The Georges Bank, a highly productive fishing area off New England, can be divided into two zones in terms of fish population. Zone 1 has the higher population per square mile but is subject to severe diminishing returns to fishing effort. The daily fish catch (in tons) in Zone 1 is F, = 250X, - 4 (X,)² where X, is the number of boats fishing there. Zone 2 has fewer fish per mile but is larger, and diminishing returns are less of a problem. Its daily fish catch is F2 = 100X2 - 1(X2)² where X, is the number of boats fishing in Zone 2. The marginal fish catch (MFC) in each zone can be represented as MFC, = 250 - 8X, MFC2 = 100 - 2Xz. There are 100 boats now licensed by the U.S. govemment to fish in these two zones. The fish are sold at $100 per ton. Total cost (capital and operating) per boat is constant at $1000 per day. Answer the following questions about this situation. If the boats are allowed to fish where they want, with no govemment restriction, how many will fish in each zone? Without government restrictions, 50 boats will fish in Zone 1 and 50 in Zone 2. (Enter your response rounded to the nearest integer.) What will be the gross value of the catch? The gross value of the catch will be $ 400,000'. (Enter your response rounded to the nearest integer.) If the U.S. government can restrict the number and distribution of the boats, how many should be allocated to each zone? (Assume the total number of boats remains at 100). Assuming the government wishes to maximize the net social value of the fish catch (i.e., the difference between the total social benefit and the total social cost) with 100 boats, then the government should assign 35 boats to Zone 1 and 65 boats to Zone 2. (Enter your responses rounded to the nearest integer.) What would be the gross value of the catch? The gross value of the catch would be S- (Enter your response rounded to the nearest integer.)
The Georges Bank, a highly productive fishing area off New England, can be divided into two zones in terms of fish population. Zone 1 has the higher population per square mile but is subject to severe diminishing returns to fishing effort. The daily fish catch (in tons) in Zone 1 is F, = 250X, - 4 (X,)² where X, is the number of boats fishing there. Zone 2 has fewer fish per mile but is larger, and diminishing returns are less of a problem. Its daily fish catch is F2 = 100X2 - 1(X2)² where X, is the number of boats fishing in Zone 2. The marginal fish catch (MFC) in each zone can be represented as MFC, = 250 - 8X, MFC2 = 100 - 2Xz. There are 100 boats now licensed by the U.S. govemment to fish in these two zones. The fish are sold at $100 per ton. Total cost (capital and operating) per boat is constant at $1000 per day. Answer the following questions about this situation. If the boats are allowed to fish where they want, with no govemment restriction, how many will fish in each zone? Without government restrictions, 50 boats will fish in Zone 1 and 50 in Zone 2. (Enter your response rounded to the nearest integer.) What will be the gross value of the catch? The gross value of the catch will be $ 400,000'. (Enter your response rounded to the nearest integer.) If the U.S. government can restrict the number and distribution of the boats, how many should be allocated to each zone? (Assume the total number of boats remains at 100). Assuming the government wishes to maximize the net social value of the fish catch (i.e., the difference between the total social benefit and the total social cost) with 100 boats, then the government should assign 35 boats to Zone 1 and 65 boats to Zone 2. (Enter your responses rounded to the nearest integer.) What would be the gross value of the catch? The gross value of the catch would be S- (Enter your response rounded to the nearest integer.)
Chapter1: Making Economics Decisions
Section: Chapter Questions
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Transcribed Image Text:The Georges Bank, a highly productive fishing area off New England, can be divided into two zones in terms of fish population. Zone 1 has the higher population per square mile but is subject
to severe diminishing returns to fishing effort. The daily fish catch (in tons) in Zone 1 is
F, = 250X, - 4 (X,)²
where X, is the number of boats fishing there. Zone 2 has fewer fish per mile but is larger, and diminishing returns are less of a problem. Its daily fish catch is
F2 = 100X2 - 1(X2)²
where X, is the number of boats fishing in Zone 2. The marginal fish catch (MFC) in each zone can be represented as
MFC, = 250 - 8X,
MFC2 = 100 - 2X2.
There are 100 boats now licensed by the U.S. government to fish in these two zones. The fish are sold at $100 per ton. Total cost (capital and operating) per boat is constant at $1000 per
day. Answer the following questions about this situation.
If the boats are allowed to fish where they want, with no govemment restriction, how many will fish in each zone?
Without government restrictions, 50 boats will fish in Zone 1 and 50' in Zone 2. (Enter your response rounded to the nearest integer.)
What will be the gross value of the catch?
The gross value of the catch will be $ 400,000'. (Enter your response rounded to the nearest integer.)
If the U.S. government can restrict the number and distribution of the boats, how many should be allocated to each zone? (Assume the total number of boats remains at 100).
Assuming the government wishes to maximize the net social value of the fish catch (i.e., the difference between the total social benefit and the total social cost) with 100 boats, then the
government
| assign 35 boats
Zone 1 and 65 boats to Zone 2. (Enter your responses rounded to the nearest integer.)
What would be the gross value of the catch?
The gross value of the catch would be $
(Enter your response rounded to the nearest integer.)
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