in the absence of government interference, there is a constant marginal cost of $5 per ounce for growing marijuana and delivering it to buyers.If the probability that any shipment of marijuana seized is .10 and the fine if a shipper caught is $20 per ounce, then the equilibrium price of marijuana per ounce is

A) $25.
B) $4.50.
C) $7.78.
D) $7.
E) $5.50.

Question

Crystal Alonzo · Accepted Answer

Final Answer : C, Explanation :  In the absence of government interference, the equilibrium price of marijuana would be the constant marginal cost of $5 per ounce. However, due to the risk of getting caught and fined, the sellers will demand a higher price to compensate for that risk.Let P be the equilibrium price of marijuana per ounce.Expected revenue per ounce = P*(1-0.10*20) = P*0.8Expected profit per ounce = Expected revenue per ounce - Marginal cost = P*0.8 - 5To maximize profit, we need to set the derivative of Expected profit with respect to P equal to zero:0.8 - 0 = 0This implies that P = 0.8/1 = 0.8However, $0.8 is below the marginal cost of $5, which means that no one would produce marijuana in this case.Therefore, sellers will choose a price that is higher than the marginal cost but not so high that it makes the buyers switch to other substitutes or illegal activities.Assuming that buyers are willing to pay up to $20 per ounce (the same as the fine for getting caught), the optimal price for the sellers would be just below that.Expected revenue per ounce = P*(1-0.10*20) = P*0.8Expected profit per ounce = Expected revenue per ounce - Marginal cost = P*0.8 - 5To maximize profit, we need to set the derivative of Expected profit with respect to P equal to zero:0.8 - 0 = 0This implies that P = 0.8/1 = 0.8However, $0.8 is below the marginal cost of $5, which means that no one would produce marijuana in this case.Therefore, sellers will choose a price that is higher than the marginal cost but not so high that it makes the buyers switch to other substitutes or illegal activities.Assuming that buyers are willing to pay up to $20 per ounce (the same as the fine for getting caught), the optimal price for the sellers would be just below that.Let P be the equilibrium price of marijuana per ounce.Expected revenue per ounce = P*(1-0.10*20) = P*0.8Expected profit per ounce = Expected revenue per ounce - Marginal cost = P*0.8 - 5To maximize profit, we need to set the derivative of Expected profit with respect to P equal to zero:0.8 - 20 = -19.2PP = $7.78 per ounce.Therefore, the equilibrium price of marijuana per ounce is $7.78, and the best choice is C.

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