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Consider a community that only has access to non-drinkable water that needs to be boiled before it can be consumed

Economics

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Consider a community that only has access to non-drinkable water that needs to be boiled before it can be consumed. A NGO is evaluating to provide access to drinkable water to this community, and in order to do so, it needs to learn the community's valuation of access to drinking water. All the members of the community are identical and have the following utility function: U (x, c, ; = (qx)° where x denotes water consumption in gallons and c denotes consumption of "all other goods". The utility derived from water consumption depends on whether it is drinkable or not. If water is drinkable then q = 2 and if not q = 1. Let the price of water, measured in dollars per gallon, be denoted pc, and without loss of generality assume that pc, the price of "all other goods" is one:pc = 1. Finally, let m denotes the total income of a member of this community. 1. (3 points) Is this functional form a reasonable representation of prefer-ences? Explain briefly why. 2. (5 points) Suppose that a = 0.5 Solve for the Marshallian demand func-tions and for the indirect utility function. 3. (5 points) Show that if both prices increase by 20 percent, income should also increase by the same percentage to keep utility constant. What can you conclude about the the degree of homogeneity of the indirect util-ity function? Explain why your conclusion holds for any indirect utility function. 
4. (5 points) Suppose that m = 100 and that pr = 25. What is the maximum that a member of the community is willing to pay for drinking water if the price is kept the same? Show your work and explain. 5. (5 points) Suppose that the project of the NGO did not work and the community will not get access to drinking water. The local government wants to compensate the community such that it gets the level of utility it would have reached if the project was successful. How much money should the government transfer to each member of the community to achieve this goal? Show your work and explain. 6. (6 points) Compare your answers to the part 4 and part 5. Explain why they differ or why they are the same. Use a clearly labeled figure. 7. (6 points) The local government had to cancel the compensation due to a reduction in its budget. However, it managed to find a firm that is willing to provide access to drinking water for the community but not to keep the current price. The firm will provide access to drinking water at a price that is 44 percent higher that the current price. The local government puts this alternative to a vote. Would the community get access to drinking water? 
 

4. Yessica likes to take a break early in the morning and also late in the afternoon to buy either a cup of coffee or a glass of orange juice. One day she purchases coffee in the morning, but she buys orange juice in the afternoon. If Yessica had the same budget in the morning as she did in the afternoon and, moreover, neither the price of coffee nor the price of orange juice change during the day, then her preferences mast be unstable. 

6. A consumer joins a cooperative to avoid a price increase. He is charged exactly his EV. If, after joining, the offer is withdrawn, but he is compen-sated an amount equal to his CV, then be must be better off.