10.5 Pricing Indian gold: import parity

10.5.1The parity formula#

Derivation

An importer buys one troy ounce abroad at $P^{\text{USD}}_{oz} + q$ dollars, which costs $X(P^{\text{USD}}_{oz}+q)$ rupees. Customs charges $d$ on that value, so the duty-paid cost is $X(P^{\text{USD}}_{oz}+q)(1+d)$ rupees per ounce, i.e. $X(P^{\text{USD}}_{oz}+q)(1+d)/G$ per gram and ten times that per 10 g. If the domestic price were above this, importers would import and sell, pushing the local premium down; below it, imports would stop and the local discount would widen until smuggling, recycling and lower demand clear the market. GST is a pass-through value-added tax on the duty-inclusive value, so it multiplies the result.∎

Second-order corrections

• Tariff value. Customs duty on gold is levied not on the invoice price but on a tariff value in USD per 10 g that CBIC revises roughly every fortnight (reported by tax publications such as TaxGuru and Taxscan, 2026). When the market moves sharply between revisions, the effective duty differs from $d$ times the market price.
• Purity. The USD price is per fine ounce; a 995 bar contains 0.995 of fine gold per gram.
• Carry. A futures price is a forward price: multiply spot parity by $e^{(r_{\text{INR}} - \ell)\tau}$. Strictly, the forward parity uses a COMEX futures price for the same month and the USDINR forward rate, which embeds the INR–USD interest differential (M11).

Proof

Take logs of (10.15) at both dates and subtract; $G$ and the factor 10 cancel.∎

So rupee gold is long gold and long the dollar against the rupee. "Gold falls 2% in dollars and the rupee weakens 1%" gives $0.98 \times 1.01 - 1 = -1.02\%$ in rupees.

10.5.2Duty history and the 2026 changes#

Effective	BCD	AIDC	Total $d$	With 3% GST	Source and status
until 23 Jul 2024	10%	5%	15%	18.45%	Budget-day reports, 23 Jul 2024 (WION, Tribune); widely reported
24 Jul 2024 (Budget 2024–25)	5%	1%	6%	9.18%	Same; effective 24 Jul 2024
13 May 2026	10%	5%	15%	18.45%	CBIC Notification No. 15/2026-Customs (BCD 5% → 10%) and No. 16/2026-Customs (AIDC/SWS), both dated 12 May 2026, effective 13 May 2026 (texts read from a tax publication's copy, because https://www.cbic.gov.in failed a TLS check on 6 Nov 2026)

The "with GST" column is $(1+d)(1.03) - 1$. One source (Drishti IAS) reported the 2026 duty as "18.4%". The other sources give 15%. The 18.4% figure matches $1.15 \times 1.03 = 1.1845$, the all-in incidence including the 3% IGST at import, so the conflict is probably one of definition. That reconciliation is an inference made for this course, not something a source states.

Context for the May 2026 hike: the rupee was near record lows after the Hormuz shock; reserves had fallen from a reported all-time high of about $728 bn in February to about $690 bn by 1 May (as reported by Business Today and others; secondary; the primary series is the RBI Weekly Statistical Supplement). Reserves later set a new record of US$785.7 bn as on 4 Sep 2026 and stood at US$717.1 bn as on 30 Oct 2026 (RBI WSS; see M11 · 11.11). The Prime Minister had asked citizens on 11 May to pause non-essential gold buying. After the hike, gold import volumes fell about 70% to 25–30 t a month (official quoted by Outlook Business; secondary), and ₹10,463 cr of duty was collected between 13 May and 2 Aug 2026 (a Lok Sabha written reply as reported by the press; the reply itself was not opened).

Mechanical effect of the hike With everything else fixed, (10.16) gives a duty term of $\ln(1.15/1.06) = 8.15\%$, i.e. a jump of 8.49% in the domestic price.

10.5.3Worked example: reproducing MCX on 2 November 2026#

Inputs (approximate, 2 Nov 2026): international gold about $3,975/oz (secondary price reports; the LBMA Gold Price is the benchmark but its history is licence-restricted), USDINR about 94.5 (FBIL reference rate, as published on the RBI homepage), duty 15% (10.5.2). MCX GOLD December 2026 future: ₹1,38,839/10 g (2 Nov 2026; secondary news reports; MCX's own bhavcopy is the primary record).

1. Dollars per gram: $3975 / 31.1034768 = 127.799$.
2. Per 10 g: $1,277.99.
3. In rupees: $1277.99 \times 94.5 = \text{₹}1{,}20{,}770$.
4. With 15% duty: $1{,}20{,}770 \times 1.15 = \text{₹}1{,}38{,}886$.
5. MCX: ₹1,38,839. Difference: $138{,}886/138{,}839 - 1 = 0.034\%$.

The implied duty from the MCX quote is $138{,}839/120{,}770 - 1 = 14.96\%$.

Refinement Steps 1–4 price spot fine gold. MCX GOLD is a 995 contract for December delivery. Purity lowers the parity by 0.5% (to ₹1,38,191); about 33 days of carry at 5.5% raises it by $e^{0.055 \times 33/365} - 1 = 0.50\%$ (to ₹1,38,880). The two corrections almost cancel, which is why the crude formula works so well. Do not rely on that coincidence when rates or the expiry gap change. The code in m10_gold_parity.py reproduces steps 1–5; the test checks the 0.1% tolerance.

Retail Add 3% GST: $1{,}38{,}886 \times 1.03 = \text{₹}1{,}43{,}052$ per 10 g before making charges.

10.5.4The 2026 cushion#

Between the late-January 2026 peak (about $5,608) and 2 November (about $3,975), dollar gold fell about 29%. MCX gold fell much less over a similar stretch: from about ₹1.60 lakh on 13 March 2026 (secondary market report) to ₹1,38,839 on 2 November, about −13%. By (10.16), two terms cushioned the rupee price: the duty term (+8.15% log from 13 May) and the FX term (the rupee weakened sharply in March and stayed weak). Problem 11 asks you to do the decomposition with stated inputs. Note that the comparison above uses different start dates for the two series, so it shows the direction, not the size, of the cushion.