Question

Assume the following demand curve: Q = 100,800 – 3,943(P). Calculate elasticity for a price change from $17.30 to $18.50. Report your answer as a POSITIVE number, rounded to one decimal place.

Assume the following demand curve: Q = 1,425 – 134(P). Variable costs = $3.60. Calculate the optimal price. Round to two decimal places.

Answer 1

Ques 1). Demand Curve:

Q = 100800-3943*P

For P = 17.3, Q = 100800-3943*17.3 = 32586.1 units

For P = 18.5, Q = 100800-3943*18.5 = 27854.5 units

So, pecentage change in price = (18.5-17.3)/17.3 = 6.18%

Percentage change in quantity = (27851.5 - 32586.1)/32586.1 = -14.52%

So, price elasticity for demand = Percentage change in quantity/Percentage change in price = -14.52/6.18 = -2.35

Ques 2). Demand Curve:

Q = 1425-134*P

=> P = (1425 - Q)/134

Variable cost = 3.60

So, Revenue = P*Q = (1425*Q - Q2)/134

Marginal revenue = dTR/dQ = (1425 - 2*Q)/134

So, optimal quantity sold is at Marginal revenue = Marginal cost(Variable cost)

So, (1425 - 2*Q)/134 = 3.6

So, 2*Q = 942.6

or, Q = 471.3

The 471.3 quantity is rounded up to 471 and then substituted into the P = (1425 - Q)/134 equation

P = (1425 - 471)/134 = 7.12

So, optimal price = $7.12