By , Business correspondent of The Christian Science Monitor

''California Dreaming.'' The West Coast economists at Claremont Economics Institute were in New York last week advising some of their 130 corporate and institutional clients on the shape of the economy and the future direction of interest rates.

John Rutledge, the institute president, said he expects interest rates to continue to fall, scraping bottom in April. At that point he expects Treasury bill rates will hit 5 1/2 percent, compared with 8.25 percent today; the prime interest rate will be 8 1/2 to 9 percent, compared with 11 percent today; and mortgage rates will fall to 10 1/2 percent, as against 12 percent today.

Behind this forecast is the belief that the economic recovery will not begin a broad upturn until summer because consumer buying remains weak. It's forecasting that current strength in the housing sector ''will not last for long.''

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The institute is more optimistic than most forecasters, however, for when the recovery begins. It's predicting the budget deficit will shrink to $100 billion by 1988 as the economy soars.

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