Experts in the field of microeconomics study basic financial units: people, families, and (very) small businesses. As you learn about marginal revenue, you’ll gain an understanding of various other microeconomics terms and concepts you can use to analyze your price strategies.
A simple definition:
Marginal revenue means the amount of change in total revenue created by the sale of one additional unit.
Let’s get intuitive before we dig into numbers and formulas. Think about it this way: if you charge a lower price for your products, you’ll sell more of them, right?
If you charge higher prices, you’ll sell fewer units but make more per item. This creates a quandary: does the amount you gain by raising your profits offset the losses you incur by selling fewer products?
Theory Tip: In a perfectly-competitive market, no relationship would exist between sale price and quantity. Your marginal revenue would always equal your sale price; in fact, we wouldn’t even consider the concept. However, in the real world, monopolies create a need for businesses to calculate their marginal revenues.
As the holiday season approaches, you fire up your Etsy account and prepare to market your creations. Inspired to maximize your profits by your desire to give your friends high-end, artisan fruitcakes as holiday gifts, you ask yourself, “How much should I charge for each of these doggy sweaters to earn the highest possible revenues?”
You might be tempted to set a high price and enjoy high unit prices; conversely, you may feel the urge to knit more sweaters, offer them at a low price, and maximize your sales. However, you know, deep in your gut, that a “happy medium” is probably best.
Let’s say you knitted 10 dog sweaters last year and sold 5 of them for $50 each. Your total revenues came to $250. This year, you knitted 10 more – and want to maximize your revenues.
If you offer your 15 sweaters (you have 5 left over from last year) at the same price as last year, you can expect to sell only 5 of them. You’ll have 10 sweaters in stock, increasing your need for storage space – and not your revenues.
So, what if you lowered your price to $45 and sold one more sweater than last year? Would you make an extra $45 in revenue?
By lowering your price, you would lose $5 on each of the 5 other sweaters. By selling 6 sweaters at $45, you would earn $270. By selling one more sweater, you would make $20 more than last year – your marginal revenue.
Marginal Revenue (MR) equals the change in total revenue (ΔTR) divided by the change in quantity sold (ΔQ):
MR = ΔTR / ΔQ
(If you’re a visual learner, check out the compelling graphs in this textbook.)
In your dog sweater business, you hope to sell more than just one extra sweater this year. In a best-case scenario, you would sell all 15!
Let’s say you reduced your price further to $35, sold 8 sweaters (3 more than last year), and made $280 in revenues. Your marginal revenue would equal $10:
MR = $30 revenue increase / 3 extra sweaters
In the previous example, you lowered your price by $5, sold one extra sweater, and made an extra $20 in revenues. Your marginal revenue was $20.
This time, you lowered your price by $15, sold three more sweaters than last year, and made an extra $30. Your marginal revenue was $10.
It’s time to ask yourself: Was it worth your effort (visiting the yarn store, knitting, etc.) to only get $10 for each of these additional sweaters? Remember, you sold 5 for $50 each last year!
Let’s say you wanted to sell all 15 sweaters, no matter what. Imagine you slashed your price to $15 each, sold out your entire 15-sweater stockpile, and made $225. Your marginal revenue would equal -$2.50:
MR = $25 revenue decrease / 10 extra sweaters
All that work, and you’re losing money! In fact, you’re paying people $2.50 per sweater to take them off your hands!
Simple Shortcut: If you know your total revenue both before and after you sell an extra unit, you can just subtract the older number from the newer one.
Imagine you farm alpacas and harvest their wool. Your partner sells this organic alpaca yarn to people who knit dog sweaters at a local farmers’ market, typically bringing home $100. This month, you added an herbal remedy to your alpaca feed and these beasts became even hairier than usual.
When your partner (who loves showing off their antique spinning wheel at the farmer’s market) came home from market, they bragged about twisting an extra skein of yarn from this extra wool and making $120. However, when you asked them how many skeins they sold, in total, they couldn’t remember.
Luckily, you know that (regardless of quantity) the difference in total revenue ($20) equals marginal revenue and avoided a quarrel with your forgetful partner.
In microeconomics, average revenue (AR) simply means the average price customers pay for one unit of a product/service. You can calculate AR by dividing your total revenue (TR) by your quantity sold:
AR = TR/Q
Because of their similarities, people often confuse average revenue (AR) with marginal revenue (MR). However, it’s simple to tell the difference by noticing the Greek letter delta (Δ) which appears twice in the marginal revenue formula:
MR = ΔTR / ΔQ
AR = TR/Q
Remember, delta refers to change. Marginal revenue measures the relationship between the change in total revenues and the change in quantity. Average revenue only refers to the basic relationship between these factors, and doesn’t take into account any changes over time. Use average revenue to determine prices; use marginal revenue for price optimization.
Keep an eye on your average revenues, however. If they decrease, your marginal revenue must be even lower.
Imagine you sell solar-powered alpaca shears to conscientious organic farmers. If you sell 10 shears at $100 each, your revenues equal $1,000 (your average revenue is $100). If you lower your price to $95 and sell 11 of these shears (due to an increase in alpaca hairiness), you will make $1,045. Your average revenue is $95 (5 bucks lower than before) and your marginal revenue is $45:
MR = ΔTR (1,045 - 1,000) / ΔQ (11 - 10) = 45
If you lower your price to $90 and sell 12 pairs of shears, you will make $1,080. By lowering your average revenue by $5, you’ve lowered your marginal revenue by $10:
MR = ΔTR (1,080 - 1,045) / ΔQ (12 - 11) = 35
Remember, as you lower your price, your marginal revenue will decrease even faster. For this reason, we use marginal revenue to track the diminishing returns in revenue that accompany price decreases.
However, this concept also works in reverse. As you raise prices, your marginal revenue will increase.
Total revenue (TR) measures a business’ total sales or total income for a given amount of goods/services. From another perspective, it equals the total amount customers paid for a given set of goods.
You can calculate total revenue by multiplying price by quantity sold:
TR = P x Q
Again, some people become confused when dealing with the different types of revenue discussed by microeconomics scholars and savvy businesspeople. Just as you did in the average revenue sections, look for deltas (Δ) in the marginal revenue formula. The total revenue formula has no deltas because it measures direct sales, not the relationship between a change in sales and a change in quantity.
Imagine you sell designer alpaca earmuffs for stylish quadrupeds. If you sell 50 of these at $10 each, your total revenue equals $500. All you have to do is multiply price by quantity:
TR (500) = P (10) x Q (50)
If, instead, you sold 55 sets of earmuffs at $9.99 (because customers love numbers that end in nine), your total revenue would equal $549.45 and your marginal revenue would come to $9.89:
MR = ΔTR (549.45 - 500) / ΔQ (55 - 50) = 9.89
Typically, your MR will be much less than your TR (unless you’re selling only one unit), making these numbers easy to tell apart.
The more you sell of a product, your average and marginal revenues will decrease. At some point, your total revenue will also begin to decrease (if you’ve underpriced your goods far enough, this will happen as soon as you increase your sales).
To boost your revenues, you need to consider marginal cost, the amount it costs your business to produce one more unit. If your marginal income is greater than your marginal cost, you should produce and sell more units; if not, don’t!
Consider your imaginary earmuff business again. Your marginal revenue was $9.89. If you can produce another set of earmuffs for less than that amount, you should. Even though marginal revenues track diminishing returns, these are still returns (profits) for your business, if they exceed marginal cost!
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