3. Suppose that a principal wishes to procure a public good x that affects the welfare...

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3. Suppose that a principal wishes to procure a public good x that affects the welfare of two individuals, i = 1,2. Suppose that both individuals have quasi-linear preferences over public good x = [0,1] and monetary transfers m (m1, m2). Suppose individual 1's = = preferences are represented by the utility function v(x, m, 01) 01x1/2 1 x + m1, while individual 2's preferences are represented 02x1/2 = x + m2. Suppose that individual 1's = by v2(x, m2, 02) realised type (i.e., his taste parameter 01) is his private information, while it is common knowledge that 01 O with probability 1/3 and 01 = = 1 with probability 2/3. On the other hand, it is common knowledge that 02 = 1 for sure. (a) Identify all possible states (i.e., type profiles) and find the first- best decision rule. (b) Find the pivotal mechanism transfer rule and verify that budget balancedness is not satisfied. (c) Find the expected externality transfer rule and show that budget balancedness is satisfied. (d) Verify that the expected externality mechanism you found above. is incentive compatible. (e) Verify that the expected externality mechanism you found above is individually rational. 3. Suppose that a principal wishes to procure a public good x that affects the welfare of two individuals, i = 1,2. Suppose that both individuals have quasi-linear preferences over public good x = [0,1] and monetary transfers m (m1, m2). Suppose individual 1's = = preferences are represented by the utility function v(x, m, 01) 01x1/2 1 x + m1, while individual 2's preferences are represented 02x1/2 = x + m2. Suppose that individual 1's = by v2(x, m2, 02) realised type (i.e., his taste parameter 01) is his private information, while it is common knowledge that 01 O with probability 1/3 and 01 = = 1 with probability 2/3. On the other hand, it is common knowledge that 02 = 1 for sure. (a) Identify all possible states (i.e., type profiles) and find the first- best decision rule. (b) Find the pivotal mechanism transfer rule and verify that budget balancedness is not satisfied. (c) Find the expected externality transfer rule and show that budget balancedness is satisfied. (d) Verify that the expected externality mechanism you found above. is incentive compatible. (e) Verify that the expected externality mechanism you found above is individually rational.

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a Possible states type profiles are 1 0 with probability 13 for individual 1 2 1 with probability 23 ... View the full answer