please only do: if you can teach explain steps of how to solve each partwhat is the optimizatio formula to use for foc? please solve 4. A decision-maker with initial wealth w faces a probability of incurring a loss. If the lossoccurs, with probability p the amount of the loss is ₁ and with probability 1-p the amountof the loss is £2, where ₁ > ₂ > 0. The decision-maker can buy insurance against both lossesat a price of q dollars per unit. If she purchases a units of insurance, she receives a dollars ifeither loss occurs, even if z is greater than the amount of the loss. There is no limitto the amount of insurance she can purchase.(a) First suppose that the decision-maker is a risk averse expected utility maximizer withvon Neumann-Morgenstern utility u(y) over quantities of wealth y.i. () Write down the first-order condition characterizing the optimal choice of a whenit is interior.Solution: The first-order condition is(1-q)πpu' (w-l₁ + (1 − q)x)+(1−q)π(1−p)u' (w − l₂ + (1 — q)x) = q (1-7)u' (w-qx).ii. (, Is the highest price q at which the decision-maker fully insures against the largerloss ₁ greater than, equal to, or less than ? Prove your answer.Solution: At q = n, the above FOC simplifies topu' (wl₁ + (1-q)x)+ (1 − p)u' (w−l₂ + (1 − q)x) = u'(w — qx).If x= ₁, the left-hand side of this equation is smaller than the right-hand side.Since u' is decreasing, we must have x < ₁ for this equation to hold as decreasingx causes the left-hand side to increase and the right-hand side to decrease. (Thisargument implicitly assumes that p1; if p = 1 then this is essentially a standardinsurance problem and r = l₁ is optimal when q = n.)

The propensity to avoid risk is defined as Risk Aversion. An investor who favors capital…

A decision-maker with initial wealth w faces a probability of incurring a loss. If the loss occurs, with probability p the amount of the loss is ₁ and with probability 1-p the amount of the loss is £2, where ₁ > ₂> 0. The decision-maker can buy insurance against both losses at a price of q dollars per unit. If she purchases z units of insurance, she receives z dollars if either loss occurs, even if z is greater than the amount of the loss. There is no limit to the amount of insurance she can purchase. (a) First suppose that the decision-maker is a risk averse expected utility maximizer with

A decision-maker with initial wealth w faces a probability of incurring a loss. If the loss occurs, with probability p the amount of the loss is ₁ and with probability 1-p the amount of the loss is £2, where ₁ > ₂> 0. The decision-maker can buy insurance against both losses at a price of q dollars per unit. If she purchases z units of insurance, she receives z dollars if either loss occurs, even if z is greater than the amount of the loss. There is no limit to the amount of insurance she can purchase. (a) First suppose that the decision-maker is a risk averse expected utility maximizer with

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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