Chapter 19 Problem Set pages 384–385
Problem 2
a. what is the break-even level of output for each scale of operation?
Total cost for the first scale of operation; TC= $3,000 +$2.8Q
Sale Price/unit = $4
Q = break even quantity,
4 x Q = Revenue = TC = 3,000 + 2.8 x Q
4Q = 3,000 + 2.8Q
Q = 3,000 / (4 - 2.8)
Q = break even quantity = 2,500
Total cost for the second scale of operation = TC = $5,000+$2.4Q
4 x Q = Revenue = TC = 5,000 + 2.4 x Q
4Q = 5,000 + 2.4Q
Q = 5,000/ (4 -2.4)
Q = break even quantity = 3,125
b. What will be the firm’s profit for each scale of operation if sales reach 5,000 units?
Profit = Revenue - TC = 4 x Q - TC
Q = 5,000 units
First scale of operation:
Profit = 4Q - (3,000 + 2.8Q) = 4 x 5,000 - (3,000 + 2.8 x 5,000)
Profit = $ 3,000
Second scale of operation:
Profit = 4Q - (5,000 + 2.4Q) = 4 x 5,000 - (5,000 + 2.4 x 5,000)
Profit = $ 3,000
C. One-half of the fixed cost are noncash (depreciation). All other expenses are for cash. If sales are 2,000 units, will cash receipts cover cash expenses for each scale of operation?
First scale of operations:
Cash receipts = Revenue = 4 x Q = 4 x 2,000 = $8,000
Cash expenses = Half fixed expenses + variable expenses
= 3,000 / 2 + 2.8 x 2,000 = $7,100
Yes, cash receipts can cover the cash expenses
Second scale of operations:
Cash receipts = Revenue = 4 x Q = 4 x 2,000 = $8,000
Cash expenses = Half fixed expenses + variable expenses
= 5,000 / 2 + 2.4 x 2,000 = $7,300
Yes, cash receipts can cover the cash expenses
d. If the management selects the scale of production with higher fixed cost, what can it expect in years 1 and 2?
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Year 1:
TC = 5,000 + 2.4 x Q
TC= $5,000+$2.4(4000) = $14,600
TR= $4 x 4000= $16,000
Total Profit = TR-TC = $16,000-$14,600 = $1,400
Year 2:
TC= $5,000+ $2.4 (5000) = $17,000
TR= $4 x 5000= $20,000
Total Profit= TR- TC = $20,000-$17,000= $3,000
ii. On what grounds can management justify selecting this scale of operation?
Management may justify selecting this scale of operation since all the costs are covered and they bring in more than the break-even point.
iii. If sales reach only 5,000 a year, was the correct scale of operation chosen?
TC = $5,000+ $2.4 (5000) = $17,000
TR = $4 x 5000= $20,000
Total Profit = TR- TC = $20,000-$17,000= $3,000
Yes, the correct scale of operation will have been chosen because they will be making more than the break-even point.
Problem 3
A firm has the following total revenue and total cost schedules: TR = $2Q and TC = $4,000 + $1.5Q.
a) i. What is the break-even level of output?
TR=TC
$2Q = $4,000 + $1.5Q
Q = $4,000 / (2 - 1.5)
Q = $8,000
ii. What is the level of profits at sales of 9,000 units?
Total Profit = TR-TC
TC = $4,000 + $1.5Q (9,000 units) = $17,500
TR = $2Q = $2 x 9, 000 units = $18,000
Profit = TR – TC = $18,000- $17, 500 = $500
Profit = $500
b) TC = $6,000 + $0.5Q. What is the break-even level of output?
$2Q = $6,000 + $0.5Q
$2Q - $0.5Q= $6,000
$1.5Q= $6,000
Q = Break= $4,000
ii. What is the level of profits at sales of 9,000 units?
TC = $6,000 + $0.5Q (9,000 units) = $10,500
TR = $2Q = $2 X 9, 000 units = $18,000
Profit = TR – TC = $18,000- $10,500= $7,500 profit
Profit = $7,500
Problem 4
a. What level of sales is necessary to break even if the product is sold for $4.25?
Q= $125,000/ ($4.25 - $2.50) = 71,429 units
What will be the manufacturer ‘s profit or loss on the sales of 100,000 units?
TC = $125,000 + $2.50Q = $125,000 + $2.50 x 100,000= $375,000
TR = $4.25Q = $4.25 x 100,000 = $425,000
Profit = $425,000 – 375,000 = $50,000 profit
b. If fixed cost rise to $175,000, what is the new level of sales necessary to break even?
$4.25Q = $175,000 + $2.50Q
$1.75Q= $175,000
Q= 100,000 units
c. If variable cost decline to $2.25 per unit, what is the new level of sales necessary to break-even?
$4.25Q = $125,000 + $2.25Q
$2Q= $125,000
Q = 62,500 units
d. If fixed cost were to increase to $175,000, while variable cost declined to $2.25 per unit, what is the new break-even level of sales?
$4.25Q = $175,000 + $2.25Q
$2Q = $175,000
Q = 87,500 units
