Question

Provide all work as well as a supply & demand model applied to the explanation

Assume the demand for crack cocaine is inelastic and that users get the funds to pay for their crack by stealing. Suppose that the government increases penalties on suppliers of crack cocaine, which reduces the number of dealers. Using only this information, predict what will happen to the revenues of remain ing crack dealers and the amount of crime committed by crack users. Full credit 1. answers will incorporate a supply & demand model into their explanation.

Answer 1

Answer

The demand for crack cocaine is inelastic, i.e., the quantity demanded for crack cocaine is not very responsive to the change in its price, or the change in quantity demanded for crack cocaine is less than the change in its price.

Now, the government increases the penalties on suppliers of crack cocaine, and as a result the number of dealers of crack cocaine has decreased in the market. As the number of dealers of crack cocaine has decreased, the supply of crack cocaine will decrease in the market. On the demand side, the users of crack cocaine are addicted to it. So the demand will remain unchanged.

Now, let us see what happens to the demand and supply curves of crack cocaine in the market.

In the above figure, we are measuring the quantity of crack cocaine on the horizontal axis, and the price of crack cocaine on the vertical axis. The curve 'D' is the demand curve of crack cocaine, and curve 'S₁' is the initial supply curve of crack cocaine. Initially, the equilibrium market price of crack cocaine is 'P₁', and the quantity demanded is 'Q₁'. Now, after the increase of government penalties on crack cocaine suppliers, the number of dealers of crack cocaine has decreased in the market. As a result, the supply curve of crack cocaine will shift leftward. As the supply curve shifts leftward, the quantity supply of crack cocaine will decrease. The demand curve of crack cocaine remains unchanged. So, at the prevailing price level, i.e., at price 'P₁', there will emerge an excess demand of crack cocaine in the market. As a result, the price will rise until the market gets clear at price 'P₂'. So the new equilibrium price, and quantity will be 'P₂' , and 'Q₂' respectively.

이 없었

Now, as the price of crack cocaine rises, and the price elasticity of demand for crack cocaine is inelastic, the revenues of the remaining crack cocaine dealers will rise.

Price elasticity of demand($\varepsilon$_d) = - (dQ / Q) / (dP / P)

Or, $\varepsilon$_d = - (dQ / dP) * (P/Q) .... (1)

Revenue(R) = Price(P) * Quantity(Q)

R = P * Q

Differentiating both sides of the above equation with respect to price, we get,

dR / dP = Q * (dP / dP) + P *(dQ / dP)

Or, dR / dP = Q + P *(dQ / dP)

Or, dR / dP = Q[1 + (P/Q) * (dQ / dP)] .... (2)

From equation(1), we know, that '(P/Q) * (dQ / dP)' is '-$\varepsilon$_d'

Now, putting this value in equation (2), we get,

dR / dP = Q[1 -  $\varepsilon$_d]

The term 'dR / dP' is the change in revenue from selling a good for the change in its price.

Now, as the price elasticity of demand for crack cocaine is inelastic, the '$\varepsilon$_d' $<$1.

$\therefore$[1 -  $\varepsilon$_d] $>$0

So, dR / dP = Q[1 -  $\varepsilon$_d] $>$0

Thus, we see that the revenues of the remaining crack dealers will increase, as the price of crack cocaine rises..

Now, in case of crime, we can predict that the amount of crime committed by crack users will rise. The crack users get the funds to pay for their crack by stealing. They are addicted to crack,and the price elasticity of demand for crack cocaine is inelastic, i.e., their quantity demanded for crack cocaine will not be very responsive even when its price rises.

So, from the given information, we can predict that the revenues of the remaining crack cocaine dealers will rise, and the amount of crime committed by the crack cocaine users will increase.

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