Answer to Question #298661 in Microeconomics for Jesse

Question

Ernie 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 3

Cost of third bottle 5

Cost of fourth bottle 7

a. From this information, derive Ernie’s supply schedule. Graph his supply curve for bottled water.

b. If the price of a bottle of water is $4, how many bottles does Ernie produce and sell? How much producer surplus does Ernie get from these sales? Show Ernie’s producer surplus in your graph.

c. If the price rises to $6, how does quantity supplied change? How does Ernie’s producer surplus change? Show these changes in your graph.

Answer 1

a. From this information, derive Ernie’s supply schedule. Graph his supply curve for bottled water.

Ernie’s supply schedule for water is:

Graph:

b. If the price of a bottle of water is $4, how many bottles does Ernie produce and sell? How much producer surplus does Ernie get from these sales? Show Ernie’s producer surplus in your graph.

Ernie sells two bottles of water when the price of a bottle of water is $4.

Surplus and graph

His producer surplus is depicted in the diagram below as region A. Ernie receives $4 for his first bottle of water, but it only costs $1 to make, therefore he has a $3 producer surplus. He also gets $4 for his second bottle of water, which costs $3 to make, so he has a $1 producer surplus. As a result, Ernie's total producer surplus is $3 + $1 = $4, which corresponds to the area of A shown in the picture below.

c. If the price rises to $6, how does the quantity supplied change? How does Ernie’s producer surplus change? Show these changes in your graph.

When the price of a bottle of water increases from $4 to $6, Ernie sells three bottles, a one-percentage-point gain.

Surplus change and graph

His producer surplus is comprised of both areas A and B in the figure below, with the size of area B increasing. He receives a $5 producer surplus from the first bottle ($6 price minus $1 cost), a $3 producer surplus from the second bottle ($6 price minus $3 cost), and a $1 producer surplus from the third bottle ($6 price minus $5 price), for a total producer surplus of $9. When the price of a bottle of water goes from $4 to $6, the producer surplus increases by $5 (the size of area B).