The demand curve for product X is given by Q X d = 340 - 4P X . a. Find the inve

Question

The demand curve for product X is given by QXd = 340 - 4PX.

a. Find the inverse demand curve.

PX = - QXd

Instructions: Round your answer to the nearest penny (2 decimal places).

b. How much consumer surplus do consumers receive when Px = $45?

$

c. How much consumer surplus do consumers receive when Px = $30?

$

d. In general, what happens to the level of consumer surplus as the price of a good falls?

The level of consumer surplus (Click to select)increasesdecreasesdoesn't change as the price of a good falls.

Explanation / Answer

The demand curve for product X is given by QXd = 340 - 4PX.

a. Find the inverse demand curve.

  QXd = 340 - 4PX

4PX = 340 - QXd

  PX =85 - 0.25 * QXd

b.How much consumer surplus do consumers receive when Px = $45?

At Px = $40, we have QXd =340 - 4*(45) = 160

The demand curve has a vertical intercept at P=85.

Consumer Surplus is equal to the area of a triangle with height (85 - 45) = $40/unit and width = 160 units.

Te consumer surplus is = 1/2 * QXd *(104 - Px)  = 1/2 * 160 * 40= $3200

c. How much consumer surplus do consumers receive when Px = $30?

At Px = $30, we have QXd = 340 - 4*(30) = 220

The demand curve has a vertical intercept at P=85.

Consumer Surplus is equal to the area of a triangle with height (85 - 30) = $55/unit and width 220 units.

Te consumer surplus is = 1/2 * QXd *(104 - Px)  = 1/2 * 220 * 55= $6050

d. In general, what happens to the level of consumer surplus as the price of a good falls?

The consumer surplus increases as the price of a good falls because buyers who were already buying the good receive an increase in consumer surplus because they are paying less

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