Using price elasticity of demand to evaluate a price cut

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 $10 each. Fixed costs amount to $60,000, and total variable costs equal $120,000. The production department estimates 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.

Evaluate the impact of the proposal to cut prices on (i) total revenue, (ii) total cost, and (iii) total profits.

If average variable costs are assumed to remain constant over a 10 percent increase in output, evaluate the effects of the proposed price cut on total profits.