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classical follow the basic assumption that 
1.economy is in ful employment.... 
2. the wages and prices are very flexible
3. there is no need of fiscal or monitary policy
4. the invisible hand make the economy self correctable
5. so the Aggregate supply curve is Vertical according to classicals so any rise inaggregate demand will increase prices not production

Keynesian follow the basic assumptions that 
1. economy may not be in full employment in short run
2. wage are rigid and prices are sticky (menu cost etc)
3. fiscal as well as monitory policy my be needed to correct the disequilibrium or improve the efficiency of economy 4. aggregate supply is upward sloping in the short run so a rise in aggregate demand may rise the production as well

Differences Between Classical & Keynesian Economics
by Osmond Vitez, Demand Media
Economics is the quantitative and qualitative study on the allocation, distribution and production of economic resources. Economics often studies the monetary policy of a government and other information using mathematical or statistical calculations. Qualitative analysis is made by making judgments and inferences from fiscal information. Two economic schools of thought are classical and Keynesian. Each school takes a different approach to the economic study of monetary policy, consumer behavior and government spending. A few basic distinctions separate these two schools. Basic Theory

Classical economic theory is rooted in the concept of a laissez-faire economic market. A laissez-faire--also known as free--market requires little to no government intervention. It also allows individuals to act according to their own self interest regarding economic decisions. This ensures economic resources are allocated according to the desires of individuals and businesses in the marketplace. Classical economics uses the value theory to determine prices in the economic market. An item’s value is determined based on production...
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