Suppose the price-demand relationship is given by 
﻿﻿
where *p* is the price and *q* corresponds to the demand. Show your working for the following questions. 

a) Calculate the revenue function ﻿﻿ in terms of demand for the given price function. 

b) Calculate the marginal revenue for demand *q* = 23. 

Let's walk through these questions one step at a time.

### Part (a) — Calculating the Revenue Function

The **revenue function** \( R(q) \) represents the total revenue earned by selling \( q \) units of a product at price \( p(q) \). The relationship is given by the product of the price \( p \) and the demand \( q \):
\[
R(q) = p(q) \cdot q
\]
If the price-demand relationship is provided (though it was not visible in your message), we can substitute that into this formula. For now, I'll assume a generic price-demand relationship \( p(q) \) and show you the procedure. Let me know if you have a specific price-demand function in mind.

### Part (b) — Marginal Revenue at \( q = 23 \)

The **marginal revenue** is the derivative of the revenue function \( R(q) \) with respect to \( q \):
\[
MR(q) = \frac{dR(q)}{dq}
\]
To find the marginal revenue when \( q = 23 \), we will first calculate the derivative \( MR(q) \), then substitute \( q = 23 \) into the result.

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Could you share the price-demand equation you have in mind so that I can provide more specific calculations? If you have an equation in mind, I'll proceed with detailed steps.

Suppose the price-demand relationship is given by where p is the price and q corresponds to the demand. Show your working for the following questions.

a) Calculate the revenue function in terms of demand for the given price function.

b) Calculate the marginal revenue for demand q = 23.

Learn how to calculate the revenue function in terms of demand for a given price-demand relationship. This guide provides step-by-step instructions, including the formulas for total revenue and marginal revenue, with an example of marginal revenue when demand q = 23. Suitable for undergraduate students.

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