Part B. Read the following story of a village and solve questions 24-28.
Suppose that there is a community having 1000 residents. There is one public good, the irrigation well. Residents have the same utility function u(x_(i),G)=x_(i)-(90)/(G), where x_(i) is a numeraire good, measured by the money spent on private consumption and G is the size of the irrigation well. The unit price of the public good is 10 yuan. Every resident has an income of 1,000 yuan per year.
24. (3 points) Write down the expression for the marginal rate of substitution between private consumption and the public good for any resident.
25. (5 points) How to find the Pareto efficient size of the public good? Set up the problem and show the condition.
25. (5 points) Suppose that everyone in the community pays an equal share of the cost of the public good. What is the amount of public good preferred by an individual resident?
27. ( 3 points) If the town supplies the public good that is the size demanded by the residents in question 26, will it be larger than, smaller than, or the same size as the Pareto optimal size?
23. (5 points) If residents are allowed to contribute voluntarily instead of sharing the cost of the public good equally, how much would each resident prefer to contribute given their prediction of others contribution /bar (G) ? What do you find compared with the case in question 25 ?
Part B. Read the following story of a village and solve questions 24-28
Suppose that there is a community having 1000 residents. There is one public
good, the irrigation well. Residents have the same utility function u(x,G)=x,-90/G, where x, is a numeraire good, measured by the money spent on private consumption and G is the size of the irrigation well. The unit
price of the public good is 10 yuan. Every resident has an income of 1,000 yuan
per year. 24. (3 points) Write down the expression for the marginal rate of substitution
between private consumption and the public good for any resident.
25. (5 points) How to find the Pareto efficient size of the public good? Set up the
problem and show the condition.
25. (5 points) Suppose that everyone in the community pays an equal share of the cost of the public good. What is the amount of public good preferred by
an individual resident?
27. (3 points) If the town supplies the public good that is the size demanded by
the residents in question 26, will it be larger than, smaller than, or the same
size as the Pareto optimal size?
23. (5 points If residents are allowed to contribute voluntarily instead of
sharing the cost of the public good equally, how much would each resident prefer to contribute given their prediction of others contribution G ? What do you find compared with the case in question 25?