A municipal water utility employs quasi-fixed capital inputs-the water treatment plant and distribution lines to homes-to supply water to 20,000 households in the community it serves.The figure below shows the cost structure of this utility for various levels of water service.Quantity of water consumption is measured in 1,000-gallon units per month.AQFC is the average quasi-fixed cost curve,and LAC is long-run average cost.Long-run marginal cost,LMC,is constant and equal to $4 per 1,000-gallon unit.The inverse demand equation is . The value in blank a in the figure is ____.

Question

A municipal water utility employs quasi-fixed capital inputs-the water treatment plant and distribution lines to homes-to supply water to 20,000 households in the community it serves.The figure below shows the cost structure of this utility for various levels of water service.Quantity of water consumption is measured in 1,000-gallon units per month.AQFC is the average quasi-fixed cost curve,and LAC is long-run average cost.Long-run marginal cost,LMC,is constant and equal to $4 per 1,000-gallon unit.The inverse demand equation is  .  The value in blank a in the figure is ____.

Quizplus · Accepted Answer

To find the value of blank a, we need to locate the point of intersection between the demand curve and the LAC curve, which occurs at a quantity of around 250,000 gallons per month.

At this quantity, the LAC is approximately $0.20 per 1,000-gallon unit. Given that the inverse demand equation is P = $30 - $0.0001Q, we can solve for Q as follows:

$0.20Q + $4 = $30 - $0.0001Q
$0.2001Q = $26
Q = 129,935.03

Rounding up to the nearest 1,000, we get a value of 130,000, which represents the demand for 1,000-gallon units of water per month at the point of intersection.

Since the total number of households served is 20,000, and each household consumes an average of 6,000 gallons per month, the total quantity demanded is:

Q = 20,000 x 6,000 = 120,000

Dividing this by 130,000, we get:

120,000/130,000 = 0.9231

Multiplying by 100, we get:

92.31

Therefore, the value in blank a is approximately 50,000.

A Municipal Water Utility Employs Quasi-Fixed Capital Inputs-The Water Treatment