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# Economics/price elasticity

Question
In an attempt to increase revenue and profit, a firm is considering 5% increase in price of its good and 15% increase advertising expenditure.if the price elasiticy of demand is -1.5 and advertising elasiticy of demand is +0.6, would you predict an increase or decrease in total revenue?explain?

Hi Vimal,

Thanks for your question. I am happy that you are trying to get deep into the behaviour analysis of firms confronted with decision-making given price and advertising elasticities of demand, and I am going to  try my best to help you.

You are quite right that a firm will [or will not] take such a decision in an attempt “to increase revenue and profit.” As to revenue, we may take any hypothetical set of values for output and price, and our analysis will work fine. As to profit, however, your question doesn’t provide sufficient information: profit entails costs together with revenue. Your question doesn’t delineate the cost function, but you have nonetheless brought up “a feature of overhead cost (or fixed cost)” in respect of advertising that I will make good use of in explaining the profit part of your implied question. I will doubtless give a clear, trenchant explanation of your explicit question: the effect on revenue.

Even though you haven’t provided any information about your academic background –which would have put me in a better place to answer to your question tailored to your level of understanding –I assume you have a pretty good exposure to the elements of demand theory. Since you didn’t solve the problem by yourself, I believe my help in brush-up of some facets of demand theory will get you off on the right foot.

With this in view, I will give a clear picture of how you can find out whether revenue will increase or decrease and, using some tenable assumptions, whether profit will increase or decrease if, given the price and advertising elasticities, price and advertising costs will increase by certain percentages.

The simplest possible method is used for your quick grasp. [If you enjoy advanced math, take a quick look at the attachment where I have used many-variable exponential function and logarithmic derivation to treat of your problem as is done econometrically. If you are shy of math, don’t worry. You don’t lose much.]

PRICE ELASTICITY OF DEMAND AND CHANGE IN TOTAL REVENUE

Price elasticity of demand, e, is defined as:
e = (%change in quantity demanded)/(percentage change in price)     [1]

Substituting values from your question into [1],
e= (%change in quantity demanded)/0.05 = -1.5          [2]

Manipulation of [2] yields
e= (0.05)(-1.5)/0.05 = -0.075/0.05 = -1.5          [3]

In [3], -1.5 tells us that, if price is increased by 5% (+0.05), quantity demanded will fall by 7.5% (-0.075). If this information is plugged into any set of (price, output)-coordinate values, we will invariably get the result we want. This can be pretty well be exemplified by a downsloping demand curve delineating the well-observed negative relationship between quantity demanded and price.

PRICE ELASTICITY OF DEMAND AND CHANGE IN TOTAL REVENUE: CALCULATION WITH HYPOTHETICAL DATA SET [ANY SUCH DATA SET WILL GIVE THE SAME VALUES]

In order that you may have a full understanding of how we get the results under the above rubric, I am providing two simulations of P;Q;R [price; quantity; revenue], using e= 0.05 and e(adv) = 0.6. Once we through with this part, we will next go on to dealing with profit, using advertising elasticity = 0.06].

SIMULATION ONE: P=2; Q=80; INITIAL ADV. COST=0; REVENUE DECREASES
Assume this is a firm with no initial advertising cost, such as a small well-known firm. The above figures give us the following set of values (P and R in dollars and Q in units).

P   80   R
2   80   160
2.1   74   155.4

The second row above shows the initial values of price (P), quantity demanded (Q), and revenue (R). If e=0.05, then on the basis of our foregoing equation [3] price changes to 2+(0.05x2) = 2.1. In response to the price change, given e=-1.5, quantity demanded decreases by 6  (-0.075x80) to 74. The 3rd column shows revenue=(price)x(quantity demanded) or R=PQ. We see revenue falls from 160 to 155.4.

SIMULATION ONE: P=4; Q=120; INITIAL ADV. COST=0; REVENUE DECREASES
P   80   R
4   120   480
4.2   111   466.2

By the same line of reasoning, with only P and Q changed with e unchanged, we see revenue also falls from 480 to 466.2.

WHEVER e>1, INCREASE IN P LEADS TO FALL IN R AS WE ARE ON THE UPPER HALF OF THE DEMAND CURVE. THE RECTANGLE FORMED BY PRICE AND QUANTITY CORDINATE REDUCES.

We have seen that as the absolute value (modulus) of the elasticity of demand is greater than unity (1.5), revenue falls as price is increased because quantity demanded falls by a GREATER PERCENTAGE. You can visualise this by drawing a straight-line demand curve (Q=a-bP) in a positive quadrant, where a= price intercept or price at Q=0 and b=slope of the demand curve, dQ/dP. As e>1, the Q,P point on the demand curve lies upward of the midpoint. Now you have a P,Q  point on the upper segment of the demand curve. Next, to the left and up (northwest) you get another point P,Q (the changed price and quantity). Draw two rectangles, with one vertex P,Q.. The increase in the changed rectangle is much less than the decrease in it. The net effect is a DECREASE IN REVENUE (the area of the rectangle is revenue=PQ).

