Question

Royersford Knitting Mills, Ltd., sells a line of women’s knit underwear. The firm now sells about 20,000 pairs a year at an average price of $30 each. Fixed costs amount to $180,000, and total variable costs equal $360,000. The production department has estimated that a 10 percent increase in output would not affect fixed costs but would reduce average variable cost by 40 cents.

The marketing department advocates a price reduction of 5 percent to increase sales, total revenues, and profits. The arc elasticity of demand with respect to prices is estimated at −2.

The proposal to cut prices by 5 percent would   total revenues from $600,000 to

. Total costs would be

and total profits would be

.

If average variable costs are assumed to remain constant over a 10 percent increase in output, total profits after a 5 percent price cut would be

.

Answer 1

Initial Quantity= 20000

Initial price= $30

Initial Total variable cost= 360,000

Initial average variable cost= Total variable cost/Quantity= $18

Initial total revenue= $30 x 20000= $600,000

Fixed cost= 180,000

Initial total cost= 360,000+180,000= 540,000

Initial profit= 600000-540000= 60,000

New Quantity after 10% increase= 20000+20000(10%)= 22000

New price after 5% decrease= $30-$30(5%)= $28.5

New total revenue= $28.5 x 22000= $627,000

The proposal to cut prices by 5 percent would increase total revenues from $600,000 to $627,000.

New average variable cost with reduction of 40 cents= $18-0.40= $17.60

New Total variable cost = $17.60 x 22000= $387,200

New total cost= 387200+180000= $567,200 (increased)

Total profit would be (627,200-567,200=) 60,000 (same)

If Average variable cost remain same then

Total variable cost= $18 x 22000= 396,000

Total cost= 396000+180000= $576000

Profit= 627200-576000= $51,200