# Q42. How do businesses know how much to increase prices for a product or service?

The elasticity measure is very important in economics. Elasticities measure the responsiveness of price or income to changes in demand, supply, availability of acceptable substitutes, and time.

Mathematically, the elasticity of demand with respect to a change in price is the percentage change in the quantity of the product demanded for each 1% change in its price. Representing *Qx* as the first measured quantity and *Q2* as the second measured quantity, and *Px* as the first measured price, and *P2* as the second, the formula for the elasticity is given by:

To see how useful the elasticity concept is, imagine you run a summer school, and charge €30 a week for entry. You get more than 100 children in the first week applying, but you take only 100. Encouraged by your success, next week, you decide to increase the price to €50 per week. This time, you get only 80 applying. Calculating the price elasticity of demand for the summer school, you see that

(80-100)/90/(50-30)/40 = -0.44.

You're still taking in more money (€300 versus €400), and you have fewer kids to mind. Overall, a win for you.

If you're wondering where the 90 and 40 came in the formula, it's because I used the arc elasticity representation. It is usually better to calculate the arc elasticity, because this is symmetric with respect to the two prices and two quantities, independent of the units of measurement, and yields a value of unity if the total revenues at two points are equal. To see this, try for yourself to figure out how high prices should go to make the total revenues equal to one another.

The table below shows some of the features of the price elasticity of demand (PED).

**Features of Price Elasticity of Demand.**

# Q43. What happens to demand for gin when the price of tonic changes?

Elastic and inelastic goods often interact with one another. The cross-elasticity of demand measures the responsiveness of demand for one good (gin) to a given change in the price of a second good (tonic). We calculate the cross-elasticity as:

Cross-elasticity = Percentage change in quantity demanded of gin / Percentage change in the price of tonic.

If the cross-elasticity is positive, then the two goods are substitutes. If is negative, then the two goods are complements.

Two goods are substitutes if, when the price of one rises, demand for the other increases. Examples of substitutes are Mercedes and BMW cars, both luxury brands. If the price of a specific Mercedes model rises, buyers will switch to the now cheaper, equivalent BMW model.

Two goods are complements if, when the price of one rises, demand for the other decreases. Examples of complements are fish and chips. If the price of fish rises, the quantity demanded falls, and the quantity of chips demanded also falls - as few people want to eat just chips without fish.

Using the simple cross-elasticity equation of: Cross-elasticity = Percentage change in quantity demanded of gin / Percentage change in the price of tonic, do you think the cross elasticity will be negative, or positive?

# Q44. What is break-even analysis?

Businesses try to make profits - you do not need a book on economics to tell you that. How do businesses figure out when they've made a profit? When revenue is equal to costs, at the break-even point where no profit is made, but no losses are being made either. Any amount produced above the break-even line results in a profit.

To determine the *number of units of the product* you need to sell to break-even, calculate the average annual fixed cost/(average per unit sales price less average per unit variable cost).

To determine the *sales value* you have to achieve to break-even, work out the annual fixed cost/(1 -(average per unit variable cost t average per unit sales price)).

For example, imagine a new brewery selling one type of beer, with an average sale price of €20 per keg. The average variable cost for the keg is €8, and the annual fixed costs are €100,000. To break-even, 6,250 kegs - 100,000 / (20-8) = 6,250 kegs - need to be sold. The break-even sales value is €166,666 -calculated as 100,000 / (1 - (8 / 20) = €166,666. No profits will be made by this brewery until 6,250 kegs have been sold, with more than €166,666 in gross sales realised.

Break-even analysis is used extensively in business, and also in the public sector, where the impacts of running new programmes and policies are costed to estimate just how beneficial they may or may not be if run at certain scales.

# Q45. What are diminishing returns?

In a production process, as you add more of one productive factor, the extra productivity resulting from each additional unit eventually will become negative: you have reached diminishing returns.

Imagine a production line for frozen pizzas, with people putting toppings on the pizza (sauce, cheese, pepperoni, and so forth) as the base goes past. One person can do only so many pizzas per hour. Adding another person makes the process much more efficient: one person can do the sauce, the other can do everything else. Adding more people makes it even more productive: one person per topping - to a point but, eventually, they will start getting in each other's way, making mistakes, and not increasing the average return to the production of the physical product. Persons four, five, and six represents the start of diminishing returns with respect to labour.

Think about small children and sweets. Feed them one, two, three, four of the sweets, they will get progressively happier (and probably a bit hyper). Give them six, seven, eight sweets, they will probably enjoy these a lot less. By the time you're feeding them sweets 21 and 21, someone has probably called Social Services because of the diminishing returns to their utility the children are experiencing as a result of the increased number of sweets. Don't try this on your own children!

**Diminishing returns.**

We can graph the extra happiness (or utility) from successive sweets to visualise what is happening to utility. It never drops - a sweet is still preferable to no sweet - but the extra utility the person is getting from the next sweet is vanishingly small after six, seven, or eight of them.