The Journal of Commerce Industrial Price Index fell sharply last week as prices turned lower for scrap steel, scrap copper and plywood.

The index Friday stood at 102.8, down 0.8 points from the previous Friday and off 0.1 from Thursday's level.The metals subindex group - scrap steel, scrap copper, primary aluminum, zinc, lead and tin - moved down 0.6 to 110.4 Friday from 111.0 the previous Friday. Of particular weakness was the No. 1 heavy melting scrap steel, which fell by $107.50 a ton from $109.33 for the week.

Copper prices were down in response to the sluggish pace of auto sales and housing starts. No. 2 scrap copper was 86.50 cents a pound on Friday.

However, some analysts noted that Friday's news that London Metal Exchange copper warehouse stocks were off a surprising 4,225 metric tons may indicate demand has not softened as much as many industry people believed.

''If this (copper) was going to crack, you would think it would have done it this week. But it hasn't," said Bernard Savaiko, a senior commodity analyst at Paine Webber Inc. Mr. Savaiko noted that the financial community remains heavily bearish on the metal.

In the textiles subgroup, cotton remained firm although the price dipped slightly late in the week. On Friday, the natural fiber was 77.56 cents a pound, down from a level of over 79 cents a pound the previous week.

There were indications China and Japan may have purchased more U.S. cotton, exporters said. China was thought to have purchased 15,000 to 20,000 bales of Texas cotton for nearby delivery.

Japan may have bought 10,000 bales of San Joaquin Valley new-crop cotton for January through March shipment, exporters said.

Far Eastern countries continued to inquire for various styles for shipment dates ranging from prompt through the 1991 first quarter.

Most prices for lumber and plywood were lower, as demand from wholesalers and retailers remained light, Knight-Ridder Financial News reported on Friday.

Specifically, prices for plywood - a key material in The Journal of Commerce index - fell to a low of $199 per 1,000 board feet.

While prices moved up to between $203 and $205 on Friday, continued sluggish demand for single-family housing makes it unlikely prices will stick, analysts said.

This sector of the economy has seen sales erode, sharply reducing the need for wood products.

While prices have fallen, several lumber mills in the Pacific Northwest were confident that upcoming vacation and maintenance shutdowns would tighten supplies to underpin prices through the summer.