How to determine the optimal price of a product as a monopolist

economics
By Arpad

In business, finding the right price for your product is crucial. Price it too high, and few people will buy; price too low and the business leaves money on the table. But how do you determine the right price? We will explore this question with a simplified example, looking at Umbrella Corp (UCorp). Note that in this simplified case, UCorp is a monopolist and cannot charge different prices to different customers (i.e. is unable price discriminate).

Step 1: Estimate the demand curve

The first step is to estimate the demand curve of UCorp’s customers. In real-world settings, companies can use several tools to estimate the demand curve for a product such as customer surveys, market experiments, regression analysis and others. In our example, to estimate the demand for umbrellas, Ucorp asked a class of 80 students to raise hands if they are willing to buy an umbrella at various price points on a rainy day. 

The outcome of this experiment is the demand curve depicted in Graph 1: no student raised a hand at a price of $50 per umbrella and all 80 students would have taken an umbrella for free. 

Graph 1: Umbrella demand on a rainy day at various prices

Screen Shot 2021-05-19 at 3.53.09 PM

Step 2: Graph the revenue curve and determine revenue maximizing quantity/price 

Assuming the student population is representative of UCorp’s target customer, the company can now estimate its revenue at various price/quantity combinations, see graph 2. To do that with a dataset quantity sold at each price with the price to find the highest revenue. 

Graph 2: UCorp’s revenue at various quantities sold

Screen Shot 2021-05-19 at 3.53.46 PM

Note that UCorp achieves its maximum revenue ($600) selling 40 umbrellas at a price of $15 each. 

Decreasing the price by $1 would lead to falling revenue, as the loss in revenue from existing customers is greater than the revenue from new customers (the 40 existing customers would each pay $1 less, whereas only one new customer would be paying an extra $14, leading to a net revenue loss of $26).

Likewise, increasing the price by $1 would lead to a revenue of $560 or $40 less than at the revenue maximizing price point of $15. (35 customers would each pay an additional $1, however, 5 customers would be lost that had paid $15 per umbrella before, resulting in a net revenue loss of $40). 

Step 3: Find profit maximizing quantity/price

If the goal was to maximize revenue we would be done, but the goal is to maximize profit, so we have to introduce costs. Let’s assume that UCorp has some fixed costs (F) to manufacture umbrellas and that variable costs (labor, capital and material) per umbrella are constant (c). 

Cost equation:  C=F+c×q Note: In this case F = 100, c = 5;

Profit equation: P=p*q-F+c×q=p-c*q-F

Intuitively, we know that UCorp should produce umbrellas as long as the revenue from each umbrella is greater or equal to its variable cost (p=c), or in Econ language, Ucorp’s optimal output is determined at a quantity/price combination where marginal revenue is equal to marginal cost (MR =MC). 

In this case marginal revenue is equal to the price (the revenue for each additional unit sold is the price of one umbrella) and marginal cost is the variable cost (the cost of each additional umbrella produced is marginal cost), so we can substitute MR with p and MC with c.

Graph 3: UCorp’s profit at various quantities

Screen Shot 2021-05-19 at 3.54.28 PM

In this case with F=100 and c=5, UCorp would choose to only sell 18 umbrellas at a price of $30 per umbrella to generate revenue of $540. Even though this leaves revenue lower than the maximum of $600, UCorp generates higher profit ($350 vs. $300) as it saves 22 x 5$ = $110 in costs.

In summary, to determine the optimal price to charge, a business needs to understand its customers, in particular their demand behavior, and its own cost structure. 

Appendix: Data table excerpt

Screen Shot 2021-05-19 at 3.55.15 PM

Curious about the intersection of business and economics? Looking for support for a course? Our team of MBAs, PhDs in Economics, and working professionals are here to help!

Contact us!

Present Value and Interest Rates

How do I autofill formulas in Excel?

Finding the Right MBA Program

Comments

topicTopics
academics study skills MCAT medical school admissions SAT expository writing college admissions English MD/PhD admissions strategy writing LSAT GMAT GRE physics chemistry math biology graduate admissions academic advice ACT interview prep law school admissions test anxiety language learning premed MBA admissions career advice personal statements homework help AP exams creative writing MD study schedules test prep computer science Common Application summer activities history mathematics philosophy organic chemistry secondary applications economics supplements research 1L PSAT admissions coaching grammar law psychology statistics & probability legal studies ESL CARS SSAT covid-19 dental admissions logic games reading comprehension engineering USMLE calculus PhD admissions Spanish mentorship parents Latin biochemistry case coaching verbal reasoning DAT English literature STEM excel medical school political science skills AMCAS French Linguistics MBA coursework Tutoring Approaches academic integrity chinese letters of recommendation Anki DO Social Advocacy admissions advice algebra art history artificial intelligence astrophysics business cell biology classics diversity statement gap year genetics geometry kinematics linear algebra mechanical engineering mental health presentations quantitative reasoning study abroad technical interviews time management work and activities 2L DMD IB exams ISEE MD/PhD programs Sentence Correction adjusting to college algorithms amino acids analysis essay athletics business skills careers cold emails data science dental school finance first generation student functions graphing information sessions international students internships logic networking poetry resume revising science social sciences software engineering tech industry trigonometry writer's block 3L AAMC Academic Interest EMT FlexMed Fourier Series Greek Health Professional Shortage Area Italian Lagrange multipliers London MD vs PhD MMI Montessori National Health Service Corps Pythagorean Theorem Python Shakespeare Step 2 TMDSAS Taylor Series Truss Analysis Zoom acids and bases active learning architecture argumentative writing art art and design schools art portfolios bacteriology bibliographies biomedicine brain teaser campus visits cantonese capacitors capital markets central limit theorem centrifugal force chemical engineering chess chromatography class participation climate change clinical experience community service constitutional law consulting cover letters curriculum dementia demonstrated interest dimensional analysis distance learning econometrics electric engineering electricity and magnetism escape velocity evolution executive function freewriting genomics harmonics health policy history of medicine history of science hybrid vehicles hydrophobic effect ideal gas law immunology induction infinite institutional actions integrated reasoning intermolecular forces intern investing investment banking lab reports linear maps mandarin chinese matrices mba medical physics meiosis microeconomics mitosis mnemonics music music theory nervous system neurology neuroscience object-oriented programming office hours operating systems