Can someone please do this question for me and walk me through it in simplest terms? I have a midterm on this and am confused on the material. Thank you. Please note that the variables aren't 100% accurate. They won't let me copy and paste the variables correctly. variables such as "a" and "T" that I used are the closest variables I used to match the problem with. They look like a and T in symbol form on the original problem.
1. Michele, who has a relatively high income I, has altruistic feelings toward Sofia, who lives in such poverty that she essentially has no income. Suppose Micheleâs preferences are represented by the utility function
UM = (cM , cS) = c(1-a/M) c(1/S)
where cM and cS are Michele and Sofiaâs consumption levels, appearing as goods in a standard Cobb-Douglas utility function. Assume that Michele can spend her income either on her own or Sofiaâs consumption (though charitable donations) and that $1 buys a unit of consumption for either (thus, the âpricesâ of consumption are pM = pS = 1).
(a) Argue that the exponent "a" can be taken as a measure of the degree of Micheleâs altruism by providing an interpretation of extreme values of a= 0 and a= 1. What value would make her a perfect altruist (regarding others the same as oneself)?
(b) Solve for Micheleâs optimal choices and demonstrate how they change with a.
(c) Suppose that there is an income tax at rate T, i.e. net income now is just (1-T) I.
Solve for Micheleâs optimal choices under the income tax rate.
(d) Now suppose that besides the income tax rate T, there are charitable deductions, so that income spent on charitable deductions is not taxed. Argue that this amounts to changing the price pS from $1 to $(1-T). Solve for the optimal choices under both the income tax rate and charitable deductions. Does the charitable deduction have a bigger incentive effect on more or less altruistic people?
Can someone please do this question for me and walk me through it in simplest terms? I have a midterm on this and am confused on the material. Thank you. Please note that the variables aren't 100% accurate. They won't let me copy and paste the variables correctly. variables such as "a" and "T" that I used are the closest variables I used to match the problem with. They look like a and T in symbol form on the original problem.
1. Michele, who has a relatively high income I, has altruistic feelings toward Sofia, who lives in such poverty that she essentially has no income. Suppose Micheleâs preferences are represented by the utility function
UM = (cM , cS) = c(1-a/M) c(1/S)
where cM and cS are Michele and Sofiaâs consumption levels, appearing as goods in a standard Cobb-Douglas utility function. Assume that Michele can spend her income either on her own or Sofiaâs consumption (though charitable donations) and that $1 buys a unit of consumption for either (thus, the âpricesâ of consumption are pM = pS = 1).
(a) Argue that the exponent "a" can be taken as a measure of the degree of Micheleâs altruism by providing an interpretation of extreme values of a= 0 and a= 1. What value would make her a perfect altruist (regarding others the same as oneself)?
(b) Solve for Micheleâs optimal choices and demonstrate how they change with a.
(c) Suppose that there is an income tax at rate T, i.e. net income now is just (1-T) I.
Solve for Micheleâs optimal choices under the income tax rate.
(d) Now suppose that besides the income tax rate T, there are charitable deductions, so that income spent on charitable deductions is not taxed. Argue that this amounts to changing the price pS from $1 to $(1-T). Solve for the optimal choices under both the income tax rate and charitable deductions. Does the charitable deduction have a bigger incentive effect on more or less altruistic people?
