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 $$P = 24 - 0.0004 Q _ { d }$$ . The price and output of water that maximize social surplus are _____ and _____,respectively.

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 $$P = 24 - 0.0004 Q _ { d }$$ .  The price and output of water that maximize social surplus are _____ and _____,respectively.

Quizplus · Accepted Answer

To maximize social surplus, we need to find the output level where marginal cost equals marginal benefit (which is represented by the inverse demand equation).

First, we need to determine the quantity of water demanded at the price that makes LMC = $4. To do this, we set the inverse demand equation equal to $4:

$$4 = 24 - 0.0004 Q _ { d }$$

Solving for Qd, we get Qd = 50000.

So the quantity demanded at a price of $4 is 50,000 units.

Next, we need to find the corresponding price at that quantity. Plugging 50,000 into the inverse demand equation, we get:

$$P = 24 - 0.0004 \times 50,000 = $4 $$

So the price that maximizes social surplus is $4 and the output level is 50,000 units. Therefore, the answer is C.

A Municipal Water Utility Employs Quasi-Fixed Capital Inputs-The Water Treatment P=24−0.0004QdP = 24 - 0.0004 Q _ { d }P=24−0.0004Qd​

A Municipal Water Utility Employs Quasi-Fixed Capital Inputs-The Water Treatment $P = 24 - 0.0004 Q _ { d }$