Sunbest Orange Juice, is a product of California’s Orange County Growers’ Associ
ID: 1161023 • Letter: S
Question
Sunbest Orange Juice, is a product of California’s Orange County Growers’ Association. Both demand and supply of the product are highly sensitive to changes in the weather. During hot summer months, demand for Sunbest and other beverages grows rapidly. On the other hand, hot, dry weather has an adverse effect on supply by reducing the size of the orange crop.
Demand and supply functions for Sunbest are as follows:
Qd = -159.76 + 12Ps +2.2Y + 2.5T- 8P
Qs = 276.75 - 4.5PL - 6PK - 0.25T + 32P
In these equations, Q measures 1000’s of gallons per month and P is the price in dollars per gallon of orange juice. The other variables and their current values are given below.
Variable
Definition
Current Value
Ps
Wholesale price of canned soda ($ per case)
$4.25
Y
Per capita disposable income ($1,000s)
$45.8
T
Average daily high temperature (degree)
88
PL
Average price of unskilled labor ($ per hour)
8.50
PK
Risk-adjusted cost of capital (in percent)
10.75
a. Find the current equilibrium price and quantity in this market.
b. Find the total revenue function (as a function of the quantity of juice) for this market under current conditions.
c. At the market equilibrium, what is the cross-price elasticity of the demand for juice with respect to the price of soda?
Now suppose that the government decides to impose a tax of $0.25 per gallon on orange juice.
d. What will happen to the price buyers actually pay (net price) per gallon as a result of the tax?
e. What price will sellers actually receive (net price) per gallon and what quantity of orange juice will be sold each day?
f. How much revenue will this raise?
Variable
Definition
Current Value
Ps
Wholesale price of canned soda ($ per case)
$4.25
Y
Per capita disposable income ($1,000s)
$45.8
T
Average daily high temperature (degree)
88
PL
Average price of unskilled labor ($ per hour)
8.50
PK
Risk-adjusted cost of capital (in percent)
10.75
Explanation / Answer
(a) Plugging in given values,
Qd = - 159.76 + (12 x 4.25) + (2.2 x 45.8) + (2.5 x 88) - 8P
Qd = - 159.76 + 51 + 100.76 + 220 - 8P
Qd = 212 - 8P
And
Qs = 276.75 - (4.5 x 8.5) - (6 x 10.75) - (0.25 x 0**) + 32P [Since in absence of tax, T = 0]
Qs = 276.75 - 38.25 - 64.5 + 32P
Qs = 174 + 32P
In equilibrium, Qd = Qs.
212 - 8P = 174 + 32P
40P = 38
P = $0.95
Q (thousand) = 212 - (8 x 0.95) = 212 - 7.6 = 204.4
(b) From demand function, 8P = 212 - Qd, so P = 26.5 - 0.125Qd
Total revenue = P x Qd = 26.5Qd - 0.125Qd2
(c) Cross price elasticity = (dQd/dPs) x (Ps/Qd) = 12 x (4.25/204.4) = 0.25
(d) The tax will change the supply function. New supply function is:
Qs = 174 + 32(P - 0.25) = 172 + 32P - 8 = 164 + 32P
Equating with Qd,
212 - 8P = 164 + 32P
40P = 48
P = $1.2 (Price paid by buyers)
Increase in price paid by buyers = $1.2 - $0.95 = $0.25
(e) Price received by sellers = $1.2 - $0.25 = $0.95
New quantity (thousand) = 212 - (8 x 1.2) = 212 - 9.6 = 202.4
(f) Tax revenue = Tax per unit x New quantity = $0.25 x 202,400 = $50,600
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