Crepe Creations is considering franchising its unique brand of crepes to stall-h
ID: 1191743 • Letter: C
Question
Crepe Creations is considering franchising its unique brand of crepes to stall-holders on Hermoza Beach, which is five miles long. CC estimates that on an average day there are 1,000 sunbathers evenly spread along the beach and that each sunbather will buy one crepe per day provided that the price plus any disutility cost does not exceed $5. Each sunbather incurs a disutility cost of getting up from resting to get a crepe and returning to their beach spot of 25 cents for every 1/4 mile the sunbather has to walk to get to the CC stall. Each crepe costs $0.50 to make and CC incurs a $40 overhead cost per day to operate a stall.
1. Assuming one stall located in the middle of the beach, what would be the market price and assoicated profits if CC wanted to sell to all sunbathers?
2. Assuming one stall located in the middle of the beach, what if the stall restricts output? What would be the profit maximizing price?
3. Explain how and why CC could imporve their profitability if it introduced more stalls on Hermoza beach?
I would greatly appricate assistance on how to even set up a problem lke this to solve. Thank you
Explanation / Answer
1.
Total number of sunbathers is 1000 and they are uniformly distributed on a 5 mile long beach stretch. For every ¼ mile travelled to get to the stall, a sunbather incurs a disutility cost of 0.25 cents. That is, for every one mile travelled, a sunbather would incur a disutility cost of $1.
A sunbather would buy the crepe if the price plus the disutility cost is less than or equal to $5. Therefore, if the sunbather located at any of the two ends of the beach is buying a crepe, then it means everyone is buying a crepe.
The stall is located at the midpoint. Therefore, the distance that a sunbather located at the end of the beach stretch will have to travel to get to the stall is 2.5 miles. That is, his disutility cost to get to the stall is $2.5. He will buy a crepe if
$2.5 + Price 5
i.e., Price $2.5
That is, if the price is $2.5, Crepe Creations will be able to supply the whole market.
2. Find the demand function of the following form:
Q = A – BP …. (1)
where A and B are constants.
Price Quantity demanded
$2.5 1000
$5 0
Substituting P = $5 and Q = 0 in equation (1), we get
A = 5B
Substituting A = 5B, Q = 1000 and P = 2.5 in equation (1), we get
B = 400
Therefore, A = 5(400) = 2000
Therefore, the demand function is
Q = 2000 – 400P
And,
P = 5 – Q/400
The total revenue is
TR = PQ
TR = (5 – Q/400)Q
TR = 5Q – Q2/400
Therefore,
MR = 5 – Q/200
At profit maximizing quantity,
MR = MC
5 – Q/200 = 0.5
4.5 = Q/200
Q = 900
When Q = 900,
P = 5 – 900/400 = 2.75
Therefore, the profit maximizing price is $2.75 and the output is restricted to 900 units.
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