Final answer:
The price elasticity of demand at equilibrium is 0.563.
Step-by-step explanation:
The price elasticity of demand measures how responsive the quantity demanded is to a change in price. It is calculated using the formula:
Ed = (% change in quantity demanded) / (% change in price)
At equilibrium, the quantity demanded (Qd) equals the quantity supplied (Qs). This occurs when 50 - 2P = P - 1. Solving for P, we find P = 9. Plugging this value of P into the demand curve, we get Qd = 32. Plugging it into the supply curve, we get Qs = 8.
To calculate the price elasticity of demand at equilibrium, we need to find the percentage change in quantity demanded and the percentage change in price. Since these equations are linear, the percentage change in quantity demanded is equal to the coefficient of P in the demand equation (2) divided by the equilibrium quantity demanded (32). The percentage change in price is equal to the coefficient of P in the supply equation (1) divided by the equilibrium price (9).
Using these values, we can now calculate the price elasticity of demand at equilibrium:
Ed = (2/32) / (1/9) = 0.563