The table below shows complete data for buyers and sellers of a given commodity. Each buyer and seller in the market is assumed to supply or demand a single unit of the good. The sellers' column shows the number of sellers in the market at each possible production cost level. Likewise, the buyers' column shows the number of buyers in the market at each possible subjective valuation of the good. (See the notes from Lecture 3 if you need help interpreting the table.)
a) Draw the graph like the one shown in lecture to show the market supply and demand curves. Your graph should show intersecting supply and demand curves. Each should have a stair-step appearance, with the right end of each step reflecting the accumulated level of supply or demand for the corresponding price level.
Value Sellers Buyers
$2 4 6
$4 5 10
$6 5 5
$8 8 4
$10 8 5
b) Find the market equilibrium price and quantity. Is the resulting allocation efficient? Explain. (In this setting, define "efficiency" to mean that there's no alternative allocation or set of trades, which would results in larger total profits over all traders).
c) Suppose a unit tax is imposed on buyers, thus decreasing each of the net values or buyers in the table by one. Find the new equilibrium price and quantity, and compare the efficiency of the resulting allocation with the case of no tax.