Question #54057

The demand for Wanderlust Travel Services (X) is estimated to be:
QX = 22,000 – 2.5PX + 4PY – M + 1.5AX
where AX represents the amount of advertising spent on X, M is income per
capita, and the other variables have their usual interpretations.
Suppose that the price of good X is $450, good Y sells for $40, the company
utilizes 3000 units of advertising, and consumer income is $20,000.
a. Calculate the elasticity of demand for good X with respect to the price of X,
the price of Y, income, and advertising. (8 marks)
c. Calculate consumer surplus at the profit‐maximizing price if the marginal
cost is $264.

Expert's answer

QX = 22,000 – 2.5PX + 4PY – M + 1.5AX, PX = $450, PY = $40, AX = 3000 units, M = $20,000.

Then QX = 22,000 - 2.5*450 + 4*40 - 20,000 + 1.5*3,000 = 5,535 units

a. The elasticity of demand for good X with respect to the price of X,

the price of Y, income, and advertising is a coefficient before the PX, so Ed = -2.5, so the demand is elastic.

c. If the marginal cost is $264, then consumer surplus at the profit‐maximizing price will be found as follows:

P = MR = MC = $264,

Q(PX = 264) = 22,000 - 2.5*264 + 4*40 - 20,000 + 1.5*3,000 = 6,000

Q = 0, when PX = 6,660/2.5 = 2,664

Consumer surplus CS = 0.5*6,000*(2,664 - 264) = $7,200,000

Then QX = 22,000 - 2.5*450 + 4*40 - 20,000 + 1.5*3,000 = 5,535 units

a. The elasticity of demand for good X with respect to the price of X,

the price of Y, income, and advertising is a coefficient before the PX, so Ed = -2.5, so the demand is elastic.

c. If the marginal cost is $264, then consumer surplus at the profit‐maximizing price will be found as follows:

P = MR = MC = $264,

Q(PX = 264) = 22,000 - 2.5*264 + 4*40 - 20,000 + 1.5*3,000 = 6,000

Q = 0, when PX = 6,660/2.5 = 2,664

Consumer surplus CS = 0.5*6,000*(2,664 - 264) = $7,200,000

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