Practice Problem Week 6 Econ 3101
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Practice Problem
Week 6 Econ 3101
Equilibrium Wait Times
In this practice problem we redo the equilibrium wait time model from class, but we add a twist. Here consumers will differ in the waiting cost per hour.
Like before, demand is perfectly elastic. For this problem, we change the numbers a bit compared to class. Suppose everyone has a reservation price of T = $12 per widget. The inverse demand curve is given by
pD (Q) = 12.
The inverse supply curve is 45 degree line just like class,
pS (Q) = Q.
In class, consumers were the same in waiting cost, which equaled a constant of $1 per hour for each unit of demand.
Now we allow waiting cost to differ. Suppose buyers are sorted from lowest waiting cost to highest waiting cost. Suppose the waiting cost at Q units of demand is given
by
c(Q) = dollars
To understand how this works, suppose consumers for the first three units of de- mand all wait one hour. Evaluating at Q = 3 (the last on in) we get c(3) = 1 dollar. Evaluating at Q = 0 (right at the beginning ) we get c(0) = 0 dollars. The average across the first three consumers is then 0.5 dollars. The total cost of the wait time of one hour is then $1.50 = 3 × 0.5.
1. Suppose there is no possibility of waiting. What is the effect on consumers’ surplus and producers’ surplus of a price ceiling of $6.
2. Suppose that by standing in line, consumers can get priority for service in cases where there is a shortage.
(i) Define an equilibrium with waiting times. What is the equilibrium price, the equilibrium quantity, and the equilibrium waiting time?
(ii) Define consumer’s surplus as gross consumer surplus minus the dollar expendi- ture on widgets minus the value of waiting cost. What is the effect of the $6 price ceiling now that consumers have to pay with their time as well as money to get the good?
2022-12-14