Math  /  Data & Statistics

Question3. The San Francisco Chronicle reported that the toll on the Golden Gate Bridge was raised from $4\$ 4 to $6\$ 6. Following the toll increase, traffic fell by 10 percent. Stephen Leonoudakis, chairman of the bridge's finance auditing committee, expected that the toll increase could cause toll revenues to increase. Is this statement consistent with economic theory? (2)

Studdy Solution

STEP 1

What is this asking? Did raising the Golden Gate Bridge toll from $4\$4 to $6\$6 *actually* increase the total revenue, even though traffic went down? Watch out! Don't forget, less traffic doesn't *automatically* mean less money, if the price went up enough to compensate!

STEP 2

1. Calculate initial revenue
2. Calculate new revenue
3. Compare revenues

STEP 3

Let's call the **initial toll** T1=$4T_1 = \$4 and the **initial traffic** C1C_1.
We don't know the *exact* initial traffic, but we can still work with this!
The **initial revenue** R1R_1 is just the toll multiplied by the traffic: R1=T1C1=$4C1R_1 = T_1 \cdot C_1 = \$4 \cdot C_1

STEP 4

The **new toll** is T2=$6T_2 = \$6.
The traffic *decreased* by **10 percent**, which means the **new traffic** C2C_2 is 100%10%=90%100\% - 10\% = 90\% of the initial traffic: C2=0.90C1C_2 = 0.90 \cdot C_1 The **new revenue** R2R_2 is the new toll multiplied by the new traffic: R2=T2C2=$6(0.90C1)R_2 = T_2 \cdot C_2 = \$6 \cdot (0.90 \cdot C_1)

STEP 5

We can rearrange this a bit: R2=($60.90)C1=$5.40C1R_2 = (\$6 \cdot 0.90) \cdot C_1 = \$5.40 \cdot C_1 So, the new revenue is $5.40\$5.40 multiplied by the initial traffic.

STEP 6

Now, let's compare R1R_1 and R2R_2.
We have: R1=$4C1R_1 = \$4 \cdot C_1 R2=$5.40C1R_2 = \$5.40 \cdot C_1Since C1C_1 is the same in both equations, we can see that $5.40\$5.40 is bigger than $4\$4!
This means R2R_2 is bigger than R1R_1!

STEP 7

Yes! Even though traffic fell, the toll increase *did* increase the total revenue.
The chairman's statement *is* consistent with economic theory.
Raising the price while lowering demand can still increase revenue if the price increase is large enough.

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