The demand function q(p) can be derived from the revenue function R(p). The revenue function is given by R(p) = -51p^2 + 65p.

The revenue R is the product of the price p and the quantity q, i.e., R = pq.

We can express the quantity q as a function of the price p by rearranging the equation to solve for q:

q(p) = R(p) / p = (-51p^2 + 65p) / p = -51p + 65.

So, the demand function q(p) is a linear function given by q(p) = -51p + 65.

The reason for this answer is that the revenue function R(p) is a quadratic function of the price p, and the quantity demanded q(p) is inversely related to the price p, as indicated by the negative coefficient of p in the demand function. This is a common relationship in economics, reflecting the law of demand that states that as the price of a commodity increases, the quantity demanded decreases, all else being equal.

Question

The demand function q(p) can be derived from the revenue function R(p). The revenue function is given by R(p) = -51p^2 + 65p.

The revenue R is the product of the price p and the quantity q, i.e., R = pq.

We can express the quantity q as a function of the price p by rearranging the equation to solve for q:

q(p) = R(p) / p = (-51p^2 + 65p) / p = -51p + 65.

So, the demand function q(p) is a linear function given by q(p) = -51p + 65.

The reason for this answer is that the revenue function R(p) is a quadratic function of the price p, and the quantity demanded q(p) is inversely related to the price p, as indicated by the negative coefficient of p in the demand function. This is a common relationship in economics, reflecting the law of demand that states that as the price of a commodity increases, the quantity demanded decreases, all else being equal.

Knowee AI · Accepted Answer

The demand function q(p) can be derived from the revenue function R(p). The revenue function is given by R(p) = -51p^2 + 65p.

The revenue R is the product of the price p and the quantity q, i.e., R = pq.

We can express the quantity q as a function of the price p by rearranging the equation to solve for q:

q(p) = R(p) / p = (-51p^2 + 65p) / p = -51p + 65.

So, the demand function q(p) is a linear function given by q(p) = -51p + 65.

The reason for this answer is that the revenue function R(p) is a quadratic function of the price p, and the quantity demanded q(p) is inversely related to the price p, as indicated by the negative coefficient of p in the demand function. This is a common relationship in economics, reflecting the law of demand that states that as the price of a commodity increases, the quantity demanded decreases, all else being equal.

If the revenue function for a particular commodity is R(p) = −51p2 + 65p, what is the (linear) demand function q(p)?q(p) = Give a reason for your answer.R = p + qR = qp R = q − pR = pqR = pq

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