In late 2013, Nintendo found itself in a bit of a bind. A year after the release of its flagship Wii U, sales were slumping. In August, the company sold a mere 34,000 consoles in North America, far fewer than it had projected, and many wondered whether Mario & Co. were doomed.

In an attempt to boost sales, Nintendo dropped the price of the Wii U console from $300 to $250 the next month…and sales tripled. Crisis averted! Princess saved! Right?

Mmmmm, maybe not.

When Nintendo lowered the price of the Wii U, it sold more consoles. However, it also made less profit on each one. According to CNN, it costs around $228 to manufacture a Wii U. Before the discount, Nintendo made $72 on each console; after, it only made $22. Even though Nintendo sold more consoles, it ended up making less money. A lot less.

Aug. 2013 (Before Price Drop) | Sept. 2013 (After Price Drop) | |

Retail Price | $300 | $250 |

Per-Unit Profit | $72 | $22 |

Units Sold | 34,000 | 102,000 |

Total Profit | $72 × 34,000 = $2,448,000 | $22 × 102,000 = $2,244,000 |

So did Nintendo blow it? Should it have offered a discount at all and, if so, what would have been the right amount? To answer this, we need a way to estimate the total profit that Nintendo would have made on consoles at every possible price.

Total Profit = Profit per Console × Consoles Sold

At a price of $300, Nintendo made $300 - $228 = $72 on each console. At a price of $250, it made $250 - $228 = $22. At a price of $p, then, Nintendo would make $(p - 228). We can use this to model the profit per console for every possible price.

Modeling the total number of consoles sold is a bit trickier; after all, we can’t go back in time and see how many Nintendo would have sold at various prices. Fortunately, we can use the sales figures we *do* know to estimate this. At $300, Nintendo sold 34,000 consoles. At $250, it sold 102,000 consoles. Economists often assume that the relationship between price and quantity sold is linear: that for every dollar you decrease the price, the number of units you sell will increase by a constant amount.

When we calculate the equation of the line that passes through the existing sales points, we get D = -1360p + 422,000. This suggests that for every dollar that Nintendo discounts the price of the Wii U, demand increases by 1360 consoles. (It also suggests that the most anyone would be willing to pay for a console is $325.)

With these two functions — the profit per console and the demand for consoles, i.e. the number of consoles sold — we can model how much profit Nintendo would have made at every possible price.

Based on the graph, it appears that if Nintendo wanted to maximize profits from sales of the Wii U console, it shouldn’t have charged $250. It should have charged $276.50. At this price, Nintendo would have made $48.50 per console and sold 65,960 consoles, for a total monthly profit of $3.2 million. Clearly this would have been better than the $2.4 million the company *did* make. So, yeah, maybe Nintendo blew it!

Again, though, maybe not.

For one thing, our model is really simple — we assume that demand is linear, when maybe it’s something else — and surely the conversations at Nintendo HQ were a lot more detailed than this one. For another, maybe Nintendo intentionally underpriced the console. There's a precedent for this sort of strategy; for instance, Amazon sells its Kindle e-reader at a loss, which they more than make up for by selling all sorts of highly profitable digital media for consumption on the Kindle.

Like the Kindle, the Wii U is in some sense a gateway purchase. What Nintendo really wants you to buy is a Wii U...plus a whole bunch of games *for* the Wii U. Having a Wii U makes you a game-buyer for years to come, so it behooves Nintendo to get consoles into as many hands as possible, even if that means foregoing some profit on your initial purchase.

So maybe it makes sense for Nintendo to sell the Wii U for less — maybe even at a loss — if doing so will boost game sales. After all, that's where all the coins are.

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