Please help me ASAP. I will really appriciate it. Thank you **Profit Maximization in a Monopolistically Competitive Firm**You are the manager of a monopolistically competitive firm, and your demand and cost functions are estimated as $ Q = 25 - \frac{1}{2}P $ and $ C = Q^2 + 2Q + 2 $. What is the firm's maximum profit?**Understanding the Problem:**1. **Demand Function:** - $ Q = 25 - \frac{1}{2}P $: This function shows the relationship between quantity demanded (Q) and price (P). Here, as the price increases, the quantity demanded decreases, which is typical in most markets. 2. **Cost Function:** - $ C = Q^2 + 2Q + 2 $: This function represents the total cost (C) in terms of quantity produced (Q). The cost function includes fixed costs and variable costs that change with the level of output.To find the firm's maximum profit, follow these steps:**Step 1:** Find the revenue function.- Revenue (R) is calculated as price (P) multiplied by quantity (Q).- From the demand function: $ P = 50 - 2Q $- Therefore, Revenue $ R = P \times Q = (50 - 2Q) \times Q = 50Q - 2Q^2 $**Step 2:** Calculate the profit function.- Profit (π) is the difference between total revenue and total cost.- Total Cost (C) is given by $ C = Q^2 + 2Q + 2 $.- Thus, the profit function is: \[ \pi = R - C = (50Q - 2Q^2) - (Q^2 + 2Q + 2) = 50Q - 3Q^2 - 2Q - 2 = 48Q - 3Q^2 - 2 \]**Step 3:** Find the quantity that maximizes profit.- To maximize profit, take the derivative of the profit function with respect to Q and set it equal to zero: \[ \frac{d\pi}{dQ} = 48 - 6Q = 0 \]- Solving for Q: \[ 6Q = 48 \Rightarrow Q = 8

A monopolistic competitive firm maximises profit where marginal revenue is equal to marginal cost.

Answered: You are the manager of a…

You are the manager of a monopolistically competitive firm, and your demand and cost functions are estimated as Q = 25 – ½P and C = Q² + 2Q + 2. What is the firm's maximum profit? -

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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