Module 8 • Purchasing Power Parity (PPP) + Big Mac Index

Quiz Big Mac Game

1) What is Purchasing Power Parity (PPP)?

PPP says exchange rates adjust so a basket of goods has the same purchasing power across countries. If a country has higher inflation, its currency should depreciate over time to restore parity.

PPP (idea): Exchange rates move so that relative prices line up across countries over the long run.

Student-friendly definition (copyable)

Purchasing Power Parity (PPP) is the idea that the exchange rate between two currencies should equalize the purchasing power of the two currencies. If prices rise faster (higher inflation) in one country, its currency should depreciate so that goods don’t remain permanently more expensive there.

Key links

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PPP Cartoon Video

Watch a simple cartoon explanation of Purchasing Power Parity.

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PPP Calculator

Open the PPP calculator for quick practice and examples.

Exam-safe takeaway: PPP is mainly a long-run anchor. In the short run, FX is driven by news, capital flows, interest rate expectations, and risk sentiment.

Law of One Price

2) Law of One Price (LOP)

The Law of One Price says: identical goods should sell for the same price in different countries when prices are expressed in the same currency—if there are no barriers or costs.

LOP formula (one good):
P$ = P¥ × SpotRate($/¥)
Rearranged: SpotRate($/¥) = P$ / P¥

Example (laptop)

If a laptop costs $1,000 in the U.S. and ¥120,000 in Japan, then LOP implies the spot rate should be: $1,000 / ¥120,000 = $0.0083 per ¥ (or ¥120 per $).

When LOP holds vs doesn’t

Condition	Holds	Does NOT hold
Identical product	Exactly the same good	Quality/branding differs
Transport costs	Negligible	Shipping/logistics expensive
Trade barriers	No tariffs/quotas	Tariffs/controls present
Taxes/fees	No big local taxes	Sales/VAT, dealer markups
Market structure	Competitive	Monopoly/oligopoly power
FX regime	Free-floating	Intervention/capital controls

Limitations (why real-world prices differ)

Limitation	Explanation
Transportation	Shipping/insurance can widen price gaps.
Non-traded goods	Services and many local costs are not easily arbitraged.
Policy	Tariffs, subsidies, and capital controls distort prices and FX.
Market segmentation	Different demand, incomes, and competition create different markups.
FX volatility	Short-run FX moves are faster than price adjustment.
Menu costs	Firms may not reprice frequently.
Branding/preferences	Local tastes affect pricing power.

Discussion Game Quiz

In-class discussion: Can Bitcoin obey the Law of One Price?

Factor	Can BTC hold the same price globally?	Why / why not?
Global accessibility	Yes (in theory)	Trades 24/7 globally; prices should converge.
No trade barriers	Yes	No shipping/tariffs for digital assets.
Exchange-rate influence	Partly	BTC priced in local currency; FX moves can create temporary gaps.
Arbitrage	Helps maintain	Traders exploit gaps, pushing prices back together.
Transaction fees	No (distorts)	Blockchain + exchange fees reduce arbitrage profitability.
Regulations	No (major obstacle)	Restrictions fragment markets; access differs by country.
Liquidity	No (in some places)	Thin markets can show bigger spreads and gaps.
Capital controls	No (distorts)	Hard to convert to/from fiat in some countries.

Conclusion to prompt discussion: Bitcoin can get closer to the Law of One Price than many physical goods, but frictions (fees, regulation, banking access, and capital controls) can create persistent premiums/discounts.

Discussion

3) Does PPP determine exchange rates in the short term?

Short answer: No. Short-run FX is mostly news-driven (rates, growth expectations, risk, geopolitics).

Interest-rate surprises and central bank signals move FX quickly.
Risk sentiment and safe-haven flows can dominate inflation.
Prices and wages are “sticky” → goods prices adjust slowly.

Long run: PPP is a long-run anchor. Typical horizon often cited in classes is roughly 4–10 years.

What else?

Name drivers of FX that can overpower PPP in the short run: capital flows, portfolio rebalancing, carry trades, political risk, commodity price shocks, and sudden shifts in expectations.

