$2.$ Problems and Applications Q$5$

Dmitri 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 Dmitri's supply schedule.

Price

Quantity Supplied

$$1$ or less

$$1$ to $$4$

$$4$ to $$7$

$$7$ to $$9$

More than $$9$

Based on Dmitri'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 $(0,0).$

Dmitri's Supply

Price $=$ $$5$

Quantity Sold

Producer Surplus

$0$

$1$

$2$

$3$

$4$

$5$

$10$

$9$

$8$

$7$

$6$

$5$

$4$

$3$

$2$

$1$

$0$

Price of Water

Quantity 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 Dmitri will produce and sell at that price. Finally, use the purple point $($diamond symbol$)$ to shade the area that represents Dmitri's producer surplus.

In this case, Dmitri receivesin producer surplus from his water sales.

If the price rises to $$8,$ Dmitri now sellsbottles of water. This his producer surplus to$.$