's is MB(k) = 27-3q. q is the total amount of fireworks consumed. The cost of every unit of fireworks is 4. Any fireworks one purchases can be enjoyed by the other at no cost to the other.
a) What is the efficient number of fireworks for this society?
b) Suppose the government decides to provide the efficient level of output found above. To pay the fireworks, the government taxes J and K, using a Lindahl pricing Scheme. What are the Lindahl prices?
c) If J and K pay their lindahl prices, what is the consumer surplus for J and K respectively? What is the total consumer surplus for this society from consuming fireworks?
d) Instead of their lindahl prices, suppose J and K are each charged 2 per unit. How does this change the total consumer surplus for the society?