Exercise 10.7
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 $40 each. Fixed costs amount to $240,000, and total variable costs equal $480,000. 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 (decrease, or increase) total revenues from $800,000 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 $ ?.
Selling price per pair = $40
Total variable cost of 20,000 pairs = $480,000
Hence, variable cost per pair = 480,000/20,000
= $24
The arc elasticity of demand with respect to prices is estimated at −2.
Price reduction = 5%
Hence, new selling price per unit = 40 x 95%
= $38
Elasticity of demand = % change in demand/% change in price
- 2 = % change in demand/- 5%
Hence, % increase in demand = 10%
Current sales = 20,000 pairs
After price reduction, sales will increase to = 20,000 x 110%
= $22,000 units
Sales revenue after 5% price reduction = Number of units sold x Selling price per unit
= 22,000 x 38
= $836,000
The proposal to cut prices by 5 percent would increase total revenues from $800,000 to $836,000
(a) When variable cost per unit falls by 40 cents
Sales (i) | 836,000 |
Total Variable cost (22,000 x 23.60) | 519,200 |
Total fixed costs | 240,000 |
Total cost (ii) | 759,200 |
Profit (i) - (ii) | $76,800 |
(b) When variable cost per unit remains constant
Sales (i) | 836,000 |
Total Variable cost (22,000 x 24) | 528,000 |
Total fixed costs | 240,000 |
Total cost (ii) | 768,000 |
Profit (i) - (ii) | $68,000 |
Kindly comment if you have any doubt. Thanks.
Exercise 10.7 Royersford Knitting Mills, Ltd., sells a line of women’s knit underwear. The firm now...
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