Changing the values of the coinage while keeping the same name seems like it would be incredibly confusing. What was public opinion about it, and was there a generational divide? Did the economy take a hit? Did anyone find a way to profit from it? Was counterfeiting a big problem?
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The key reason that Decimal Day went smoothly was due to a substantial publicity campaign before the change, as well as introducing the 50p, 5p, and 10p coins early so that the British public would already be familiar with half of the coins. This was helped by the 5p and 10p coins having the same composition, size, and value as the shilling and two shilling. At this point, the farthing had ceased to be legal tender, and both the half-crown and halfpenny were withdrawn before Decimal Day in further preparation for the event. The song “Decimalisation” by Max Bygraves, was released, as well as television programs like ITV’s Granny Gets The Point and the BBC’s New Money Day.
This helped the transition. Young people quickly reacted to the change, helped by the 2-year information period, while the elderly often wanted conversions into the old system. Converters like Decimal Adders also helped the conversion. As for profiting, traders raised their prices, though the new currency favored the consumer. Some people used the new pennies as sixpence in vending machines. The last piece of the puzzle comes through football games, which would be broadcast for the 70-71 season as decimal first, followed by the predecimalised currency in parentheses after.
Sources:
Moore, N.E.A. “The Introduction of Decimal Currency to the UK in 1971. Comparisons with the Introduction of a Single European Currency.” Economic Papers, EUROPEAN COMMISSION DIRECTORATE-GENERAL FOR ECONOMIC AND FINANCIAL AFFAIRS, June 1995, aei.pitt.edu/41513/1/A5619.pdf.