Question

1. Knitting Mills 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 $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 is estimated at -2.
2. Evaluate the impact of the proposal to cut prices on (1) total revenue, (2) total cost, and (3) total profits.
3. 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. 

Answer 1

The following is the information about the firm:-

• Firm sells about 20,000 pairs

• Average price is $10

• Fixed cost is $60,000

• Total variable cost is $120,000

• It is expected that 10 % increase in the output would not affect fixed costs but reduce the average variable cost by 40 cents. A 5% price reduction to increase sales and elasticity arc is -2.

a.

(i) Total revenue will increase because demand is elastic and sales will increase by $=(2\times 5)=10\%$

So, $TR1=10\times 20000=\$200000$

$TR2=P\times Q=9.5\times 22000=\$209000$

(ii) The total cost will change too: $TC1=\$180000$

$TC2=(60000\times\frac {120000}{20000}-0.6\times22000)=\$178000$

Hence total costs will decrease.

(iii) Here total profits will increase .

$TP1=TR-TC=20000$

$TP2=209000-178000=\$30200$

b. When the average variable costs are assumed to remain constant over a 10 percent increase in output, $TC2=60000+(6\times22000)=\$192000$

The effects of the proposed price cut on total profits will be ,

$TP2=209000-192000=\$17000$ .so the total profits will decrease in this case.