The purchasing power of an average hour's work declined 1.3 percent last month as wages failed to keep pace with prices, the Labor Department said yesterday.

It was the second-largest such decline in a year.

The buying power of an average hour's pay is now no greater than it was in 1972, government records show.

Wage rates have risen about 50 percent in that period, but workers have nothing to show for the increase.

These figures demonstrate starkly one of the primary ways that inflation undermines the health of the economist, by cutting into consumer demand.

But that poses a dilemma for policymakers: if wages rise much faster than prices, they will spur even more rapid inflation.

According to yesterday's figures, purchasing power now is running only 1.5 percent above its level of a year ago.

The Carter administration is sensitive about purchasing power these days, not wanting to nudge the economy into a recession.

The May figures don't lend much encouragement on that score. If consumers cut back on their buying, there's not much in sight to take their place in spurring the economy.

The monthly index of purchasing power measures the take-home pay of an average married wage earner with three departments, and is adjusted for increases in consumer prices. Over the past 12 months,it has risen only 1.5 percent.