Max Contribution and VC Estimation

Hi, could you please help me understand the nightmare that is this question and suggested answer? There are clear typos and I don’t know how they magically summoned the variable cost per unit. This is a CIMA P2 Mock exam question. Thank you!

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Question: If Jojo sets a selling price for his widgets at $200 per unit, he will achieve sales of 1,000 units per month. With a selling price of $220, he will reach sales of 950 units per month. What is the maximum contribution Jojo can hope to achieve?

Maximum contribution: $ ___________

Answer: The first step is to find the gradient b. The question provides us with two selling prices and the respective level of demand at these selling prices. Therefore, we can begin by calculating the gradient of the straight line, b.

b = change in price / change in quantity

b = (220 – 200) / (950 – 1,000) = -0.4

Then we can calculate the intersect ‘a’. It can be found using either of the selling prices and demand levels given. For example, price (P) = 200 when 1,000 units are sold and substituting -.04 for b.

200 = a – (0.4 * 100) so a = 600

Therefore, the equation is P = 600 – 0.4Q

MR = 600 – 0.8 Q

MC = VC so equating MR = MC : 100 = 600 – 0.8Q

So, Q – 625 and substituting Q in the Price function we get P = $350

Contribution per unit = $350 – $100 = $250 and total contribution = $250 x 325 units = $156,250.
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