Consider an economy with two individuals, a poor individual whose income level is given by L>0 and a rich individual whose income level is given by H>L. Both consumers spend their income on a single consumption good (the price of which is normalized to unity) and share the same preferences given by u(c) = x/E, where c denotes consumption. The government considers implementing a poverty alleviation policy which guarantees a minimum level of consumption of M, where L0 denotes the stigma cost (entailed by eating in the soup kitchen). A senior economist interviewed for a talk show argued that the whole concept of opening a soup kitchen is flawed and will not save on government expenditure, as both types of agents incur identical stigma costs. Discuss the merits of this argument. 4) Denote by 720, the number of bowls offered by the soup kitchen. Show that the benefit from eating in a soup kitchen is decreasing with respect to the individual's level of income (Hint: consider an individual with an income level y, express the benefit, defined as the difference in utility b/w having or not having lunch in the soup kitchen, as a function of y, and show that this function is decreasing in y). 5) Formulate the government constrained optimization problem. You should properly define the objective function, the poverty alleviation constraint and two incentive compatibility constraints.1) Suppose rst that the government can distinguish between the two individuals. Characterize the optimal individualized transfers set by the government (individualized transfers are denoted by I} ; j=L, H, and are assumed to be non- negative). 2) Suppose alternatively that the government is unable to distinguish between the two individuals and is hence offering both of them an identical transfer, denoted by T. Formulate the government optimization problem and calculate the optimal universal transfer level and the total government expenditure on the welfare program