The market supply for potatoes in New York is 2,000 tons for a price of $200 a ton, and 5,000 tons for a price of $500 a ton. Between these two prices market supply is a straight line. What is the equation of the supply curve?
To find the equation of the supply curve, we need to determine the relationship between the quantity supplied and the price of potatoes. In this case, the market supply is given at two different price levels.
Let's consider the two points on the supply curve:
Point A: Price = $200, Quantity = 2,000 tons
Point B: Price = $500, Quantity = 5,000 tons
We can use the point-slope form of a linear equation to find the equation of the supply curve. The point-slope form is given by: y - y1 = m(x - x1), where (x1, y1) is a point on the line, and "m" is the slope of the line.
Let's calculate the slope (m) first:
m = (Change in quantity) / (Change in price)
= (5,000 - 2,000) / ($500 - $200)
= 3,000 / $300
= 10
Now, we can choose either point A or point B to find the equation of the supply curve. Let's choose point A (2000, 200) to proceed:
y - 200 = 10(x - 2000)
y - 200 = 10x - 20,000
y = 10x - 19,800
Therefore, the equation of the supply curve is:
Quantity supplied (tons) = 10 x Price ($ per ton) - 19,800.