A cellphone maker sells 6,000 units per month at $600 each.The firm is investigating whether a price cut to $500 is warranted.The firm's marginal cost of production of each phone is a constant $400 per unit.To maintain profits at their current level, quantity sold must increase to at least
A)8,000
B)10,000
C)12,000
D)15,000

Question

Quizplus · Accepted Answer

Currently, the firm's total revenue (TR) is:
TR = Price x Quantity = $600 x 6,000 = $3,600,000

The total cost (TC) is:
TC = Marginal Cost x Quantity = $400 x 6,000 = $2,400,000

Thus, the current profit (π) is:
π = TR - TC = $3,600,000 - $2,400,000 = $1,200,000

If the price is lowered to $500, the new TR would be:
TR' = $500 x Quantity

To maintain the same profit level, the new TC would have to be:
TC' = TC + (price reduction per unit x Quantity) = $2,400,000 + ($100 x Quantity)

Setting TR' = TC':

$500 x Quantity = $2,400,000 + ($100 x Quantity)

Solving for Quantity:

$400 x Quantity = $2,400,000

Quantity = 6,000

This is the breakeven point where the firm maintains its current profit level. However, the question asks for the quantity sold to increase to maintain profits. Therefore, we need to find the quantity that makes TR' = TC' greater than $3,600,000.

$500 x Quantity = $2,400,000 + ($100 x Quantity) + Profit increase

$400 x Quantity = $2,400,000 + Profit increase

Quantity = (2,400,000 + Profit increase) / 400

Plugging in the current profit level of $1,200,000, we get:

Quantity = (2,400,000 + 1,200,000) / 400 = 10,000

Therefore, to maintain profits at their current level and assuming a constant marginal cost of production, the firm would need to increase the quantity sold to 10,000 if they lower the price to $500. The answer is B) 10,000.

A Cellphone Maker Sells 6,000 Units Per Month at $600