The monthly demand (Q) for ACME Widgets\' product is related to the price per Wi

Question

The monthly demand (Q) for ACME Widgets' product is related to the price per Widget (p) and the average monthly income in the market for their product (Y), by the equation Q = 4 ln (6Y - 5 Squareroot p), where Q is measured in 1000 s of Widgets, the price is measured in dollars and income is measured in thousands of dollars. a. Compute Q_P and Q_Y when p = 9 and Y = 4 b. Compute the price - elasticity of demand when p = 10 and Y = 3. c. Suppose that the firm's price remains fixed but average monthly income in the market for the firm's product increases by exist300. Use your answer to a. to estimate the change in demand for ACME's product. Round your answers to 2 decimal places.

Explanation / Answer

a) Qp = 4/(6Y-5sqrt(p)) * (0-5/2sqrt(p))

=> Qp = -20/2(6Y-5sqrt(p))(sqrt(p))

=> Qp = -10/(24-5(3))(3) = -10/(9)(3) = -10/27

Qy = 4/(6Y-5sqrt(p)) * (6-0)

=> Qy = 24/(6Y-5sqrt(p))

=> Qy = 24/(24-15) = 24/9 = 8/3

(b) Price elasticity of demand = Qp * (p/Q)

Qp = -10/(6Y-5sqrt(p))(sqrt(p))

hence Price elasticity = -10/(6Y-5sqrt(p))(sqrt(p)) * (p/4ln(6Y-5sqrt(p))

=> Price elasticity = -10p/(6Y-5sqrt(p))(sqrt(p)) (4ln(6Y-5sqrt(p))

when p = 10 and Y = 3

=> Price elasiticity = -100/(18-5(3.162))(3.162)(4ln(18-5(3.162))

=> Price elasiticity = -100/(2.19)(3.162)(4ln(2.19))

=>  Price elasiticity = -100/27.69912*0.784 = -100/21.7161 = -4.60

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