Question

A city funds its public good provision solely from voluntary contributions from its two residents, Mr. A and Mrs. B. The total amount of spending on public good is equal to the sum of private contributions on public good, $g_A$ and $g_B$, divided by the marginal cost of public good: $G = (g_A + g_B)/c$. Assume that the marginal cost of producing public good is equal to 1 unit of income and thus we can simplify the formula for the total level of public good spending to just the sum of individual voluntary contributions: $G = g_A + g_B$. It is known, from the income tax records, that A's income is $m_A = 100$, B's income is $m_B = 1000$. Each of the two residents has a unitality function that shows preferences over a public good, G, and a private good, z: $U(z_A, G) = 0.3 \cdot ln(z_A) + 0.7 \cdot ln(G)$ and $U(z_B, G) = 0.8 \cdot ln(z_B) + 0.2 \cdot ln(G)$. Suppose Mrs. B donates nothing (remember that we are modeling voluntary contributions). How much does Mr. A donate in this case? A. 0 B. 30 C. 70 D. 100

          A city funds its public good provision solely from voluntary contributions from its two residents, Mr. A and Mrs. B. The total amount of spending on public good is equal to the sum of private contributions on public good, $g_A$ and $g_B$, divided by the marginal cost of public good: $G = (g_A + g_B)/c$. Assume that the marginal cost of producing public good is equal to 1 unit of income and thus we can simplify the formula for the total level of public good spending to just the sum of individual voluntary contributions: $G = g_A + g_B$. It is known, from the income tax records, that A's income is $m_A = 100$, B's income is $m_B = 1000$. Each of the two residents has a unitality function that shows preferences over a public good, G, and a private good, z: $U(z_A, G) = 0.3 \cdot ln(z_A) + 0.7 \cdot ln(G)$ and $U(z_B, G) = 0.8 \cdot ln(z_B) + 0.2 \cdot ln(G)$. Suppose Mrs. B donates nothing (remember that we are modeling voluntary contributions). How much does Mr. A donate in this case?
A. 0
B. 30
C. 70
D. 100

A city funds its public good provision solely from voluntary contributions from its two residents, Mr. A and Mrs. B. The total amount of spending on public good is equal to the sum of private contributions on public good, gA and gB, divided by the marginal cost of public good: G = (gA + gB)/c. Assume that the marginal cost of producing public good is equal to 1 unit of income and thus we can simplify the formula for the total level of public good spending to just the sum of individual voluntary contributions: G = gA + gB. It is known, from the income tax records, that A's income is mA = 100, B's income is mB = 1000. Each of the two residents has a unitality function that shows preferences over a public good, G, and a private good, z: U(zA, G) = 0.3 · ln(zA) + 0.7 · ln(G) and U(zB, G) = 0.8 · ln(zB) + 0.2 · ln(G). Suppose Mrs. B donates nothing (remember that we are modeling voluntary contributions). How much does Mr. A donate in this case?
A. 0
B. 30
C. 70
D. 100

Added by Martin F.

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