Suppose demand is given by Q^d = 1000 - 25P and supply is given by Q^s = 75P. At the equilibrium price and quantity, the price elasticity of demand is A) -3 B) -25 C) -1/3 D) -10

Question

Quizplus · Accepted Answer

At equilibrium, demand equals supply:

1000 - 25P = 75P

1000 = 100P

P = 10

Substitute P = 10 into either the demand or supply equation to find the equilibrium quantity:

Q = 1000 - 25(10) = 750

The price elasticity of demand at the equilibrium point can be calculated as:

% change in quantity demanded / % change in price

Using the midpoint formula:

% change in quantity demanded = (Q2 - Q1) / [(Q1 + Q2)/2] * 100%

% change in price = (P2 - P1) / [(P1 + P2)/2] * 100%

Assuming a small increase in price from $10 to $11:

% change in quantity demanded = (750 - 722.22) / [(750 + 722.22)/2] * 100% = 3.85%

% change in price = (11 - 10) / [(10 + 11)/2] * 100% = 4.55%

Price elasticity of demand = 3.85% / 4.55% = -0.84

Since the absolute value of the price elasticity of demand is less than 1, the demand is inelastic, and the correct answer is C) -1/3.

Suppose Demand Is Given by Qd = 1000 - 25P

Suppose Demand Is Given by Q^d = 1000 - 25P