Your family operates a car wash. There are many other car washes around. You have observed that the customers care only about finding the cheapest price for car washes; they do not care which company they use. To purchased the equipment and the building for the car wash, your have to take out a small business loan. The cost of the loan comes to $10 per day for the next 40 years. The business must hire labor and purchase cleaning solutions, car wax, etc. to operate the car wash. After some research you have figured out that the cost for labor and supplies is VC(Q)=Q², where Q is the number of car wash.

a. You have observed that you can charge a price of $10.00 per car wash. How many car wash should you sell to maximize the profit?
b. You have observed that you can charge a price of $6.00 per car wash. How many car wash should you sell to maximize the profit?
c. You have observed that you can charge a price of $2.00 per car wash. How many car wash should you sell to maximize the profit?

Solution Summary

This solution helps to find out profit maximizing quantity.

1. A profit-maximizing firm operating in a perfectly competitive market can sell products for $100 per unit. The firm has a cost function represented by:
C(Q) = 1000- 160Q + 10QSqr(10 q squared) . The market demand function for this product is Qd = 500 - 3P.
a.What is the profitmaximizing output for this company?
b.Wh

Suppose that a pharmaceutical company has a monopoly over the production of master cream, a drug used on skin rashes. Further suppose that the demand for master cream is given by the expression QD = 1,500 - P, where QD is the quantity demanded (in bottles) and P is the price. Assume that the company's costs are given by the expr

A firm uses a single plant with costs C = 160 + 16Q + .1Q2 and faces the price equation P = 96 - .4Q.
a. Find the firm's profit-maximizing price and quantity. What is its profit?
b. The firm's production manager claims that the firm's average cost of production is minimized at an output of 40 units. Furthermore, she claim

A monopolist has demand and cost curves given by:
Q = 1000 - 2P
TC = 5,000 + 10Q
Find average cost (AC), average variable cost (AVC), marginal cost (MC), marginal revenue (MR).
a. What is the quantity that maximizes profit? What is the revenue and profit at that point?
b. What is the quantity that maximizes revenue? Wh

A monopolist has a constant marginal and average cost of $10 and faces a demand curve of QD = 1000-10P. Marginal revenue is given by MR = 100 -1/5Q.
Calculate the monopolist's profit-maximizingquantity, price and profit.

Given the following Demand & Supply functions:
Qd = 25 – P
Qs = 10 + 2P
a – What is the equilibrium values of P and Q?
Now suppose the demand function changes to:
Qd = 10,000 – 2P
If Total Cost function is:
TC = 5000 + 50Q
b - Find the Profit – maximizingQuantity and Price.
c – Find the firm’s profit

Suppose a natural monopolist has fixed costs of $24 and a constant marginal cost of $2. The demand
for the product is as follows:
Price (per unit) $10 $9 $8 $7 $6 $5 $4 $3 $2 $1
Quantity demanded
(units per day) 0 2 4 6 8 10 12 14 16 18
Under these conditions,
(a)

PROBLEM 8- 4. Determining the Profit- Maximizing Price [ LO 1] RoverPlus, a pet product superstore, is considering pricing a new RoverPlus- labeled dog food. The company will buy the premium dog food from a company in Indiana that packs the product with a RoverPlus label. Rover pays $7 for a 50- pound bag delivered to its store.