Question

George has been selling 8,000 T-shirts per month for $9.50. When he increased the price to $10.50, he sold only 5,000 T-shirts.

Which of the following best approximates the price elasticity of demand?

-4.1538

-5.0769

-4.6154

-3.6923

Suppose George's marginal cost is $4 per shirt.

Before the price change, George's initial price markup over marginal cost was approximately ( 0.6368 OR 0.5211 OR 0.2895 OR 0.5789) . George's desired markup is   .

Since George's initial markup, or actual margin, was( LESS or GREATER) than his desired margin, raising the price was ( profitable or not profitable) .

Answer 1

Answer:

The formula for calculating elasticity of demand is

e = [(Q₂ - Q₁) / {(Q₁ + Q₂) / 2}] / [(P₂ - P₁) / {(P₁ + P₂) / 2}]

Here, Q₂ = 5000

Q₁ = 8000

P₂ = $10.50

P₁ = $9.50

e = [(5000 - 8000) / {(8000 + 5000) / 2}] / [($10.50 - $9.50) / {($9.50 + $10.50) / 2}]

e = [(- 3000) / 6500] / [(1) / 10]

e = - 4.6154

So, the following best approximates the price elasticity of demand: -4.6154.

The formula for initial markup is [(P - MC) / P] = [($9.50 - $4) / $9.50] = 0.5789.

The formula for the desired markup is [(- 1) / e] = (- 1 ) / (- 4.6154) = 0.2167.

Now, from this above calculation, we can clearly see that the initial markup is greater than the desired markup. So, according to theory, any increase in price would decrease profit.

Before the price change, George's initial markup over marginal cost was approximately 0.5789. George's desired markup is 0.2167.

Since George's initial markup or actual margin was greater than his desired margin, raising price was not profitable.