Do the following functions exhibit increasing, constant, or decreasing returns to scale? What happens to the marginal product of
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Solution :
1. The break even sales in units is given by :
Break even sales in units =
Where, contribution per unit = selling price per unit - variable cost per unit
The anticipated break even sales in units of Cleaves company in the coming year is :
Break even sales in units =
Contribution per unit = $ 100 - $ 60
= $ 40
So the company anticipates its breakeven sales at 12,000 units.
2. In order tot earn profit the sales generated should overcome the breakeven point. The desired profit is $240,000, the sales required to earn the desired profit can be computed using the formula :
Desired sales in units =
= 18,000 units
Thus, the sales in units required to earn a profit of $ 240,000 are 18,000 units.
3. The sales in excess of the breakeven point would yield a profit on the contrary the sales below the breakeven point would result in a loss.
In the given sales in dollar = breakeven sales in units x selling price per unit
= 12,000 x 100
= $ 1,200,000
∴ the sales above $1,200,000 would result in a profit whereas the sales below $1,200,000 would result in loss.
The cost volume profit chart below indicates the profit, loss, breakeven at different sales levels :
Sales levels Result
1,200,000 Breakeven
1,000,000 Loss
800,000 Loss
400,000 Loss
200,000 Loss
4. The income on sale of 16,000 units is computed below :
Particulars Amount is $
Sales 1,600,000
Less : variable cost 960,000
Contribution 640,000
Less : Fixed cost 480,000
Profit 160,000