I certainly don't mean to self promote. However, I feel this would be an interesting topic point. During my reading of the Famitsu top30 I noticed that the Vita and the 3DS had fluctuating sales around the time of the pricecut. As a fun little project I wanted to see if I could use elasticity to prove that the two were competitors. The results were not what I expected but certainly not suprising.

 With the ever fluctuating Vita sales of recently and the falling sales of the 3DS, it got me thinking about taking a closer look at how the two affect each other. Are the Vita and 3DS competitors? Naturally one would assume so but lets take a look at the numbers.

The most popular version of the Vita was the cheaper Wifi version that started at a price of 24,980 yen. On February 28th the Vita’s price was dropped to 19,980 yen for both models. The week before the pricecut the 3DS sold 74,729 unit. Before the pricecut the Vita sold 11,456 units. The week of the pricecut the 3DS sold 77,105 and the Vita sold 60,561.

Using the cross elasticity formula we get
Change in Demand of product Y – (77,105-74,184)/74,184 = .04
Change in Price of product X – (19,980-24,980)/24,980 = -.2

Demand Y/Price X = .04/-.2 = -.20

So what does this number mean? Well it would mean that there is only a slight relationship between the two products and that they are complements. That can’t be right. There is just too many variables affecting our equations. Lets try moving back one week. Some stores did break street date.

Change in Demand of product Y – (74,184-101,940)/101,940 = -.27
Change in Price of product X – (19,980-24,980)/24,980 = -.2

Demand Y/Price X = -.27/-.2 = 1.36

Using this week we see that the two are substitutes for each other. This is more what we would expect. The only problem is the Vita sales were only 11,669 units. Clearly the pricecut hadn’t taken full effect yet. The 3DS possibly dropped for another reason. If we look at the charts the 3DS had a massive sales increase thanks to Dragon Quest 7 and was simply declining from Dragon Quest 7′s boost. Lets try the formula from when the pricecut took effect to two weeks prior to the pricecut.

Change in Demand of product Y – (77,105-101,940)/101,940 = -.24
Change in Price of product X – (19,980-24,980)/24,980 = -.2

Demand Y/Price X = -.24/-.2 = 1.20

Not too much of a change. I feel we really aren’t getting an accurate picture still. About the same how about the week of the pricecut and the week after?

Change in Demand of product Y – (60,800-77,105)/77,105 = -.21
Change in Price of product X – (19,980-24,980)/24,980 = -.2

Demand Y/Price X = -.21/-.2 = 1.06

Kind of a surprise that is it same as the previous two attempts. I think we can definitely say that the two are competitors but by how much seems to be fairly difficult due to the number of variables that affect hardware sales.

We have taken a look at the 3DS was affected by the price cut, now lets look at how the Vita was affected. I will be using the official pricecut week and the week before.

Using the Price elasticity of demand formula we get
Change in Demand of product X – (60,561-11,669)/11,669 = 4.19
Change in Price of product X – (19,980-24,980)/24,980 = -.2

Demand X/Price X = 4.19/-.2 = 20.95

With price elasticity of demand we ignore the negative sign. So we can clearly see here the the Vita’s sales were highly dependent on its change in price. At least for that week. Just for fun lets try a couple of other weeks, assuming the pricecut had an effect on sales.

Using the Price elasticity of demand formula we get
Change in Demand of product X – (61,152-60,561)/60,561 = .01
Change in Price of product X – (19,980-24,980)/24,980 = -.2

Demand X/Price X = .01/-.2 = .05

Using the week after the pricecut we see that the Vita’s sales aren’t affected by price. Using this formula for this week doesn’t make any sense. The price didn’t change this week it changed last week. The increase in sales are due to new releases the Vita had particularly Soul Sacrifice. Well lets try the week before the pricecut, to see how breaking street date affected sales.

Using the Price elasticity of demand formula we get
Change in Demand of product X – (11,669-7,401)/7,401 = .01
Change in Price of product X – (19,980-24,980)/24,980 = -.2

Demand X/Price X = .58/-.2 = 2.88

This week show that the sales of the Vita are affected by the change in price. The change is demand is limited by the sale only being available at certain stores that lowered the price earlier than others. It isn’t an accurate comparison.

Now I want to look at how the change in the Vita sales affected the change in the 3DS sales. We will consider the Vita product X and the 3DS as product Y. I am going to start with the week before the price cut.

Week 8
Change in Demand of product X – (74,180-101,940)/101,940 = -.27
Change in Price of product X – (11,669-7401)/7401 = .58

Demand X/Price X = -.27/.58 = -.47

Week 9
Change in Demand of product X – (77,105-74,180)/74,180 = .04
Change in Price of product X – (60,561-11,669)/11,699 = 4.18

Demand X/Price X = .04/4.18 = .01

Week 10
Change in Demand of product X – (60,800-77,105)/77,105 = -.21
Change in Price of product X – (61,152-60,561)/60,561 = .01

Demand X/Price X = -.21/.01 = -21.00

Week 11
Change in Demand of product X – (69,326-60,800)/60,800 = .14
Change in Price of product X – (36,431-61,152)/61,152 = -.40

Demand X/Price X = .14/-.40 = -.35

What do you all think? Can we conclusively show that the 3DS and Vita are substitute products. That the sales of one affects the possible sales of another. Does the data hear clearly support the theory that games > price? What about when the consoles are both going through a dry spell? How can we find the market equilibrium of a gaming console? How do we isolate the software factor from the equation? Certainly when I worked on this more questions arose then were answered. I do know that the two are competitors and that there is some affect on sales when the other does better or worse. It is just that the degree of such is hazy at best. Kind of disappointing that the results are a bit inconclusive. Maybe I did something wrong? Or maybe there is a better formula.

I was hoping you had the answers after seeing all that math but I see you just have more questions... lol

A lot of variables here, but good study. I'm sure they have a substitute effect, they go after essentially the same market though concentrating on different sub markets. This last week the Vita's low sales are affected by a supply constraint announced by Sony. They are stepping up production to meet higher than expected demand and for Golden Week later.

It was my understanding that there would be no math.

Hm. Thread title made me think there would be some wacky video in which someone would try to pull apart a Vita and a 3DS and see which would break first.

This is why all this stuff felt so pointless when I learned it in Economics. There are far, far too many variables for concepts like elasticity to have any application in analysis.

Or maybe it's just the weekly fluctuations making things harder. Maybe using months would help?

Of course they are competitors. I could've told you that with no math lol

Maybe you thought these 2 devices targeted 2 different types of gamers? What I think that 3DS/Vita gamer is one and the same, and that really matters is the games. 3DS has all the big-name AAA titles so it is dominating the market over there. Once Vita gets something big, it'll be able to better compete with 3DS.

I think what Vita really needs now is a re-launch with a Vita Slim or something. We know how the 3DS XL worked wonders for the 3DS in Japan, it can do the same for Vita.

I got an A in economics, and i still dont know what this shit is.

Econ Major here.
Truth be told we can't use mathematics to show whether they're substitutes or not: There are too many variables. You use examples after the Vita Price cut but you assume that 3DS sales would have stayed constant if it were not for the price cut which is poor in itself. Basically: we can't say anything without some sort of control group which is very hard to do on a large scale like this.