President-Kenneth Kaunda of Zambia has just spent three days in Britain and is now going on to the United States. He is making these visits partly to press for an constitutional settlement in Rhodesia; but he is also looking for substantial support for Zambia's economy, which is in acute difficulties.

SYNOPSIS: The main problem is the price of coper. Zambia's copper belt, in the north-west of the country, earns more than half its revenue, and nearly all its foreign exchange. When copper prices were high, Zambia flourished. The living standards of its people were among the highest in Africa.

About three years ago, world copper prices collapsed. Zambian copper had been fetching 2,800 United States dollars a tonne at its peak. Now, it fetches less than half that -- less, in fact, than it costs to mine it.

The International Monetary Fund, which is helping Zambia, has demanded increased profitability in the mines. In an attempt to force up prices, Zambia, Zaire and Peru -- all important producers of copper -- have decided to cut back production by 15 percent. This, in its turn, raises a politically sensitive question: Whether or not it will be necessary to lay off miners. But the government has said it is anxious not to lose the 4,000 white employees working in the mines. They have been tending to move away, prompted by an uncertain future and a recent upsurge in violent crime.

Zambia also has difficulties in getting her coper out. The most direct route, through Rhodesia, has been closed for four years. The Benguela railway, across Angola, has not been usable since the Angolan civil war. Only the road and rail routes through Tanzania are open.

The Tazara Railway, which links the copper belt with Dar Es Salaam, has run into problems. It was financed by China, built in five years and opened in 1975. But so far, it has proved barely able to cope with the weight of traffic it had to carry as Zambia's only rail link with the outside world. There have been reports of sabotage to bridges and tunnels; serious accidents; and hundreds of wagons out of use for repair.

There is serious congestion, too, at the port of Dar es Salaam. Figures were given there last month of 50,000 tonnes of Zambian copper piled up waiting for export, and 90,000 tonnes of goods waiting for transport into Zambia. So Zambia goes short of the goods and the export earnings.

Economic experts say that one solution for Zambia's economic problems is to develop its agriculture. It is a fertile country, and should be able to feed itself and export farm produce. President Kaunda has spoken on this theme many times at agricultural shows. The copper boom encouraged people to drift to the towns, and many European commercial farmers have left since independence. Now the government is taking steps to encourage Zambians to go back to the land.