Jacoby Company received an offer from an exporter for 26,200 units of product at $18 per unit. The acceptance of the offer will not affect normal production or domestic sales prices. The following data are available: Domestic unit sales price $25 Unit manufacturing costs: Variable $12 Fixed $5 What is the differential revenue from the acceptance of the offer?

The revenue represents the total sales of the product, regardless of the costs, then If the company produced initially Q units the initial revenue will be

Initial Revenue=total sales= P₁*Q₁

- Since the offer does not alter the domestic sales prices P₁ , the price P₁ remains constant.

- Since the sales does not affect normal production , the quantity sold to the domestic market Q₁ is also not affected ( i don't need to resign units to the domestic market to sell to the exporter)

then

New revenue= Revenue from the exporter + Revenue from the domestic market = Revenue from the exporter + Initial revenue

where Revenue from the exporter=P₂*Q₂ , P₂= price sold to the exporter and Q₂= units sold to the exporter

therefore the change in revenue will be

Change in Revenue= New revenue - Initial Revenue = Revenue from the exporter

Change in Revenue=P₂*Q₂=$18 /unit* 26200 unit = $ 471600

Note:

The profit represents the revenue, taking into account the costs. Then the change the initial profit will be

initial profit = P₁*Q₁ - (CF+CV*Q₁)

the New profit

New profit = P₂*Q₂+ P₁*Q₁ - [CF+CV*(Q₂+Q₁)]

and the change in profit

change in profit= New profit - initial profit = P₂*Q₂+ P₁*Q₁ - [CF+CV*(Q₂+Q₁)] -[P₁*Q₁ - (CF+CV*Q₁)]= P₂*Q₂ - CV*Q₂ = (P₂- CV)*Q₂ = ($18 /unit- $12 /unit)* 26200 unit = $ 156000