Business Pre-Calc Help

Question

At a price of $140 there is demand for 1734 items and a supply of 980 items. At a price of $260 there is demand for 1014 items and a supply of 1820 items. Assuming supply and demand are linear, find the equilibrium price and quantity.

I need help forming the formulas for this question. I know how to find slope, and I know that I need to find the supply formula and the demand formula, I just don`t know what numbers to use and where they go?

Answer 1

Hi Sarah N.,

It is always good to see a picture or plot a graph. I plotted a graph with the price on the y-axis and items on the x-axis.

For the y-axis I went up a distance and marked $140, and then went up twice that distance plus and marked $260. On the x-axis I went to the right a distance and marked 980 and a slight bit more marked 1014, then I went almost twice that distance and marked 1734 and a bit more and marked 1820.

Next I plotted the demand points (1734, $140) and (1014, $260) and connected them with a line (negative slope). Then I plotted the supply points (980, $140) and (1820, $260) and connected them with a line (positive slope).

You can see the intersection of the two linear lines which is the equilibrium.

You can create a linear equation for both lines and find their intersections. Using m = (y₂ - y₁)/(x₂ - x₁) to find the slope. Then use (y - y₁) = m(x - x₁) to find the linear equations. At the intersection y₂ = y₁, so you can set the equations equal to each other and solve for x. Then take that x value, plug it back in to one of the equations and solve for y. Your equilibrium will be these (x, y) values.

I am hoping I didn't need to explain the last paragraph to you and you can take it from here.

I hope this helps, Joe.

P.S. The answer I came up with is (1386, $198). So at a price of $198, the supply and demand are equal at 1386. If you need more help, let me know.

Answer 2

The equilibrium price is the market price where the quantity of goods supplied is equal to the quantity of goods demanded.

1734-980 quantity=-754/$140ea.

1014-1820 quantity=+806/$260ea.

By multiplying you want the wholesale proce.