The Big Mac Index Explained: PPP, Implied Exchange Rates and Valuation

The Big Mac index is an informal measure of currency valuation that treats one Big Mac burger as a basket of goods. It divides the burger's local price by its US price to get an implied purchasing power parity exchange rate, and compares that rate with the market exchange rate. A gap between the two suggests a currency is overvalued or undervalued against the dollar.

The idea underneath is purchasing power parity applied to one product sold in many countries and made to nearly the same recipe. For the theory on its own, read the purchasing power parity guide.

The purchasing power parity logic

The index rests on the law of one price: an identical good should cost the same everywhere once its price is converted into one currency. If it did not, traders could buy where the good is cheap and sell where it is dear. That buying and selling, called arbitrage, would push the two prices together.

Purchasing power parity extends the law of one price to a whole basket of goods. The Big Mac index shrinks the basket to one item. If PPP held exactly, a Big Mac would cost the same number of dollars in every country. The exchange rate that makes that true is the burger's implied PPP exchange rate.

A currency whose burger is cheap in dollars looks undervalued. A currency whose burger is expensive in dollars looks overvalued. PPP theory predicts that market rates drift toward parity over long periods.

Big Mac index formula

Three numbers go in: the local burger price, the US price, and the market exchange rate quoted as units of local currency per dollar.

Implied PPP exchange rate = local price / US price

Local burger price in dollars = local price / market exchange rate

Overvaluation or undervaluation (%) = (implied PPP rate / market rate - 1) x 100

The last formula gives the same answer as comparing dollar prices directly: (local price in dollars / US price - 1) x 100. A negative result means the currency is undervalued against the dollar. A positive result means it is overvalued.

Worked example with hypothetical prices

Every price and exchange rate below is invented for illustration. None is a real Big Mac price or a real currency valuation, and the countries are fictional.

Suppose a Big Mac costs $6.00 in the United States. In Northland it costs 21 lumens, and the market exchange rate is 5 lumens per dollar.

Step 1: Find the implied PPP exchange rate. Implied rate = 21 / 6.00 = 3.5 lumens per dollar. At that rate the burger would cost the same in both countries.

Step 2: Convert the Northland price into dollars. Dollar price = 21 / 5 = $4.20.

Step 3: Compare. Valuation = (3.5 / 5 - 1) x 100 = (0.70 - 1) x 100 = -30%. Check with dollar prices: (4.20 / 6.00 - 1) x 100 = -30%.

The lumen is undervalued by 30% against the dollar on the burger measure. A US visitor pays 6.00 - 4.20 = $1.80 less for the same burger in Northland.

Step 4: Find how far the lumen would need to move. Parity needs the rate to fall from 5 to 3.5 lumens per dollar. In dollars per lumen, that is a move from 1 / 5 = $0.20 to 1 / 3.5 = about $0.2857. The rise is (0.2857 - 0.20) / 0.20 = 0.4286, or about 42.9%. A currency 30% undervalued has to appreciate by about 43% to reach parity, because the two percentages are measured from different bases.

Now an overvalued case. In Westmark, also fictional, a Big Mac costs 960 dalers and the market rate is 120 dalers per dollar.

• Implied rate = 960 / 6.00 = 160 dalers per dollar
• Dollar price = 960 / 120 = $8.00
• Valuation = (160 / 120 - 1) x 100 = (1.333 - 1) x 100 = +33.3%

The daler is overvalued by about 33%.

A hypothetical Big Mac index table

Four invented countries, each measured against the same $6.00 US price:

Southport works the same way: 3,300 / 6.00 = 550, then 3,300 / 750 = $4.40, then (550 / 750 - 1) x 100 = -26.7%. Eastvale sits exactly at parity.

Watch the quote direction

Some currencies are quoted as dollars per unit of foreign currency. Then the formula becomes (market rate - PPP rate) / PPP rate x 100, the form the purchasing power parity calculator uses. For Northland, the PPP rate is 6.00 / 21 = about $0.2857 per lumen and the market rate is $0.20 per lumen, so the valuation is (0.20 - 0.2857) / 0.2857 = -30%, the same answer. Mixing the two quote styles in one calculation is the usual way to get the sign backwards. The exchange rates guide covers quoting conventions.

