Figuring out the price of iron bars for construction

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

13 February 2022

Dominic Okullu says he is in the construction business and he has been wondering about the price of iron bars. He writes: “I buy them regularly in different sizes. The last [purchase]…was 8mm at Sh495, 12mm at Sh1,030 and 16mm at Sh1,910. Since all of them are the same length (6 metres)…, how come the 16mm are almost four times the price of the 8mm [yet] they are just double the size?”

Before answering the question, I must re-state a point that I have made here before: the price of an item does not depend of the cost of producing or acquiring it. It only depends on what the buyer is willing to pay for it! The willingness of the buyer is determined by many considerations, including whether he can get it somewhere else at a lower price, how desperate he is to get it, whether he has the money being charged and so on.

Now, Domonic’s questions reminds me of a similar one that I tackled ten years ago (August 2012) in this column. At that time, Charity Muli was concerned about the “unit price” of different sizes of pizza. She had divided the price of each by the diameter and the results did not make any sense.

I explained that it is wrong to divide the price of the pizza by its diameter since that is not the correct size. The right quantity to use is the area; and doing that produced more sensible results. It is the same case here.

When Dominic buys an iron bar, he is getting a certain volume of the metal. We can picture the round bar as very long cylinder. Its volume is the cross-sectional area multiplied by the length.

The area of a circle is pi times the square of the radius; and the radius is half the diameter. Thus, for the 8mm bar, the cross-sectional area is 3.14 x 4 x 4 = 50.24 square mm. For the 16mm bar, it is 200.96 sq.mm. Since both are the same length, it is easy to see that the bigger bar is exactly four times the volume of the smaller one.

Now, Sh495 x 4 = Sh1,980; so, at Sh1,910, the 16mm bar is actually cheaper than the 8mm one – albeit slightly. However, unlike the case of pizza, Dominic cannot just decide to use 16mm bars instead of the 8mm! He must follow the directions given by the engineers.