(Solved): Mathematical Example: Demand and Supply Demand and supply curves can also be represented with equat ...

Mathematical Example: Demand and Supply Demand and supply curves can also be represented with equations. Suppose that the quantity demanded, \( Q=90-2 P \) and the quantity supplied, \( Q=P \) a. Find the equilibrium price and quantity. b. Suppose that the price is \( \$ 20 \). Determine the quantity demanded and quantity supplied. c. At a price of \( \$ 20 \), is there a surplus or a shortage in the market? d. Given your answer in part \( c \), will the price rise or fall in order to find the equilibrium price? Answers: a. The first step is to set quantity demanded \( = \) quantity supplied at equilibrium. Doing so gives us \( 90-2 P=P \). Solving for \( P \), we find that \( 90=3 P \) And \( P=30 \). We may plug \( P \) into any of the equations and solve for the quantities. So quantity demanded at equilibrium \( =Q=90-(2 \times 30) \) \( =90-60=30 \). Or we can plug \( Q=30 \) for the quantity supplied at equilibrium. b. At the price of \( 20, Q=90-2(20)=50 \). And \( Q=20 \). c. Since quantity demanded is greater than quantity supplied, there is a shortage of \( 50-20=30 \) units. d. Whenever there is a shortage of a good, price will rise in order to find the equilibrium point. We are given the following equations where \( P \) is price and \( Q \) is quantity: Equation \( 1: P=300-10 Q \) Equation 2: \( P=5 Q \) a. Which equation represents the demand curve? Why? b. What is the equilibrium price and equilibrium quantity? c. At a price of \( \$ 150 \), is there a shortage, surplus, or neither? If there is a shortage or surplus, what is the amount of that shortage or surplus?