Question

Suppose that Glitter Gulch, a gold mining firm, increased its sales revenues on newly mined gold from \(100 million to \)200 million between one year and the next. Assuming that the price of gold increased by 100 percent over the same period, by what numerical amount did Glitter Gulch’s real output change? If the price of gold had not changed, what would have been the change in Glitter Gulch’s real output?

Short answer

If the price of gold increased by 100%, the output would have decreased by half of the initial output.

If the price of gold had not changed, Glitter Gulch’s real output would have increased by 100%.

Step-by-step solution

Change in real output when price increases by 100%

The total revenue is the product of price per unit and total quantity.

TR = PQ or 100 = PQ

Here, the price has increased 100%, the change in price is P (𝛥P = P),and the change in revenue is $100 million in one year. Therefore, the change in revenue is

$100=2P△Q$.

Divide the initial revenue by the change in the revenue in the following manner:

$$\begin{gathered} \frac{100}{100}=\frac{PQ}{2P△Q} \\ \frac{Q}{△Q}=2 \\ \frac{△Q}{Q}=\frac{1}{2} \\ △Q=0.5Q \end{gathered}$$

This implies that the output has decreased by half of the intial output.

Change in real output when the price is constant

The revenue has increased by $100 million without any change in the price (𝛥P= 0).

Therefore, the change in revenue is again the same as $100=P△Q$.

Divide the initial revenue by the change in the revenue in the following manner:

$$\begin{gathered} \frac{100}{100}=\frac{PQ}{P△Q} \\ Q=△Q \end{gathered}$$

This implies that the output has increased by 100%.

Therefore, if the price had not changed, the Glitter Glutch’s output would have increased by 100%, doubling the total revenue.