Given a firm’s market demand curve as: P = -2.5Q + 300, where Q is quantity of the firm’s output sold, at price P per unit. (i) Obtain the firm’s Marginal Revenue function (MR). (ii) Verify that the slope of the MR function is twice the slope of the Demand function. (iii) Determine the firm’s Total Revenue when it sells 30 units of output.

Given a firm’s market demand curve as: P = -2.5Q + 300, where Q is quantity of the firm’s output sold, at price P per unit. (i) Obtain the firm’s Marginal Revenue function (MR). (ii) Verify that the slope of the MR function is twice the slope of the Demand function. (iii) Determine the firm’s Total Revenue when it sells 30 units of output.

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

ChapterB: Differential Calculus Techniques In Management

Section: Chapter Questions

Problem 5E

See similar textbooks

Related questions

Q: If demand function is p = 160 - 0.0025x and Cost function is C = 15x + 0.0025x². Find the quantity…

A: The total cost incurred by a firm operating in a market includes fixed costs and variable costs.…

Q: A firm has estimated the following demand function for its product: Q- 258 - 2 P,+ 0.101+ 1.0 P,+…

A: Elasticity measures the responsiveness of change in one variable due to changes in the other…

Q: Suppose a firm has estimated the function of its demand (Qv) as follows: Qv =…

A: Given Qv = 400000-10Pv+10Pc+0.5I+0.5A where, Qv = quantity demand of good V Pv = price…

Q: 19) A beverage company works out a demand function for its sale of soda and finds it to be…

A: Price Elasticity of Demand measures the percentage change in quantity demanded of a good or service…

Q: Assume you are managing a food processing plant in Ethiopia. The demand function for one of your…

A: a) First we will find Qd when price equal to 15 Qd = 50 - 2p Qd = 50 - 2×15 = 50 - 30 = 20 Point…

Q: Best Orange Juice Company is located in Oman. The cost function for total orange juice production…

A: Profit maximizing quantity is where marginal revenue (MR) equals marginal cost (MC).

Q: The demand function for a certain brand of compact discs is given by p = -5x² 3x + 35 where p is the…

A: The concept of price elasticity of demand is used to explain the responsive nature between the…

Q: A toy company is trying to determine the optimal price for their weekly supply to meet the demand…

A: The supply function is given as The demand function is given as

Q: Q1: Analytical part - 8% Best Orange Juice Company is located in Oman. The cost function for total…

A: MC = dC(q)/Dx = 0.5x = 0.5xm + 0.5xs

Q: A cable TV company has 5,600 customers paying $130 each month. Suppose each $1 reduction in price…

A: Since you have posted a question with multiple sub-parts, we will provide the solution to only the…

Q: A firm faces a demand function D(p), for which the revenue- maximizing price is $10. The demand…

A: A demand function is a list of prices and the corresponding quantities that individuals are willing…

Q: Suppose the demand equation is where x is the number of items sold when the per unit price is p…

A: - Demand equation: , where is the number of items sold, and is the price per unit in dollars.

Q: Given the following model; Qd= a-50 P Qs= -100 + 20P

A: Demand function is the function which shows relationship between quantity demanded and price of a…

Q: The marketing research department for a company that manufacturers and sells gaming systems…

A: The value of all goods and services sold by a corporation in a certain period is referred to as…

Q: At a price of R 8 per item consumers will buy 1500 units. If the company increases the price by R1…

A: Price refers to the monetary value assigned to a product or service in a market. It represents the…

Q: Imagine the demand function for your firm’s product is q = 1500 – 4P. How much is the Total revenue…

A: q = 1500 – 4P 4P=1500-q P=(1500-q)/4 Total Revenu=Price*Quantity TR=Pq TR=[(1500-q)/4]*q

Q: If the demand function for a company is given by the equation p= -(16+4)q+(16+16000), and the supply…

A: Given data: Demand function p=-16+4qd+16+16000 Supply function qs=16+550-pp=16+550-qs

Q: A demand function is given by: Qd = 52 - P2 %3D At the point (P,Q) = (2,48) the price elasticity of…

A: Point Price elasticity of demand: Ed = (dQ / dP)*(P / Q) ------------------------------- Q = 52 - P2…

Q: The demand function for a product is p = 40 – 29 where p is the price in dollars when q units are…

A: In Economics, Revenue functions are used to determine the maximum possible output which could…

Q: The demand functions for a pineapple is given by p=-0.10x+15. a.) find the revenue function b.)…

A: Total Revenue is calculated by multiplying price with quantity. It refers to the total revenue…

Q: The profit function of a good is given by the following: n = -5Q2 + 631Q – 3255 where P is the price…

A: The relationship between the quantity demanded a commodity (dependent variable) and the price of the…

Q: (d) Solve for the equilibrium outputs (996). (e) Solve for the equilibrium price. (f) Solve for firm…

Q: The Edgewater Hotel in Seattle has 210 guest rooms. When they charge a discounted rate of $250 per…

A: The total rooms available in the hotel = $250 At a price of $250 per night, 80% room is occupied. If…

Q: Manager Mutua comes to you as a consultant armed with the demand function of his firm and wishes to…

A: Answer: Given, Firm's demand function: P=1000-1.5Q Explanation: Total…

Question

Given a firm’s market demand curve as: P = -2.5Q + 300, where Q is quantity of the firm’s output sold, at price P per unit.

