Assume the government of a desert community wants to punish the excessive water usage, where "excessive" is defined as any usage greater than 100 gallons/week. To do this, the government paces a flat $100 income tax on anyone who consumes more than 100 gallons/week of water in any given week (so this tax could theoretically be levied 52 times per year). People who use less than 100 gallons of water each week will not face this $100 special tax. For these problems, consider the decisions between water consumption, X (sub) w and consumption of a composite good, X (sub)c, where P(sub)w =$2/gallon and the composite good's price is numeraire. Suppose Michael lives in this desert community and has a weekly income of $1000.
1. Graphing Michaels budget constraint over (X(sub)w , X(sub)c) bundles, what is the slope of his budget constraint for bundles containing MORE than 100 gallons of water?
2. Determine the slope of Michaels budget constraint at the point (X (sub)w, X(sub)c)=(100,750)?
3. Calculate the maximum amount of water Michael could possibly consume in a week in the presence of this tax? (Assume that Michael's $1000 per week budget is fixed and that the tax is levied instantly once X (sub) w>100)