Question 900809



A South African country exports gold and estimates the demand function to be D(p)=400√2600-p.  If the country wants to raise revenues to improve the balance of payments, should it raise or lower the price from the present level of $1600 per ounce?

Little help please.  I have always struggled with word problems.
<pre>
{{{highlight(D(p) = 400sqrt(2600 - p))}}}

Based on the demand equation/function, and a price of $1,600, per oz, the demand for gold would be:
{{{highlight_green(highlight_green(12649.11))}}} oz, with revenues of approximately $M{{{highlight_green(highlight_green(20.24))}}}. 

Based on the demand equation/function, and a $100, per oz price INCREASE, to $1,700, per oz, the demand
for gold would be: {{{highlight_green(highlight_green(12000))}}} oz, with revenues of $M{{{highlight_green(highlight_green(20.4))}}}

Based on the demand equation/function, and a $100, per oz price REDUCTION, to $1,500, per oz, the demand
for gold would be: {{{highlight_green(highlight_green(13266.49916))}}} oz, with revenues of approximately $M{{{highlight_green(highlight_green(19.9))}}}. 

It is quite obvious that in this situation, and most similar ones, the cheaper the price, the higher the demand.
However, in this case, an INCREASE in price, which leads to a lower demand would DEFINITELY garner higher revenues.
Thus, the price should be INCREASED.