代写Midterm Assignment代做Python程序

2025-05-26

Midterm Assignment (due Monday May 26)

There are 3 questions and 30 points in total

You need to show all steps of your work, only writing the final answer is not enough.

Question 1 [8 points] Consider a household that has two members. Each member has the same individual capacity curve, given below. Note that the capacity curve gives the relation between income today and income tomorrow. The identical individual capacity curve, together with the 45 degree line, is shown in the following diagram. Suppose OA = AB and OC = CE.

Suppose the household’s income today is OD. The household divides today’s income between its two members with the objective of maximizing tomorrow’s household income (which is the sum of tomorrow’s incomes ofthe two members). Showing all steps of your work, determine whether dividing today’s income equally or unequally is best for the household.

Question 2 [10 points] A region has 300 people and three income groups A,B,C. Group A has population 150, group B has population 90 and group C has population 60. Each person in group A has income $40, each in group B has income $80 and each in group C has income $200. The poverty line isp = 100 (anyone with income below $100 is considered poor).

You are given a budget of $4500 to allocate among groups whose income is below p = 100.

Assume that each person within the same group must receive the same amount. Also assume that every dollar received by an individual is invested and this raises the income of the individual by a dollar. Consider the following policies:

Policy I: allocate $2700 to group A, $1800 to group B;

Policy II: allocate $1800 to group A, $2700 to group B.

Showing all steps of your work, find HCR, PGR, IGR under each of the two policies and determine (i) which policy/policies give the lowest HCR, (ii) which policy/policies give the lowest PGR and (iii) which policy/policies give the lowest IGR.

Question 3 In a credit market any borrower needs to borrow one unit of capital to invest in its project. Any project results in one of the two outcomes: success (positive return), or failure (zero return). There are two types of borrowers: type s (safe) and type r (risky). The probability of success is 5/6 for type s and 3/4 for type r.

Consider a slightly modified version of the problem studied in the class:

• For the project of any type s borrower, success gives return $1240 to the borrower and failure gives return $0 to the borrower.

• For the project of any type r borrower, success gives return $1096 to the borrower and failure gives return $0 to the borrower.

Loans are given to groups of two borrowers through the joint liability contract (520, 216), where 520 is the individual liability component and 216 is the joint liability component.

Denote by yab the average net income of a borrower whose own type is a and whose group partner is of type b.

(a) [10 points] Showing all steps of your work, determine ysr, yrs, yss, yrr.