Question

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Let q = demand for a product and p = price of a product in dollars. Suppose that q = 10,000p-³. Then a 1% increase in price will decrease demand by approximately ______ percent.​

Answer 1

Step-by-step explanation:

p^4 = 10,000 / q

take the fourth root of both sides of the equation to get:

(p^4)^(1/4) = (10,000/q)^(1/4)

simplify to get:

p = 10,000^(1/4) / q^(1/4)

simplify further to get:

p = 10 / q^(1/4).

this can also be expressed as p = 10 * q^(-1/4)

check to see if you got it right.

start with q = 10,000 * p^(-4)

since p^-4) = 1/p^4, your equation becomes:

q = 10,000 / p^4

assume that p equals any random number.

i chose p = 3.

formula becomes:

q = 10,000 / 3^4 which becomes q = 10,000 / 81 which becomes q = 123.4567901.

now start with p = 10 / q^(1/4)

when q = 123.4567901, this becomes:

p = 10 / 123.4567901^(1/4) which becomes p = 10 / (10/3) which becomes:

p = 10 * 3/10 which becomes p = 3.