Big Mac (PPP) Game Quiz

4) Big Mac Index: “PPP with one standardized product”

PPP compares baskets of goods. The Big Mac Index is a simplified PPP using the price of a Big Mac across countries. It is intuitive, but still imperfect because inputs (wages, rents, taxes) differ across countries.

Big Mac implied FX: S* = Price_USD / Price_FCY (expressed as USD per 1 FCY, or invert as needed).

Why Big Mac is imperfect (quick)

Big Macs use local labor and rent (non-traded inputs), taxes differ, and pricing strategy varies by market. So it’s a “fun” proxy for PPP, not an arbitrage machine.

Big Mac Game (implied rate + over/undervaluation)

Enter Big Mac prices and the actual market FX. Choose quote direction.

Big Mac price in U.S. (USD)

Big Mac price in foreign country (FCY)

Market FX (choose quote below)

Quote convention

Foreign currency label (optional)

Notes (optional)

Output will appear here.

Visual: market FX vs implied PPP FX (same quote convention you selected).

Calculator PPP IFE

PPP and IFE Calculators

Do not mix these up:
PPP uses inflation rates and is mainly a long-run currency idea.
IFE uses nominal interest rates and says the currency with the higher nominal interest rate is expected to depreciate.

Concept	Main input	Main idea	Why we need it
PPP	Inflation differential	Higher-inflation country’s currency tends to depreciate over time.	Helps explain long-run FX movement and whether a currency may be over/undervalued.
IFE	Nominal interest-rate differential	Higher-interest-rate currency is expected to depreciate.	Helps investors think about returns on foreign deposits/bonds after currency changes.

Relative PPP (inflation-based)

Formula:
If spot is quoted as quoted currency per 1 base currency (example: USD/GBP or $/£), then

E[S1] = S0 × (1 + π_home) / (1 + π_foreign)

Approximation:
%ΔS ≈ π_home − π_foreign

What is PPP, and why do we need it?

PPP = Purchasing Power Parity.

It says currencies should adjust over time so that purchasing power stays comparable across countries. If one country has higher inflation, its goods become relatively more expensive, so its currency should tend to depreciate in the long run.

Why we need PPP:

To connect inflation to exchange-rate movement.
To explain long-run currency changes.
To discuss whether a currency may be too strong or too weak.
To compare inflation effects across countries in a simple way.

Very clear worked example (PPP)

Suppose spot is 1.60 USD/GBP, U.S. inflation is 9%, and U.K. inflation is 5%.

Then:
E[S1] = 1.60 × (1.09 / 1.05)
E[S1] = 1.60 × 1.038095 ≈ 1.6610 USD/GBP

So the spot rate is expected to rise from 1.60 to about 1.6610.
Because the quote is USD per GBP, that means the pound appreciates and the dollar depreciates.

Relative PPP Calculator

This version shows the formula substitution clearly so students can see each step.

Current spot S0 (quoted currency per 1 base currency) (example: USD/GBP)

Home inflation π_home (%) (quoted-currency country, e.g., U.S.)

Foreign inflation π_foreign (%) (base-currency country, e.g., U.K.)

Base currency label (example: GBP)

Quoted currency label (example: USD)

Show which result?

Output will appear here.

IFE (International Fisher Effect)

IFE formula:
If spot is quoted as quoted currency per 1 base currency (example: USD/GBP), then

E[S1] = S0 × (1 + i_home) / (1 + i_foreign)

Approximation:
%ΔS ≈ i_home − i_foreign

What is IFE, and why do we need it?

IFE = International Fisher Effect.

It says the currency with the higher nominal interest rate is expected to depreciate. The intuition is that higher nominal rates often reflect higher expected inflation.

Why we need IFE:

To connect interest rates to expected exchange-rate movement.
To think about whether a higher foreign interest rate is really better after FX changes.
To help explain why chasing the highest interest rate can be risky.
To compare with PPP: PPP uses inflation, but IFE uses nominal interest rates.

Very clear worked example (IFE)

Suppose spot is 1.60 USD/GBP, U.S. nominal interest rate is 8%, and U.K. nominal interest rate is 4%.

