Question

An ongoing policy debate concerns whether to legalize the use of drugs such as marijuana and cocaine. Some researchers estimate that legalizing cocaine would cause its price to fall by as much as 95 percent. Proponents of legalization argue that legalizing drug use would lower crime rates by eliminating the main reason for the murderous gang wars that plague many big cities and by reducing the incentive for drug addicts to commit robberies and burglaries. Opponents of legalization argue that lower drug prices would lead more people to use drugs.14$11.44$10.478.148.01$11.47a)Suppose the price elasticity of demand for cocaine is -2. If legalization causes the price of cocaine to fall by 95 percent, what will be the percentage increase in the quantity of cocaine demanded?EpDemand = % change Qd or , 2 = % change Qd= 190% change P95The percentage increase in the quantity demanded for cocaine would be 190%. In this scenario, you know that the price elasticity of demand for cocaine is elastic because of its coefficient of 2.You are asked to calculate the % change in quantity demanded knowing the other two variables (elasticity and % change in price). A 95% decrease in the price of cocaine would then lead to an increase in the quantity demanded for cocaine of 190%. b)If the price elasticity is -0.02, what will be the percentage increase in the quantity demanded?EpDemand = % change Qd or , .02 = % change Qd= 1.90% change P95Clearly, the higher the absolute value of the price elasticity of demand for cocaine, the greater the increase in cocaine use that would result from legalization. If the price elasticity is as high as in question A, legalization will lead to a large increase in use. If, however, the price elasticity is as low as in question B, legalization will lead to only a small increase in use. 36. In summer 2007, Sony decided to cut the price of its Playstation 3 video game console from $600 to $500. One industry analyst forecast that the price cut would increase sales from 80,000 units per monthto 120,000 units per month. Assuming the analystâs forecast is correct, calculate the price elasticity of demand for Playstation 3.$500 / $600 -1 = 17% cut in price; 120,000 / 80,000 = 50% increase in salesEpDemand = % change Qd or , = 50%= 2.94% change P17%The coefficient for the price elasticity of demand is 2.94, meaning that the cut in price of Playstation 3 is very elastic as is also evidenced by the 50% increase in quantity demanded from a lesser percentage decrease in the price of the video game console.

Answer 1

A) If the price elasticity of demand of any product is -2, a decrease in its price will result in a larger increase of the quantity demanded.

In this case, a 95% decrease in price will result in a:

-2 = % change in quantity demanded / -95%

% change in quantity demanded = -2 x -95% = 190% increase in quantity demanded

B) if the PED = -0.02 then it is very inelastic

-0.02 = % change in quantity demanded / -95%

% change in quantity demanded = -0.02 x -95% = 1.9% increase in quantity demanded.

Depending on the PED of cocaine, the quantity demanded might increase severely or bare increase if the price falls. If the PED is inelastic (PED < 1, in absolute terms), then a decrease in the price will result in a smaller proportional increase in the quantity demanded. If the PED is elastic (PED > 1, in absolute terms), then a decrease in the price will result in a larger proportional increase in the quantity demanded.

36. In this case, again the math is right, a 16.67% decrease in price will lead to a 50% increase in quantity demanded, so the PED = 50% / 16.67% = 3 (PED in absolute terms). This means that the demand for Playstations is very elastic, meaning that Sony's total revenue should increase by lowering its price.

We can also calculate the PED using the midpoint method to determine how other price cuts could affect the demand:

PED using midpoint method = {(120,000 - 80,000) / [(120,000 + 80,000) / 2]} / {(500 - 600) / [(500 + 600) / 2]} = (40,000 / 100,000) / (100 / 550) = 0.4 / 0.1818 = 2.2

The PED is still very elastic, but the largest the decrease in price, the more elastic the demand. So if Sony decided to lower the price to $450, the PED will probably be around 4 or even more.