Questlon 2 (25 paints) A person has westh of $500,000 in case of a fleod her wealth will be reduced to $50,000. The probablity of flooding is 1/10. The person can buy flood insurance at a cost of $0.10 for each $1 worth of coversge. Suppose that the sathiaction the derives from c dollars of wealth (or consumption) is given by u(c)=c. Let c, denote the contingent commodity dollars if there is a flood (horizontal asis) and cNr denote the contingent commodity dollars if there is no flood (vertical axiz). (a) Determine the contingent consumption plan Hi she does not buy insurance. (b) Determine the contingent consumption plan it she buys insurance 5x, (c) Use your answer in (b) to eliminate x and construct the bodget constraint (DC) that gives the feasible contingent consemption pians for different amounts of imurance K. Determine the slope of bucket line (both gaphically and by formirg. the price ratio). (d) Assume that the persan has von Neurrann-Mergensteen atility function on the contingent consumption plans. Write dewa the expected utilfy U(cr,cNr) and detive the MRS. (e) Solve for optimal (cr,Sr). To twis end, first we the tangensy condition (TC) to find the relation betwoen the two contingent contiodites (rNr). Noxt, use (BC) to solve for their values. What is the optimal amount of insurance k the perion will boy? Cipes the general theory developed in lertures ations to know the outcoren of the exerese. Qut it is a gosd itea to work out the protiem from fits prinoplem.) Questisen 1 (20 goints] iledo the probiem in quwistion 2 undet the acwimptert that the perwoncan bov food imurance at a caut of 50.15 for each 5t werth of creverage. Maintain the remaining Question 2 and cominent. Question a cad neints Questlon 2 (25 paints) A person has westh of $500,000 in case of a fleod her wealth will be reduced to $50,000. The probablity of flooding is 1/10. The person can buy flood insurance at a cost of $0.10 for each $1 worth of coversge. Suppose that the sathiaction the derives from c dollars of wealth (or consumption) is given by u(c)=c. Let c, denote the contingent commodity dollars if there is a flood (horizontal asis) and cNr denote the contingent commodity dollars if there is no flood (vertical axiz). (a) Determine the contingent consumption plan Hi she does not buy insurance. (b) Determine the contingent consumption plan it she buys insurance 5x, (c) Use your answer in (b) to eliminate x and construct the bodget constraint (DC) that gives the feasible contingent consemption pians for different amounts of imurance K. Determine the slope of bucket line (both gaphically and by formirg. the price ratio). (d) Assume that the persan has von Neurrann-Mergensteen atility function on the contingent consumption plans. Write dewa the expected utilfy U(cr,cNr) and detive the MRS. (e) Solve for optimal (cr,Sr). To twis end, first we the tangensy condition (TC) to find the relation betwoen the two contingent contiodites (rNr). Noxt, use (BC) to solve for their values. What is the optimal amount of insurance k the perion will boy? Cipes the general theory developed in lertures ations to know the outcoren of the exerese. Qut it is a gosd itea to work out the protiem from fits prinoplem.) Questisen 1 (20 goints] iledo the probiem in quwistion 2 undet the acwimptert that the perwoncan bov food imurance at a caut of 50.15 for each 5t werth of creverage. Maintain the remaining Question 2 and cominent. Question a cad neints
