Demand and supply

Question

The demand for a product d in items per month is given by:

d(p) = 17600e

−0.18p

, (1)

where p is the price in kwacha of the product.

(a) (i) p = 5.

(ii) p = 15.

(iii) p = 45.

(iv) p = 150.

(v) p = 400.

(b) What will happen to the demand as the price increases

without bound. Note that without bound means it goes to

infinity.

Answer 1

Hello Wilford,

The d(p) is a given function of price p. Essentially, you may just substitute the given number of price p, say p = 5, into the d(p) formula or function.

The “e” in d(p) is about 2.17. That “e” part is to take the power of (-0.18*5) on the “e”, i.e. 2.17 to the power of -0.9. You then multiply this result to 17600. You do this for all the given p in the list, say 5, 15, 45, 150, 400. You then will see a pattern of the result numbers of calculated d(p).

You may then guess that when price p goes beyond 400, to bigger and bigger numbers, the demand will still follow the observed pattern you see in your calculated demand for the price list of 5, …, 400.

In fact, ultimately the demand will be 0 as price p goes up without a bound. This is consistent to our common sense that eventually no one wants to buy the product when the price goes up to an unbounded number. In math, this is a concept called “limit”.