Question

Below are the supply and demand equations for umbrellas in a certain market. In these equations, p represents price, d represents demand, and s represents supply. d = -4/3p + 22, s = 3p - 36. What is p at the point of equilibrium, to the nearest tenth?

1) 19.3
2) 16.5
3) 13.4
4) 12.0

Answer 1

By setting the demand equation equal to the supply equation and solving for p, the price at the equilibrium point is found to be approximately $13.4.

Step-by-step explanation:

In economics, economic equilibrium is a situation in which economic forces such as supply and demand are balanced and in the absence of external influences the (equilibrium) values of economic variables will not change. For example, in the standard text perfect competition, equilibrium occurs at the point at which quantity demanded and quantity supplied are equal.

To find the value of p at the point of equilibrium for the supply and demand equations d = -4/3p + 22 and s = 3p - 36, you set the demand d equal to the supply s. You have: -4/3p + 22 = 3p - 36. Adding 4/3p to both sides and adding 36 to both sides yields: 22 + 36 = 3p + 4/3p. Combining like terms, we combine the p's coefficients to get: 58 = (13/3)p. Dividing both sides by 13/3 gives: p = 58 / (13/3) = 174/13 ≈ 13.4. Therefore, the price at equilibrium, rounded to the nearest tenth, is $13.4.