Why a Big Mac

A good PPP test item has to be the same product everywhere, sold in many countries, and easy to price. The Big Mac fits all three.

• One recipe. The burger is built to a standard specification, so a price gap is not a quality gap.
• Wide availability. It is sold in many countries, which gives a long list of currencies to compare.
• A mix of inputs. The price bundles traded ingredients such as beef, cheese and wheat with local wages, rent and electricity, so one burger is a small model of a whole economy's costs.

Why the Big Mac index differs from market exchange rates

The law of one price relies on arbitrage, and nobody can ship a hot burger across a border to profit from a price gap. So market rates and burger parity drift apart for reasons that are part of what the measure captures.

Non-traded inputs: wages and rent

A large part of a burger's cost is local labor, rent and utilities. Those inputs cannot be traded, so their prices can differ between countries with no arbitrage to close the gap. In theory, where wages for non-traded work are lower, the non-traded part of a burger costs less in dollars. The Balassa-Samuelson hypothesis, named for the economists Bela Balassa and Paul Samuelson, explains why: higher productivity in traded-goods industries in richer countries pushes up wages there, and those higher wages raise the prices of non-traded services such as restaurant labor.

Here are the two hypothetical burgers from the example split into invented cost parts:

The traded ingredients cost the same in both places, as the law of one price predicts. The whole gap comes from the non-traded rows: 1.20 + 0.40 + 0.20 = $1.80. Here the lumen's 30% undervaluation reflects cheaper local labor, rent, and taxes and margin, not a currency traders have mispriced.

Taxes

Sales taxes and value-added taxes are built into the menu price. Two countries with identical costs but different tax rates show different burger prices, and the index records a gap that comes from the tax code.

Trade barriers and transport costs

Tariffs and quotas on beef, cheese or wheat raise the local cost of the traded ingredients, so even the traded part of the burger need not obey the law of one price. The tariffs, quotas and trade barriers guide shows how a tariff raises the domestic price of an imported good.

Capital flows set short-run exchange rates

In the short run, exchange rates are driven mostly by interest rates, investment flows and expectations, not goods prices, so nothing in the theory forces a currency to burger parity quickly. The index is better read as a long-run benchmark than a short-run forecast.

What the index predicts on a foreign exchange graph

Draw the market for lumens. The horizontal axis is the quantity of lumens. The vertical axis is the price of one lumen in dollars. Demand slopes down, supply slopes up, and they cross at the market rate of $0.20.

If Northland's traded goods, not just its burgers, are cheap at $0.20, foreign buyers come for Northland exports. They need more lumens, so the demand curve for lumens shifts right, and the new equilibrium sits higher up the supply curve: the lumen appreciates. If the gap comes only from non-traded costs, as in the cost table above, PPP gives no such pressure, and the lumen need not reach $0.2857. You can shift the curves in the exchange rates sandbox, and the currency appreciation vs depreciation guide covers who gains when a currency rises.

See it move

Make it move

The foreign exchange market for dollars at equilibrium. Tap it to drag the curves, open the full version, or put it on your own site free, or turn it into a five-minute class activity.

Big Mac index and AP Macroeconomics

The Big Mac index and purchasing power parity go beyond the AP Macroeconomics course. They build on topic 6.2, Exchange Rates, and topic 6.3, The Foreign Exchange Market: quoting an exchange rate both ways, converting prices between currencies, and reading appreciation off a graph. See the AP Macro 6.2 topic page, the exchange rates module and the exchange rate vs purchasing power parity comparison.

Common mistakes:

• Dividing the wrong way. With rates quoted as local currency per dollar, the implied rate is local price / US price.
• Treating every gap as mispricing. Much of a gap can come from low local wages and rents.
• Expecting a short-run forecast. PPP is a long-run anchor.
• Assuming the percentages are symmetric. A 30% undervaluation needs about a 43% appreciation to close.