Exercise 2.3 Suppose that the supply and demand sets for a particular market are S= (q,p)vert 3p-q=5 , D= (q,p)vert 3p+q^2+2q=9 __ Sketch S and D and determine the equilibrium set E=Scap D . Comment briefly on the interpretation of the results.

To find the equilibrium set, we need to find the intersection of the supply set S and the demand set D. This means we need to find the values of q and p that satisfy both equations.Let's start by solving the system of equations: We can solve this system of equations using substitution or elimination method. Let's use substitution method:From the first equation, we can express p in terms of q: Now, substitute this expression for p into the second equation: Simplify the equation: Combine like terms: Subtract 9 from both sides: Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. Let's use the quadratic formula: In this case, a = 1, b = 3, and c = -4. Plugging these values into the quadratic formula, we get: Simplify the expression inside the square root: This gives us two possible solutions for q: Now, let's substitute these values of q back into the expression for p:For : For : So, the equilibrium set E is: The interpretation of these results is that there are two equilibrium points in this market. The first equilibrium point is when the quantity demanded is 1 and the price is 2. The second equilibrium point is when the quantity demanded is -4 and the price is . These points represent the prices and quantities at which the supply and demand sets intersect.