(i) Obtain the firm’s Marginal Revenue function (MR).

(ii) Verify that the slope of the MR function is twice the slope of the Demand function.

(iii) Determine the firm’s Total Revenue when it sells 30 units of output.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 2 steps with 1 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.

Similar questions

The demand function for a product is p = 40 – 29 where p is the price in dollars when q units are demanded. Find the level of production that maximizes the total revenue and determine the revenue. q = units R =$
A firm has estimated the following demand function for its product: Q = 258 - 2 Px + 0.101 + 1.0 P, + 14A, Where Qx is the quantity demanded of X per month (in thousands), P is the price of X, I is an index of consumer income, Py is the price of competing product Y, and Ax is the advertising expenditures for X per month (in thousands). Assume that Px = 10, I = 120, Py = 10, and A, = 10. The Income Elasticity of Demand (E) is: A. 3 B. 0.3 0.03 0.003
Q1: Analytical part – 8% Best Orange Juice Company is located in Oman. The cost function for total orange juice production (x) is given by C(q) = 0.25x². Their orange juice is demanded only in Muscat (Muscat demand is xm- 100-2Pm) and Salalah (Salalah demand is x,- 100-4P,). Therefore, the total demand is x-Xm+ Xs# If the company can control the quantities supplied to each market, how many should it sell in each location to maximize total profits? What price would it charge in each location? Answer:
A cable TV company has 5,600 customers paying $130 each month. Suppose each $1 reduction in price attracts 50 new customers. Let x represent the amount of reduction in price (in dollars). Find R(x), the total revenue function (in dollars). R(x)= Find R(x). R'(x) = Find the price that yields maximum revenue. $ Find the maximum revenue.
Manager Mutua comes to you as a consultant armed with the demand function of his firm and wishes to know the quantity that the firm can produce in order to maximize revenue. His firm’s demand function is P=1000 – 1.5Q.
The demand functions for a pineapple is given by p=-0.10x+15. a.) find the revenue function b.) how many pineapples will you sell when you are maximizing revenue? c.) what price gives the maximum revenue and what is the maximum revenue?
A firm faces a demand function D(p), for which the revenue- maximizing price is $10. The demandfunction is altered to 2D(p). What is the new revenue maximizing price?
At a price of R 8 per item consumers will buy 1500 units. If the company increases the price by R1 per item, the number of items that the consumers will buy will decrease by 75. i) Does the function described represent a supply or demand curve? Find the formula of the function given that it is a linear function. ii) Find the price that will maximize the revenue.
Q1: Analytical part - 8% Best Orange Juice Company is located in Oman. The cost function for total orange juice production (x) is given by C(q) = 0.25x2. Their orange juice is demanded only in Muscat (Muscat demand is Xm- 100-2Pm) and Salalah (Salalah demand is X 100-4Ps). Therefore, the total demand is x-xm+ Xs. If the company can control the quantities supplied to each market, how many should it sell in each location to maximize total profits? What price would it charge in each location? Answer:
Assume you are managing a food processing plant in Ethiopia. The demand function for one of your product is given as Qd=50-2p. a) Find the point price elasticity if price is 15 ETB? Is it elastic or inelastic? b) How do you interpret the elasticity result? c) In order to get more revenue what will be your recommendation. Is it to increase price or decrease price? Why?
The demand function for a certain brand of compact discs is given by p=-5x² 3x + 35 where p is the wholesale unit price in dollars and x is the quantity demanded each week, measured in units of a thousand. (a) Compute the price, p, when x = 2. Price, p= dollars (b) Use implicit differentiation to compute the rate of change of demand with respect to price, p, when x = 2. Do not round your answer. Rate of change of demand, x' thousands of units per dollar (c) Compute the elasticity of demand when x = 2. Do not round your answer. Elasticity of Demand =
E.g.1: A demand function is given by the equation P = 24 6lnQ ➤ Find the equation of TR (total revenue) and determine for which value of Q is TR maximised. Find MR (marginal revenue) as a function of Q Show that MR is a positive decreasing, concave up function.