Question

Photon Lighting Company determines that the supply and demand functions for its most popular lamp are as follows: S(p) = 300 – 3p + 0.000015p4and D(p) = 2100 – 0.0009p3, where p is the price. The market equilibrium happens when the price is $ A, and the supply and demand are equal to A/ lamps. (round your answer to nearest cent for dollars and nearest integer for lamps)

Answer 1

To find the equilibrium point for Photon Lighting Company, we would set the supply function equal to the demand function and solve for the price. This can be done using algebra or graphically by plotting the supply and demand curves and finding their intersection point.

Step-by-step explanation:

The equilibrium point in economics is where the supply and demand curves intersect, indicating the price and quantity at which the market is balanced. For the Photon Lighting Company, to find this equilibrium, we need to set the supply function S(p) equal to the demand function D(p) and solve for the price, p. This can be done either algebraically or graphically. The algebraic method involves equating the two functions and solving for p, whereas the graphical method involves plotting both the supply and demand curves on a graph and finding their intersection point.

For instance, if we consider the given equilibrium example where the quantity demanded and supplied is 12 at a price of $2, we would graph the demand curve as P = 8 - 0.5Qd and the supply curve as P = -0.4 + 0.2Qs. The equilibrium is achieved where these two curves intersect, meaning the quantity demanded equals the quantity supplied. Knowing this equilibrium allows businesses and consumers to make informed decisions in the market.