Question #49918

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

Expert's answer

Q = 20,000 pairs a year, P = $10, FC = $60,000, VC = $120,000. 10 percent increase in output would not affect fixed costs but would reduce average variable cost by 40 cents.

Price reduction of 5 percent to increase sales, total revenues, and profits. Ed = −2.

a. Evaluate the impact of the proposal to cut prices on

(i) total revenue will increase, because demand is elastic and sales will increase by 2*5 = 10 percent. So, TR1 = 10*20,000 = 200,000, TR2 = P*Q = 9.5*22,000 = $209,000

(ii) total cost will change too: TC1 = $180,000, TC2 = 60,000 + ((120,000/20,000) - 0.6)*22,000 = $178,800, so total costs will decrease.

(iii) total profits will increase TP1 = TR - TC = 20,000, TP2 = 209,000 - 178,800 = $30,200.

b. If average variable costs are assumed to remain constant over a 10 percent increase in output, TC2 = 60,000 + 6*22,000 = 192,000, the effects of the proposed price cut on total profits will be TP2 = 209,000 - 192,000 = 17,000, so total profits will decrease.

Price reduction of 5 percent to increase sales, total revenues, and profits. Ed = −2.

a. Evaluate the impact of the proposal to cut prices on

(i) total revenue will increase, because demand is elastic and sales will increase by 2*5 = 10 percent. So, TR1 = 10*20,000 = 200,000, TR2 = P*Q = 9.5*22,000 = $209,000

(ii) total cost will change too: TC1 = $180,000, TC2 = 60,000 + ((120,000/20,000) - 0.6)*22,000 = $178,800, so total costs will decrease.

(iii) total profits will increase TP1 = TR - TC = 20,000, TP2 = 209,000 - 178,800 = $30,200.

b. If average variable costs are assumed to remain constant over a 10 percent increase in output, TC2 = 60,000 + 6*22,000 = 192,000, the effects of the proposed price cut on total profits will be TP2 = 209,000 - 192,000 = 17,000, so total profits will decrease.

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