2. When water is scarce, as is the case in much of the western United States, many water utility companies use an increasing-block-rate pricing structure. Under this type of pricing structure, the price per cubic foot (or cf, about 7.5 gallons) of water is low at first. Once a household’s consumption passes some threshold, the price per cf increases (They have entered a new “block” where each additional cf now costs more). Usually there are at least three blocks of pricing, sometimes more. For example, for a household in Colorado Springs, CO, the first 1,000 cf of water costs about 4 cents per cf. The next 1,500 cf cost about 7 cents per cf. Any additional water (purchased after the first 2,500 cf) costs about 10 cents per cf.
(a) We want to see how this type of pricing structure would affect a household’s budget set. Let’s think about a Colorado Springs household choosing between bundles of two goods: cf of water (on the horizontal axis) and non-water expenditure (measured in dollars and on the vertical axis). Suppose that the household has allocated a maximum of $300 to be spent on water, so m = 300. The prices of water are given above. If the household allocated this entire budget to non water expenditures, how much could they spend (i.e. what is the vertical axis intercept)? If they allocated their entire budget towards water, how many cubic feet could they afford (i.e. what is the horizontal axis intercept)?
(b) The slope of the budget line will not be constant. Why is that the case?
(c) Where does the budget line kink (i.e. where does the slope change)? What is the slope of the budget line for each section?(d) Using the information you found in parts (a) through (c), plot the budget line for this household. Note that it will probably be useful to use different scales for the two axes. Be sure to label the axes, the intercepts, and the combinations of non-water expenditure and water consumption at each kink