is the long run elasticity of demand is ever smaller than the short run elasticity of demand.
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Both.
In the long run, manufacturers and producers can respond to consumer demand by analyzing trends that develop over time. Short-term, this is less practical because adjustments often cannot be made quickly enough to accommodate changes.
Short Run: A time period in which the amounts of some inputs are fixed. Long Run: During which there is sufficiently long to allow full flexibility in all inputs used.
In the short run, consumers have fewer options to adjust their purchasing behavior, making demand more sensitive to price changes. In the long run, consumers have more time to find substitutes or adjust their budgets, making demand less elastic.
Most economists agree on the application of supply, demand & elasticity. Here three examples of these factors in the world of economics: A. The demand for food is for the most part "inelastic" because food is inexpensive and a necessity. Concurrent with new technologies in agriculture, this has ironically has reduced total revenue paid to the farming sector; B. Oil as an example. In the 1970's OPEC reduced the supply of oil in order raise its price. Yes, in the short run, the demand for this product ( never a cheap one as agriculture above ) tended to be inelastic as consumers were pressed to find substitutes. As expected, the decrease of this essential commodity raised prices & profits for OPEC. Long term, however, more fuel efficient automobiles and other sources of energy such as increased gas & oil production caused the oil demand towards elasticity, inducing producers to search for more oil causing this commodity to become more elastic. Thus the short term run up in prices did not carry into the long run. Result: back to normalcy. C. Illegal drug market. The short term demand for additive drugs is relatively inelastic. Government policies & practices dove tail to enhance the climb in price for drugs. Yet consumption, based on addiction, remains level and revenue paid by users increases. This places pressure on users to increase their own revenues and perhaps causes crime rates to rise to fund their addictions. Studies however show that long term drug usage must level out. The price in this example reduces demand and we see elasticity. Law enforcement, price reduce demand which reduces total revenue, and this industry flattens out. The above examples enable the economist to analyze important events and policies that shape the economy.