production that escapes seizure. Thus, q + X is total industry production. Let C(q + X) denote the total cost of producing this amount of cocaine. Let Q be the equilibrium 'quantity of cocaine that escapes seizure and left P be the equilibrium price.
As in the RAND study, assume that equilibrium price equals the average cost of cocaine production, measured as total cost divided by the amount of cocaine that escapes seizure. Thus,
The equilibrium quantity that escapes seizure equals the quantity demanded at the equilibrium price. Thus,
Combining these two conditions yields
Solving this equation for Q yields the equilibrium consumption of cocaine as a function of the magnitude X of seizures. Given specifications for the demand function D(•) and the cost function C(•), one may use (3) to study how cocaine consumption responds to variations in seizures.
As in the RAND study, assume that demand has the constant-elasticity form
In a departure from the RAND study, assume that the cost function has the power-function form
The average cost per unit of production that escapes seizure is then
The RAND study essentially assumes the special case of (5) and (6) in which d = 1, implying constant marginal costs and downward sloping average costs. Here we entertain the possibility that d > 1, implying that