Question

Nick owns a water pump. Because pumping large amounts of water is harder than pumping small amounts, the cost of producing a bottle of water rises as he pumps more. Here is the cost he incurs to produce each bottle of water:

Cost of first bottle:	$1
Cost of second bottle:	$4
Cost of third bottle:	$7
Cost of fourth bottle:	$9

From this information, complete the following table by deriving Nick's supply schedule.

Price	Quantity Supplied
More than $9
$7 to $9
$4 to $7
$1 to $4
$1 or less

Based on Nick's willingness to sell, plot his supply curve as a step function on the following graph using the orange points (square symbol). Be sure to plot your first point at (0, 0).

Nick's SupplyPrice = $5Quantity SoldProducer Surplus012345109876543210Price of WaterQuantity of Water

Suppose the price of a bottle of water is $5.

Use the black line (plus symbol) to draw a price line at $5. Next use the grey point (star symbol) to indicate how many bottles of water Nick will produce and sell at that price. Finally, use the purple point (diamond symbol) to shade the area that represents Nick's producer surplus.

In this case, Nick receives $____ in producer surplus from his water sales.

If the price rises to $8, Nick now sells ____ bottles of water. This increases / decreases his producer surplus to $____.

Answer 1

As per the cost for each bottle given, we know that Nick will be willing to charge a price which at least covers the cost of production of number of bottles. Then we can say that Nick will sell 1 bottle of water only if the price he receives for is at least $1 (and won't make any sale if price is lower than $1). Similarly, till the price doesn't reach $4, he will not increase the supply. Only when price crosses the $4 threshold, will Nick increase the bottle supply from 1 to 2 bottles. Going this way, we have the following supply schedule:

Price	Quantity Supplied
More than $9	4 bottles
$7 to $9	3 bottles
$4 to $7	2 bottles
$1 to $4	1 bottle
$1 or less	No bottle (0 bottle)

Taking the price on vertical axis and quantity of water bottles supplied on the horizontal axis, and using the above supply schedule, we have the following supply curve (in form of step function):

Now, if the price of bottles is $5, notice it lies in price range of $4 to $7, so Nick will supply 2 bottles (as can also be seen from the graph below).

Producer surplus (PS) is the gain or surplus Nick receives due to price above the cost he incurs. So his producer surplus in this case (the purple area) can be calculated as:

PS = sum [change in quantity supplied*(price - cost at that quantity)]

PS = (1-0)*(5-1) + (2-1)*(5-4) = 4 + 1 = $5

If the price increase to $8, notice that it lies in the price range of $7 to $9, so 3 bottles will be supplied.

Producer surplus in this case is:

PS' = (1-0)*(8-1) + (2-1)*(8-4) + (3-2)*(8-7)

PS' = 7 + 4 + 1 = $12

Clearly, such price change increases his producer surplus to $12.