Robert E. Lee Grade School is contemplating a chocolate bar fund raiser. Weekly sales data from Mrs. Grant's fifth grade class indicate that:
Q = 4,000 - 1,000P
where Q is chocolate bar sales and P is price.
i) How many chocolate bars could be sold at RM2 each?
ii)
iii) What price would have to be charged to sell 2,500 chocolate bars?
iv)
iii) At what price would sales equal zero?
v) How many chocolate bars could be given away?
vi) Calculate the point price elasticity of demand at a price of RM2.
To answer these questions, we will use the equation Q = 4,000 - 1,000P, where Q is the quantity of chocolate bars sold and P is the price in RM.
i) To find out how many chocolate bars could be sold at RM2 each (P = 2), we can substitute P = 2 into the equation and solve for Q:
Q = 4,000 - 1,000(2)
Q = 4,000 - 2,000
Q = 2,000
So, 2,000 chocolate bars could be sold at RM2 each.
ii) No specific question was provided.
iii) To determine the price that would have to be charged to sell 2,500 chocolate bars (Q = 2,500), we can rearrange the equation and solve for P:
2,500 = 4,000 - 1,000P
1,000P = 4,000 - 2,500
1,000P = 1,500
P = 1.5
Therefore, the price that would have to be charged to sell 2,500 chocolate bars is RM1.50.
iv) At what price would sales equal zero (Q = 0)? We can substitute Q = 0 into the equation and solve for P:
0 = 4,000 - 1,000P
1,000P = 4,000
P = 4
Therefore, at a price of RM4, sales would equal zero.
v) The equation provided does not account for giving away chocolate bars. So, we cannot determine the number of chocolate bars that could be given away from this equation alone.
vi) To calculate the point price elasticity of demand at a price of RM2, we need to use the formula:
E = (dQ/dP) * (P/Q)
To find (dQ/dP), we take the derivative of the equation Q = 4,000 - 1,000P:
(dQ/dP) = -1,000
Substituting the values into the formula:
E = (-1,000) * (2/2,000)
E = -1
The point price elasticity of demand at a price of RM2 is -1. Note that this value indicates an elastic demand because it is less than -1.