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Demand Analysis for Robinson Plastics.

Robinson Plastics makes clear plastic products with injection molding techniques. Their latest invention is a plastic cup with a sharp blade mounted inside to cut prescription pills into small pieces. The cup is placed over the pill and as the cup is pressed down, the pill is split into pieces which are contained inside the cup. Because the cup is above the pill, persons can see how the pill is cut and keep the pieces contained. The presumed market is drugstores who would then sell to customers who want to reduce dosage size.
A survey of local drug manufacturers and retailers suggest that market demand over the next year can be characterized by:
Q = 2,000,000 - 100,000*P + 5*A
Where Q=unit sales, P=price in dollars, and A=advertising expenditure in trade journals and publications.
Robinson is considering a price of either $1 or $2 and an advertising budget of $10,000. Robinson has estimated production cost at $0.75 per unit.

a. Compute the quantity sold and the own price elasticity's at the $1 and $2 sales prices, assuming the stated advertising budget.
b. What is the advertising elasticity at the sales price of $2 assuming the stated advertising budget.
c. How useful is this demand equation for forecasting demand for the pill slicer in the next five years? Explain.

Solution Preview

a. First we plug in 10000 for A

Q = 2,000,000 - 100,000P + 50,000 = 2,050,000 - 100,000P

If P = 1, Q = 1,950,000 units
If P = 2, Q = 1,850,000 units

Price elasticity of demand at P = 1 is P/Q * dQ/dP = 1/1,950,000 * -100,000 = -0.0513 (or 0.0513, depending on which convention of elasticity you use)

PED at P = 2 ...

$2.19