The market for cod liver oil pills is characterized by the demand and supply equations: Q^D = 100 - 4P and Q^S = -20 + 2P, where P is the price per bottle and Q is the quantity of bottles. If consumers want to purchase 60 more bottles at any given price, what is the new equilibrium price?

Question

Quizplus · Accepted Answer

To find the new equilibrium price after the increase in demand by 60 bottles at any given price, we adjust the demand equation to reflect this increase. The original demand equation is $Q_d = 100 - 4P$. With an increase in demand by 60 bottles, the new demand equation becomes $Q_d = 160 - 4P$. The supply equation remains unchanged at $Q_s = -20 + 2P$.To find the equilibrium, we set $Q_d = Q_s$:$$160 - 4P = -20 + 2P$$Solving for $P$, we get:$$180 = 6P$$$$P = 30$$However, this calculation mistake led to the wrong conclusion. Correctly solving the equation should give us the right answer. Let's correct the calculation:$$160 - 4P = -20 + 2P$$$$180 = 6P$$$$P = 30$$The mistake in my explanation was acknowledging an error that wasn't there and incorrectly suggesting a recalculation. The correct calculation indeed leads to $P = 30$, which matches one of the provided options. However, the initial instruction was to solve for the new equilibrium price with the correct setup, which was done, but my explanation mistakenly introduced a doubt that was not necessary. The correct equilibrium price, based on the correctly solved equations, should have been confidently stated as per the options given.

The Market for Cod Liver Oil Pills Is Characterized by the Demand