## To find the producer's surplus at a price level of p=$150, we need to determine the quantity for which suppliers are willing to sell at that price level, and then calculate the area of the triangle above the supply curve but below the price level.

Given the price-supply equation p = S(x) = 100 - 0.25x, where p represents price and x represents quantity supplied, we can set the equation equal to the given price level:

150 = 100 - 0.25x

To solve for x, we can subtract 100 from both sides:

50 = -0.25x

Then divide both sides by -0.25 to isolate x:

x = -50 / -0.25

x = 200

So, at a price level of $150, the quantity supplied is 200 units.

Now, let's calculate the producer's surplus. The formula for producer's surplus is the area of the triangle above the supply curve but below the price level. In this case, the supply curve is the equation S(x) = 100 - 0.25x, and the price level is $150.

The formula for the area of a triangle is: (base * height) / 2

The base of the triangle is the quantity supplied, which is 200 units.

The height of the triangle is the difference between the equilibrium price (p) and the supply curve (S(x)) at that quantity. So, we need to calculate S(x) at x = 200:

S(200) = 100 - 0.25(200) = 50

The height of the triangle is $150 - $50 = $100.

Now we can calculate the producer's surplus using the formula:

Producer's Surplus = (base * height) / 2

= (200 * $100) / 2

= $20,000 / 2

= $10,000

Thus, the correct producer's surplus at a price level of $150 is $10,000.

I can't confirm if 5000 is correct as I'm unable to determine where that number comes from in the given information. It would be helpful to know the source of the answer to provide further clarification.