Gurgling Springs, Inc. is a bottler of natural spring water distributed througho
ID: 1134842 • Letter: G
Question
Gurgling Springs, Inc. is a bottler of natural spring water distributed throughout the New England states. Five-gallon containers of GSI spring water are regionally promoted and distributed through grocery chains. Operating experience during the past year suggests the following demand function for its spring water:
Q = 250 - 100P + 0.0001Pop + 0.003I + 0.003A
where Q is quantity in thousands of five-gallon containers, P is price ($), Pop is population, I is disposable income per capita ($), and A is advertising expenditures ($).
A.
Determine the demand curve faced by CPI in a typical market where P = $4, Pop = 4,000,000 persons, I = $50,000 and A = $400,000. Show the demand curve with quantity expressed as a function of price, and price expressed as a function of quantity.
B.
Calculate the quantity demanded at prices of $5, $4, and $3.
C.
Calculate the prices necessary to sell 1,250, 1,500, and 1,750 thousands of five gallon containers.
A.
Determine the demand curve faced by CPI in a typical market where P = $4, Pop = 4,000,000 persons, I = $50,000 and A = $400,000. Show the demand curve with quantity expressed as a function of price, and price expressed as a function of quantity.
B.
Calculate the quantity demanded at prices of $5, $4, and $3.
C.
Calculate the prices necessary to sell 1,250, 1,500, and 1,750 thousands of five gallon containers.
Explanation / Answer
(A)
Demand function for its spring water -
Q = 250 - 100P + 0.0001Pop + 0.003I + 0.003A
Where,
Pop = 4,000,000
I = 50,000
A = 400,000
Q = 250 - 100P + (0.0001 * 4,000,000) + (0.003 * 50,000) + (0.003 * 400,000)
Q = 250 - 100P + 400 + 150 + 1,200
Q = 2,000 - 100P
Thus,
The demand curve with quantity expressed as a function of price is as follows -
Q = 2,000 - 100P
Q = 2,000 - 100P
Q - 2,000 = -100P
100P = 2,000 - Q
P = (2,000 - Q)/100
P = 20 - 0.01Q
Thus,
The demand curve with price expressed as a function of quantity is as follows -
P = 20 - 0.01Q
(B)
Q = 2,000 - 100P
When P = $5
Q = 2,000 - 100P = 2,000 - (100*5) = 2,000 - 500 = 1,500
So, the quantity demanded at prices of $5 is 1,500 thousand of five-gallon containers.
When P = $4
Q = 2,000 - 100P = 2,000 - (100*4) = 2,000 - 400 = 1,600
So, the quantity demanded at prices of $4 is 1,600 thousand of five-gallon containers.
When P = $3
Q = 2,000 - 100P = 2,000 - (100*3) = 2,000 - 300 = 1,700
So, the quantity demanded at prices of $3 is 1,700 thousand of five-gallon containers.
(C)
P = 20 - 0.01Q
When Q = 1,250
P = 20 - (0.01 * 1,250) = 20 - 12.5 = 7.5
Thus,
The price necessary to sell 1,250 thousand of five gallon containers is $7.5.
When Q = 1,500
P = 20 - (0.01 * 1,500) = 20 - 15 = 5
Thus,
The price necessary to sell 1,500 thousand of five gallon containers is $5.
When Q = 1,750
P = 20 - (0.01 * 1,750) = 20 - 17.5 = 2.5
Thus,
The price necessary to sell 1,750 thousand of five gallon containers is $2.5.
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