please only do: if you can teach explain steps of how to solve each part: b what is the optimization to use for foc? please solve for xalso the other part Consider the insurance problem from class in which an agent with wealth w dollars faces aprobability € (0,1) of incurring a loss of dollars, where 0 < l< w. He can purchaseinsurance at a price q € (0,1) per unit that pays 1 dollar per unit purchased if the loss occurs.Suppose the agent is an expected utility maximizer with von Neumann-Morgenstern utilityu(x) = ln(x + 1). You may assume throughout this question that the parameters are suchthat the agent's expected utility maximization problem has an interior solution.(a) Find the certainty equivalent of the lottery corresponding to no insurance.Solution: We have (1-7) ln(w+1) + π ln(w −l + 1) = ln(CE+1) and hence CE =(w+1) ¹ (w − l + 1)" - 1.(b) Suppose insurance is actuarially fair. What is the effect on demand for insurance of amarginal increase in l? That is, if x is the quantity of insurance demanded, what is thevalue of əx/al?Solution: Since the DM fully insures, the quantity of insurance increases by exactly theamount of the increase in l.(c) Suppose q>. What is the effect on demand for insurance of a marginal increase in l?Solution: The FOC iswhich is equivalent toHence-q(1-π)(1-q)π(w-qx+1) (w+(1-q)x-l+1)+= 0,(w+(1-q)x-l+1)q(1 − π) = (1 − q)n(w− qx + 1).dxq(1 — q)(1 − n) — q(1 — π) = −(1 — q) q-дгde

Utility function : U(x) = ln (x+1 ) Probable loss = l Probability of loss = π Probability of no…

Consider the insurance problem from class in which an agent with wealth w dollars faces a probability € (0,1) of incurring a loss of dollars, where 0 < l< w. He can purchase insurance at a price q € (0, 1) per unit that pays 1 dollar per unit purchased if the loss occurs. Suppose the agent is an expected utility maximizer with von Neumann-Morgenstern utility u(x) = ln(x + 1). You may assume throughout this question that the parameters are such that the Ai b. Jution nel antilid stomi

Consider the insurance problem from class in which an agent with wealth w dollars faces a probability € (0,1) of incurring a loss of dollars, where 0 < l< w. He can purchase insurance at a price q € (0, 1) per unit that pays 1 dollar per unit purchased if the loss occurs. Suppose the agent is an expected utility maximizer with von Neumann-Morgenstern utility u(x) = ln(x + 1). You may assume throughout this question that the parameters are such that the Ai b. Jution nel antilid stomi

ENGR.ECONOMIC ANALYSIS

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Question

please only do: if you can teach explain steps of how to solve each part: b

what is the optimization to use for foc?

please solve for x

also the other part

Consider the insurance problem from class in which an agent with wealth w dollars faces a
probability € (0,1) of incurring a loss of dollars, where 0 < l< w. He can purchase
insurance at a price q € (0,1) per unit that pays 1 dollar per unit purchased if the loss occurs.
Suppose the agent is an expected utility maximizer with von Neumann-Morgenstern utility
u(x) = ln(x + 1). You may assume throughout this question that the parameters are such
that the agent's expected utility maximization problem has an interior solution.
(a) Find the certainty equivalent of the lottery corresponding to no insurance.
Solution: We have (1-7) ln(w+1) + π ln(w −l + 1) = ln(CE+1) and hence CE =
(w+1) ¹ (w − l + 1)" - 1.
(b) Suppose insurance is actuarially fair. What is the effect on demand for insurance of a
marginal increase in l? That is, if x is the quantity of insurance demanded, what is the
value of əx/al?
Solution: Since the DM fully insures, the quantity of insurance increases by exactly the
amount of the increase in l.
(c) Suppose q>. What is the effect on demand for insurance of a marginal increase in l?
Solution: The FOC is
which is equivalent to
Hence
-q(1-π)
(1-q)π
(w-qx+1) (w+(1-q)x-l+1)
+
= 0,
(w+(1-q)x-l+1)q(1 − π) = (1 − q)n(w− qx + 1).
dx
q(1 — q)(1 − n) — q(1 — π) = −(1 — q) q
-
дг
de

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