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Mahatma Gandhi National Rural Employment Guarantee Act (MGNREGA), is an Indian labour law and social security measure that aims to guarantee the 'right to work'. This act was passed in September 2005 under the UPA government of Prime Minister Dr. Manmohan Singh. It aims to enhance livelihood security in rural areas by providing at least 100 days of wage employment in a financial year to every household whose adult members volunteer to do unskilled manual work. Another aim of MGNREGA is to create durable assets (such as roads, canals, ponds and wells). Employment is to be provided within 5 km of an applicant's residence, and minimum wages are to be paid. If work is not provided within 15 days of applying, applicants are entitled to an unemployment allowance. That is, if the government fails to provide employment, it has to provide certain unemployment allowances to those people. Thus, employment under MGNREGA is a legal entitlement. Apart from providing economic security and creating rural assets, NREGA can help in protecting the environment, empowering rural women, reducing rural-urban migration and fostering social equity, among others. Recently the central government announced that the national average wage under MGNREGA will increase to INR 202 per person per day from INR 182.

Given this backdrop, assume that a rural worker has some job in the agricultural field for the remaining 265 days. He has these 100 days to choose between enjoying leisure (spending these days as vacation with the family) or work under the MGNREGA scheme. The MGNREGA wage reflects the trade-off between his leisure and income generated (specially spent on childs education) while working these 100 days. For every day, he decides not to work he loses INR 182 (before the wage hike). You may further assume that his preferences between leisure and expenditure on childs education are such that the indifference curves are downward sloping and convex.

Use this information, to draw a clearly labelled budget constraint. Find the optimum number of days he will spend in leisure and optimum income he generates through this MGNREGA wage at INR 182 to spend on your childs education.

Assume that the decision of wage increase from INR 182 to INR 202 has been implemented. Given this increase in wages, show the change in the optimum such that the labor supply curve for the scheme is upward sloping. Give a brief description explaining the transition from the old optimum to the new optimum. (Note: Labor supply curve is upward sloping if there is a positive relationship between wages and optimum number of days worked)