Question

Let the following be the supply and demand for coconuts.

P            2            3            4            5            6            7            8            9            10            11            12

Q_s         100       200      300        400       500       600    700       800      900     1000    1100

Q_D        550       500      450        400       350       300    250       200      150     100    50

Now imagine that there is a price ceiling on coconuts at $3 but in order to prevent wasting peoples' time by making them wait in line, the government hands out ration coupons to people. In order to buy a coconut you need a coupon. Assume that the number of coupons is the appropriate number to clear the market with the price ceiling (you should know what that is). Now notice that the government probably doesn't know who has the highest marginal value for coconuts so, while this will eliminate the waste from the line it will most likely not allocate the coconuts efficiently. However, we can solve this problem by allowing people to trade the coupons! So imagine that there is such a market and it is perfectly competitive.

a. What will the price of a coupon be in this market?

b. Draw the price ceiling graph and identify the consumer and producer surplus, and the dead weight loss. There should be an area in there which would have been the cost of the line had there been a line. Label this area "A." Who gets this surplus now?

Answer 1

As per the given information, demand = supply for price $5. At this price, the QD = QS = 400.
Now as government imposes price ceiling, the price will drop to the ceiling if it is below equilibrium. Ceiling is $3. Equilibrium price is $5. Hence price will decrease to $3. This can be shown as follows:

Here the equilibrium quantity is 400 units and price is $5. The green line shows the price ceiling. Hence price will drop to $3. From the table we can see, at this price, QD = 500 and Qs = 200.
Hence there arises a shortage of supply by 300 units.

a) To avoid crowd, government decides to distribute coupon. The price of coupon will be $3, equal to the ceiling.

b) The required areas are as follows :

The yellow area is the consumer surplus after price ceiling. (increases)
Gray area is producer surplus after ceiling. (decreases)
Red area is deadweight loss.

Since the price has decreased due to ceiling, this area goes to the consumer in terms of increase in consumer surplus. (marked pink and A)

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