Consider an economy with two individuals, a poor individual whose income level is given

by L=50 and a rich individual whose income level is given by H=100. 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)=c, where c denotes consumption. The government considers implementing a poverty alleviation policy which guarantees a minimum level of consumption of M, where M=80, for all individuals, at the minimal cost.

a) Suppose 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.

b) Now suppose that type L is suffering from a rare disease. Type L is aware of his medical condition but the disease has no observable symptoms. The FDA has recently approved a simple blood test which detects the disease with a 50 percent probability. The probability of a 'false positive' (healthy individuals being diagnosed with the disease) is zero. The cost of the blood test is denoted by C, where 30>C>15. Show the government can economize on its costs by conditioning the transfer on a positive result of the blood test. Explain the mechanism at work. (Hint: You should formulate the government constrained minimization problem specifying the objective function, the poverty alleviation constraint and the relevant

incentive compatibility constraints. Verify that, by virtue of the parametric assumptions, only one of the constraints is binding in the optimal solution).