Robinson Plastics makes clear plastic products with injection molding techniques

Question

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 Estimating Demand 42 placed over the pill, and as the cup is pressed down, the pill is split into pieces, and contained inside the cup. Because the cup is above the pill, persons can see how the pills are cut, and keep the pieces of the pill contained. The presumed market is pharmacies, which would then sell to customers who want to reduce dosage size. A survey of local drug manufacturers and retailers suggests that the market demand for the next year can be characterized by: Q = 2,000,000 - 100,000P + 5A where Q = unit sales, P = price in dollars, and A = advertising expenditure in dollars 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 $.75 a unit.

a. Compute the quantity sold and elasticity at a price of $1, and also at a $2 price, assuming the given advertising budget.

b. What is the advertising elasticity at a price of $2? Give an interpretation of the advertising coefficient..

Explanation / Answer

A) Q = 2,000,000 - 100,000P + 5A for determining quantity sold at P =1 and A = 10,000. Put the values in above equation Q = 2,000,000 - 100,000 * 1 + 5 * 10000 = 2,000,000 - 100,000 + 50000 = 1950000. Similarly for determining quantity sold at P =2 and A = 10,000. Put the values in above equation Q = 2,000,000 - 100,000 * 2 + 5 * 10000 = 2,000,000 - 200,000 + 50000 = 1850000. (dQ/dP) = -100000 For price elasticity,formula is price elasticity = -(dQ/dP)/(Q/P) price elasticity(p=1) = -(-100000)/(1950000/1) = 0.0512 price elasticity(p=2) = -(-100000)/(1850000/2) = 0.0540 B) (dQ/dA) = 5 Advertising Elasticiy = (dQ/dA)/(Q/A) = (5)/(185000/10000) = 0.2702 Advertising coefficiect is 5 which shows it will increase Q by 5 units on increasing advertising amount by 1 unit

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