Question

Bicycle suppliers will make 250 bicycles available in the market per month, represented by x, when the unit price, p, is $55 and 1500 bicycles available per month when the unit price is $155. Find the supply equation if it is known to be linear.

Answer 1

The supply equation for bicycles is calculated from two points given and is p = 0.08x + 35. The quantity supplied at a price of $210 is 2187.5 bicycles, and the price at which quantity supplied is 48,000 is $3865. Equilibrium price and quantity are where the demand and supply curves intersect, which can also be found in a table where quantities demanded and supplied are equal.

Step-by-step explanation:

Finding the Supply Equation

First, let's find the linear supply equation using the two points given: (250, 55) and (1500, 155). The general form of the linear equation is: p = mx + b, where m is the slope and b is the y-intercept. To find m, we use the slope formula:

m = (p2 - p1) / (x2 - x1) = (155 - 55) / (1500 - 250) = 100/1250 = 0.08.

The equation can now be written as: p = 0.08x + b. We can find b by substituting one of the points, say (250, 55):

55 = 0.08(250) + b → b = 55 - 20 = 35.

So the complete supply equation is: p = 0.08x + 35.

Answers to Questions

If the price were $120, we would substitute in the supply equation to find the quantity supplied: x = (120 - 35)/0.08 = 1062.5 bicycles. Without a demand curve, we cannot determine the quantity demanded or whether a shortage or surplus exists.