Question

3. Colin's demand for golf at his local club each season is P = 50 - 2Q. If the golf course charges $26 dollars per round of golf. a. What is the maximum annual membership fee Colin would be willing to pay to join the club? b. If the golf course reduces the price of a round of golf to $16, how much consumer surplus does Colin gain from the decrease in price?

Answer 1

(a)

Demand function of Colin is as follows -

P = 50 - 2Q

If price per round is $26 then demand would be,

P = 50 - 2Q

26 = 50 - 2Q

2Q = 24

Q = 24/2 = 12

Calculate price when demand is zero -

P = 50 - 2Q

P = 50 - (2*0) = 50

Calculate the consumer surplus -

CS = 1/2 * (Price when demand is zero - Current price) * Current demand

CS = 1/2 * (50 - 26) * 12 = 1/2 * 24 * 12 = 144

The consumer surplus is $144.

Colin would be willing to pay, at maximum, an amount equal to consumer surplus.

So,

The maximum annual membership fee Colin would be willing to pay to join the club is $144.

(b)

Demand function of Colin is as follows -

P = 50 - 2Q

If price per round is decreased to $16 then demand would be,

P = 50 - 2Q

16 = 50 - 2Q

2Q = 34

Q = 34/2 = 17

Calculate the consumer surplus -

CS = 1/2 * (Price when demand is zero - Current price) * Current demand

CS = 1/2 * (50 - 16) * 17 = 1/2 * 34 * 17 = 289

The consumer surplus after decrease in price is $289.

The consumer surplus before decrease in price is $144.

Thus,

Colin has gained consumer surplus of ($289 - $144) $145 from the decrease in price.