What is the ex post redistribution, Operation Management

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1. Two individuals, Vic and Val, are both working. Vic faces a 10 percent chance of becoming unemployed for three months and losing $12,000 of income. Val's probability of becoming unemployed is lower at 8 percent but she too would be unemployed for three months and would lose $12,000 of income.

a. Suppose the employment insurance benefit rate is 55 percent so that 55 percent of lost earnings are replaced. Calculate the expected payouts for Vic and Val.

b. Suppose that participating in the national employment insurance program is compulsory and that the annual premium of $594 is paid monthly by both individuals. Does this scheme involve ex-ante redistribution? If so, who gains and who loses?

c. If an actuarially fair premium was to be charged for each worker, what annual premium would Vic face and what annual premium would Val face?

d. Suppose that this year Val is in fact laid off and Vic is not. What is the ex post redistribution?

2. Consider Blanche, who expects to live for two periods: "now" (period 0) and the "future" (period 1). She earns an income of $40,000 dollars now, but zero in the future since she will be retired. Her problem is to decide how much to consume in period 0 and how much to save for period 1. The market interest rate is 6%. Her utility function is U = ( C0)3/ 4( C 1)1/ 4 and hence her marginal rate of substitution between present and future consumption is [dC1/dC0] = 3C 1/C0.  Use a consumer's choice diagram with future consumption on the vertical axis and present consumption on the horizontal axis to address the following points.

a. In the absence of a public pension, show how much she will save?

b. Suppose that there is a pay-as-you-go public pension system in place which charges Blanche a premium of $6,000 in period 0 and pays her benefits of $6,360 in period 1. How much will Blanche save now?

c. How will the pay-as-you-go public pension affect total saving in society?(Explain your answer.)

d. What is meant by the "wealth substitution effect" of a public pension?

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