Which person developed new economic ideas based on governments borrowing and spending more money during an economic crisis?

That would be the British economist, John Maynard Keynes. His philosophy of deficit spending (known as Keynesianism) developed and received attention during the period of global depression (especially in the US during the Great Depression) during the 1920s and 30s. While President Roosevelt took up the idea of Keynesianism later on in his New Deal, he originally set out with the then-age-old idea of having a balanced budget. President Hoover had operated under the same thought process during the 1920s (he actually developed some work programs before the New Deal), but since neither were willing to run a deficit, the programs never succeeded until FDR began to practice Keynesian economics.

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