Suppose you own a firm that produces widgets and is a monopoly. The market demand is given by the equation P = 100 - 2Q, where P is the price of gadgets and Q is the quantity of gadgets sold per week. The firm's marginal costs are given by the equation MC = 16Q. When the monopolist maximizes profits the price elasticity of demand for widgets is
A)9.
B)36.
C)0.5.
D)0.02.

Question

Quizplus · Accepted Answer

The price elasticity of demand (PED) is calculated using the formula PED = (P/Q) * (1/slope of demand curve). First, we find the quantity (Q) where marginal revenue (MR) equals marginal cost (MC). The demand curve is P = 100 - 2Q, so the total revenue (TR) is TR = P*Q = (100 - 2Q)Q. The marginal revenue (MR) is the derivative of TR with respect to Q, which gives MR = 100 - 4Q. Setting MR equal to MC (16Q) and solving for Q gives 100 - 4Q = 16Q, or 20Q = 100, so Q = 5. Substituting Q = 5 into the demand equation gives P = 100 - 2*5 = 90. The slope of the demand curve is -2 (from P = 100 - 2Q). Therefore, PED = (P/Q) * (1/slope of demand curve) = (90/5) * (1/-2) = 18 * -0.5 = -9. The negative sign indicates the direction of the relationship between price and quantity demanded, but when discussing the magnitude of elasticity, we look at the absolute value, which is 9.

Suppose You Own a Firm That Produces Widgets and Is