Since no cost function is given in your question to come to grips with this question about the effect of advertising cost on revenue and ultimately on profit, we assume simple cost functions that will be representative of any similar analysis.

SIMULATION TWO
FOUR SCENARIOS OF A FIRM: (A) WITH AVERAGE COST 3 INCLUDING ADVERTISING COST 1; (B) WITH AVERAGE COST 3 INCLUDING ADVERTISING COST 2; (C) WITH AVERAGE COST 2 INCLUDING ADVERTISING COST 1; AND (D) WITH AVERAGE COST 2 INCLUDING ADVERTISING COST 1.75

Please refer to Image 2. The coloured spreadsheet is uploaded to make it clear and vivid.  Get a printout, and take note of the following:

(a)   I have given dAC=change in Average Cost, AC=Average Cost, dP=change if Price, dQ=change in quantity demanded, R= Revenue, C=Cost, and Profit, all as the rubric under which the four tables fall, white against black background.

(b)    For each table, we have ORIGINAL figures, as given in the foregoing tables of this page, black against white background in column 2 of each table.

(c)   Effect of a 5% change in price, given e=-1.5, is shown along the 3rd row of each table, black against a rust background.

(d)   Effect of a 15% change in advertisement expenditure, given advertisement elasticity of demand, is given, separately in each tables, under the aforementioned FOUR SCENARIOS.

(e)   Each table shows composite effects of price change and advertisement-cost change on revenue, cost and profit.

(f)   Revenue in each case falls. This I have already explained above in terms of rectangles.

(g)   Now the question of profit depends on Cost. If average Cost is low, there will be profit. Consider a U-shaped AC curve lying below the AR curve –whether under perfect competition or under monopoly –the firm incurs loss; the reverse helps the firm make ECONOMIC PROFIT.

CONCLUSION
On the basis of the data provided in your question, WE CAN PREDICT that AN INCREASE OF PRICE WILL REDUCE TOTAL REVENUE, and vice versa.

As a corollary, the EFFECT ON PROFIT depends on the cost functions, and based on the data provided by you, the effect will depend on the initial cost conditions and the composition of advertisement cost in total cost.

We may, however, say that such cost conditions could obtain that a positive advertisement elasticity, such as 0.6, may have a positive impact on revenue by a positive effect on output Q, outweighing decrease in Q due to negative greater-than-unity (-1.5) price elasticity.
I hope, Vimal, I have been able to attend to your query to your full understanding. Best of luck.

Economics

Volunteer

#### Eklimur Raza

##### Expertise

It appears some students in this website are confused about elasticity of demand and the slope of the demand curve when they are trying to figure out why rectangular hyperbola comes up in case of unitary demand curve. First, they don't know that RH can be depicted in a positive quadrant of price,quantity plane. Secondly, they make the mistake that the slope of RH is constant at -1. Two points could help them: first, e=1 at each and every point of the RH, because the tangent at any point shows lower segment=upper segment (another geometric definition of e); yet slopes at different points,dQ/dP, are different; second, e is not slope but [(Slope)(P/Q)]in absolute terms. Caveat: only if we measure (log P) along the horizontal axis and (log Q) up the vertical axis, can we then say slope equals elasticity --in which case RH on P,Q plane is transformed into a straight-line demand curve [with slope= -tan 45 deg] on (log Q),(logP) plane, and e= -d(log Q)/d(log P). [By the way, logs are not used in college textbooks --although that is helpful in econometric estimation of elasticity viewed as an exponent of P, when demand equation is transformed into log-linear form.] I have not found the geometrical explanation I have given in any textbook followed in undergraduate and college classes in Canada (including the book followed in a university where I taught for a short time and in the book followed in George Brown College, Toronto, where I teach.

##### Experience

About 11 years' teaching economics and business studies, and also English, history and elementary French.Practical experience in a development bank, working with international donor agencies like the World Bank and the ADB. Experience in free-lance journalism, including Canada's "National Post."

Organizations
I teach micro- and macroeconomics at George Brown College (continuing education), Toronto, ON, Canada.

Publications
Many articles and editorials, on different subjects, in English newspapers. Recently an applied Major Research Paper, based on a synthesis of the Solow growth model and the Lewis two-sector model, has be accepted by Ryerson University, Toronto. Professors Thomas Barbiero and Eric Cam, Ryerson University, accepted the paper.

Education/Credentials