Question

Pete's Power Pizzas sells a chocolate/tofu filled pastry. Pete's currently sells this pastry for $13.15, and makes it for a variable cost of $5.35 per pie. A drop in cocoa prices will reduce variable cost for this product by $0.52 per pie. Pete's is thinking of reducing the pie's selling price by $0.94. By what percent must Quantity demanded increase so that Pete's just maintains its current total contribution margin (margin per unit times units sold)? (Report your answer as a percent. Report 25.5%, for example, as "25.5". Rounding: tenth of a percent.) The answer is 5.7. Please show all work to get to the answer of 5.7.

Answer 1

Answer: So Margin is the difference between Selling price and Cost price

Since fixed cost is the same for both cases we can take it out of the equation.

So SP1= $13.15(Selling price in the first case)

He wants to reduce it by $0.94. So, in that case, SP2= 13.15-0.94 = $12.21 (Selling price in the second case)

Let take Q1, Q2 as Quantity demanded at first and second cases respectively. {assumption that produced and demanded quantity is the same}

V1(variable cost in the first case)= $5.35

V2(variable cost in the second case) = 5.35- .52 = $4.83 { A drop in cocoa prices will reduce variable cost for this product by $0.52per pie.}

So to maintain the current total contribution margin.

SP1Q1- Q1V1 =M= SP2Q2- Q2V2 {Margin is the difference between revenue and cost}{M is the margin}

13.15Q1-5.35Q1=12.21Q2-4.83Q2

7.8Q1=7.38Q2

Q2/Q1 = 1.057

SO Q2 is 1.057 times Q1

Put Q1=1 And Q2 will be 1.057 change in demand percentage =(Q2-Q1)/Q1 *100

= (.057)/1 *100=5.7 percentage increase.

So The demand should be raised by 5.7 percent.

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