Question

The manager of a funfair realizes that demand for rides is more elastic among males. He is evaluating different pricing stategies. The manager estimates the following demand curves:

Males: q=18-5p

Females: q=10-2p

Assume that a ride costs the funfair $2 each.

a) (10 pts.) If the market cannot be segmented, what is the uniform monopoly price?

b) (6 pts.) If the funfair can charge according to whether or not the consumer is a male but is limited to linear pricing, what price per ride should be set for each group?

c) (8 pts.) If the funfair can apply a block pricing strategy, what block price should the manager choose for each group? How many rides will each group be offered

Answer 1

a) In case the segmentation is not done, the demand function is added up

Q= (18 - 5p) + (10 - 2p)

=> Q= 28 - 7p

So, p = 4 - Q/7  

Total revenue = p.Q = 4Q - Q²/7

Therefore marginal revenue MR = 4 - 2Q/7

The Marginal cost is constant and equal to the cost Incurred to the funfair = 2

MR = MC

=> Q = 7

Now substituting Q in our demand equation, the uniform monopoly price = $3

b)

In this case, we need to solve for each demand curve separately. First case scenario: males

q = 18 - 5p

=> p = 3.6 - ⅕q

Total revenue = p.q = 3.6q - ⅕q²

Now Marginal revenue = 3.6 - ⅖q

And we know the constant marginal cost = $2

MR = MC

3.6 - ⅖q = 2

=> q = 4

Substituting q in the demand equation above, we get p= $2.8 which is the price set for male group

Similarly doing the math for females, we get the price to be set equal to $3.5

c)

In this case, let's take the demand in block 1 equals

q1 = 18 - 5p1

=> p1 = 3.6 - ⅕q1

And block 2 equals

q2 = 10 - 2p2

=> p2 = 5 - ½q2

As per the blocking price strategy, the revenue of block 1

= p1.q1

= 3.6q1 - 0.2q1² ....(1)

Revenue in the second block is given by price times the difference between quantities q1 and q2.

= p2. (q1 - q2)

= (5 - ½q2)(q1 - q2)

= 5q1 - 5q2 - 0.5q1q2 + 0.5q2² ...(2)

Total profits for the funfair equals to (1)+(2) - Total costs

Total costs = 2× q1 =2q1

= 3.6q1 - 0.2q1² + (5q1- 5q2- 0.5q1q2 + 0.5q2²) - 2q1

Taking partial derivatives with respect to q1 and equatiing it to 0 for profit maximizing we get

= 3.6 - 0.4 q1 + 5 - 0.5q2 -2 = 0

=> 0.4q1 + 0.5q2 = 6.6 ...i

Similarly taking partial derivatives w.r.t q2 and equating it to 0 we get

-5 - 0.5q1 +q2 = 0

=> q2 - 0.5q1 = 5 ....ii

q1 = 6.31 , q2 = 8.15

Respective prices for each group are

p1 = $2.34 p2 = $0.925

Hope this helps. Do hit the thumbs up. Cheers!