1. Two homeowners (indexed by A and B) possess the following demand curves for the consumption of landscaping water.
a) What is the maximum price each consumer is willing to pay for a unit of water? At what quantities is the marginal benefit to each consumer of more water equal to zero?
b) Calculate the price elasticities of demand for A and B at P=30, 20 and 10. How does the elasticity change as you move down the demand curve?
c) Assuming these are the only consumers of water, calculate the total ("market") demand curve, making sure to write it in a form where P is on the left hand side of the equation. Graph these equations neatly.
d) Calculate the price elasticities of demand for the market demand curve you calculated in c) at the prices specified in part b).
e) Suppose the local water utility charges consumers P=$10 for each unit of water. How much will be consumed overall? The utility, facing reduced deliveries
from the Bureau of Reclamation due to a wide-scale drought, enlists you to figure out the effect of an increase in rates to $15. What is the new level of consumption and by how much does each consumer alter their consumption?
f) Given the scenario in e), what is the consumer surplus (total benefits net of expenditures) to consumers from the water they consume after the price increase? How is this surplus divided across the individuals?
2. Continuing from question 1, suppose there is a newcomer (indexed by C) to this (very small!) community with the following demand curve for water
What is the new market demand curve (be careful)? Draw this demand curve and represent it in equation form.
3. The elasticity of demand (at currently consumed quantities) for one good is ½ while that for another is 2. Both goods are consumed in identical quantities. Suppose your objective is to raise revenue for education by imposing a 5% tax on purchases of one or the other good.
Assuming you only care about raising the largest amount of money possible, which good would you tax? Why? Does your answer help to explain the high tax rates observed on potentially addictive substances?
4. The price of gasoline spikes by 50% due to a major hurricane wiping out a large amount of US refinery capacity. A week after the price spike, it is observed that Americans reduce their consumption by only 20%. Is demand on this time scale elastic or inelastic (circle
one)? Suppose the price remains at this new level for a period of months and consumers expect it to persist indefinitely. Do you expect the reduction in consumption observed in the first week to increase/decrease/remain the same (circle one)? Briefly in the space below explain your answer in terms of long-run vs. short-run demands.