Then:
E[S1] = 1.60 × (1.08 / 1.04)
E[S1] = 1.60 × 1.038462 ≈ 1.6615 USD/GBP

Since the quote is USD per GBP, the rate rises, so the pound appreciates and the dollar depreciates.

Easy memory trick:
PPP → inflation
IFE → interest rates

IFE Calculator

Use this when you want to explain expected currency change using nominal interest rates, not inflation.

Current spot S0 (quoted currency per 1 base currency)

Home nominal interest rate i_home (%)

Foreign nominal interest rate i_foreign (%)

Base currency label

Quoted currency label

Show which result?

Output will appear here.

PPP vs IFE in one sentence each

PPP: higher inflation → currency tends to depreciate.
IFE: higher nominal interest rate → currency tends to depreciate.

Law of One Price (one good)

SpotRate = P_home / P_foreign (be consistent with quote direction)

LOP Spot Rate Calculator

Example: US price and Japan price → implied $/¥ or ¥/$.

Home price (e.g., USD price)

Foreign price (e.g., JPY price)

Output quote

Home label

Foreign label

Notes

Output will appear here.

Teaching note: PPP and IFE both give an expected FX direction, but they use different inputs.

PPP asks: Which country has higher inflation?
IFE asks: Which country has the higher nominal interest rate?

One more thing students often confuse

IFE is not the same as IRP.

IFE predicts the expected future spot rate from interest-rate differences.
IRP is a no-arbitrage relationship using spot, forward, and interest rates.

For this module, the key point is simply:

PPP → inflation
IFE → nominal interest rates

Quiz Practice

Module 8 Quiz

Practice before homework. Open the quiz in a new tab.

Open Quiz (Module 8) Big Mac Game (Full)

Tip: Use the Big Mac game first, then take the quiz. Watch quote direction (USD/FCY vs FCY/USD).

Homework Due with final

Homework (PPP + Arbitrage)

PPP Homework #1 (UK vs Norway, NOK/£)

A product costs £1 in the UK and 16 NOK in Norway. Next year, UK inflation is 5% and Norway inflation is 9%.

Compute new product prices in both countries.
Compute implied new exchange rate NOK/£ using PPP.
Compute implied % change in NOK/£.

Show hint (PPP #1)

Step 1: Update each country’s price using inflation: P1 = P0 × (1 + π).
Step 2: Use PPP to compute the implied new rate: S1 = P_NO,1 / P_UK,1 (NOK/£).
Step 3: Percent change: %ΔS = (S1 − S0) / S0.
Interpretation: If NOK/£ rises, the pound buys more NOK (GBP strengthens vs NOK).

PPP Homework #2 (EUR/USD)

Current rate is 1€ = $1.10. Eurozone inflation is 6%; U.S. inflation is 3%.

Using Relative PPP (approx), compute expected % change.
Estimate new USD/€ rate.
Will the euro appreciate or depreciate vs the dollar? Explain.

Show hint (PPP #2)

Quote check: You are given $ per € (USD/€).
Approx PPP: %ΔS ≈ π_US − π_EZ.
Exact PPP: S1 = S0 × (1+π_US)/(1+π_EZ).
Direction: If S falls in USD/€, that means € buys fewer dollars (euro depreciates vs USD).

Critical Thinking: Physical arbitrage (gold Dubai vs New York)

Dubai: $5,000/oz. New York: $5,100/oz. Shipping + insurance: $20/oz.

Is arbitrage possible? Show calculation.
Name real products where international arbitrage is common and why.
What barriers prevent arbitrage (regulations, tariffs, logistics, perishability)?
Does physical arbitrage improve market efficiency? Why/why not?

Show hint (Gold arbitrage)

Step 1: Compute total cost to deliver to NY: Cost = DubaiPrice + Shipping.
Step 2: Compare with NY price. Profit per oz: Profit = NYPrice − Cost.
Decision: Arbitrage exists only if profit is positive (and large enough to cover real frictions).
Real-world barriers: taxes, delays, bid–ask spreads, financing, regulation, storage/insurance.

Educational disclaimer: Examples assume simple conditions (no taxes, no delays, no capital controls). Real-world FX and goods markets include frictions.