Question

2. The table below gives information on the distance from various nearby towns to the famous Cupcake Town Lake (distance is in miles). There is no admission fee. The only cost of visiting Cupcake Lake is the travel cost, which costs $1/mile. The researcher estimates the relationship between the number of visits per capita (per person), x, and the one-way travel cost from the town in which people live, p. He finds this demand function to be: x = 30 – 1.2*p .

CITY OF ORIGIN POPULATION DISTANCE

ALABASTER 2000 12

BEAUTIFUL 4000 18

CORNUCOPIA 3000 20

DELIGHT 5000 30

(a) What is the cutoff price (the price at which demand falls to zero) with this demand function?

(b) Add columns to the table above identifying the cost of a visit to Cupcake Lake from each town, the predicted number of visits per capita from that town, and the total number of visits from the town (i.e., the visits per capita multiplied by the population).

(c) Why doesn’t the researcher observe anyone coming from certain places to Cupcake Lake?

(d) The authorities decide to make improvements at Cupcake Lake (they build a boathouse), which only residents of Alabaster are allowed to use. In consequence, Alabaster resident’s 2 demand function for Cupcake lake changes to x = 50 – 1.2p. The demand functions of residents of the other towns do not change. What is the economic value of this improvement to Alabaster residents?

Answer 1

Demand function is of the form

Q(d)= a-bp where a is all factors except price which affects it b is the slope and p is the price of the good

a) Therefore Cutoff Price in the above case will be(x=0)

Therefore 0= 30- 1.2p

Which is 30=1.2p or p is 25

b) the cost per mile is $1

City	Population	Distance	per capita visit (x)	total no of visits
ALA	2000	12	15.6	31200
BEA	4000	18	8.4	33600
CORN	3000	20	6	18000
DELI	5000	30	- 6	-

x is calculated using the above given demand function with p= no of miles * 1

Therefore x= 30-1.2p

c) The researcher doesn't get to observe people from delight city as its travel cost is higher than 25(30>25) which is the least and below which negative demand starts so a consumer won't travel to such a place or a consume a product which has negative demand.

d) Now demand function for Alabaster residents has changed to x= 50-1.2p and for the rest it is the same.

City	population	distance	per capita visit	total visits
ALA	2000	12	35.6	73200
BEA	4000	18	8.4	33600
COR	3000	20	6	18000
DEL	5000	30	- 6	-

We observe that the per capita visit has increased drastically from 15.6 to 35.6 and so the total number of visits.

Therefore the economic value of this improvement to Alabaster residents is 20 as it is providing the residents of Alabaster higher number of visits at the same travel cost.