Question

Suppose the demand curve for a public park is Q = 80 – 2p, where Q is the number of visitor-days and p is the entry price. The marginal cost of operating the park is MC = 10.

What is the efficient level of entrance fee and the number of visitors at this fee level (assume no congestion problems)?

At the price/quantity combination of (a), what is the price elasticity of demand for park visitation? (To find this, take a small change in price, say, $1. Figure out the elasticity with the change in quantity resulting from this price change. The percentage change in price and quantity is different depending on whether the price has gone up by one dollar or down by one dollar. Take the average of the two estimates.)

What is the price-quantity combination that maximizes revenues, and what is the price elasticity of demand at this point on the demand curve?

Graphically illustrate this scenario, showing the demand curve, the MC curve, the efficient outcome from (a), and the revenue max outcome from (c)

Answer 1

The effiecient level of entrance fee and number of visitors is derived by equation D =MC

market demand= 80-2P

or inverse demand P = 40 -0.5Q

40-0.5Q = 10

Q = 60

P = 40 -30 = $ 10

so, efficient entrance fee is $10 and numebr of visitos are = 60 .

a) ELasticity of demand ,

when P = 10 , Q = 60

WHen P = 11 , Q = 58

elasticity of demand = percentage change in quantity demanded / percentage change in price

elasticity = -0.3559

so , elasticiy is inelastic demand.

b) The price and quantity combination that maximize revenue .is where MR =MC

P = 40-0.5Q

MR = 40 - Q and MC = 10

40-Q = 10

Q = 30

P = 40-0.5*30

P = $25

price elasticity of demand at this point = partial derivative of market demand function with respect to P * P / Q

partial derivative = -2

price elasticity of deman = -2 * 25/30

price elasticity of demand = -1.7