To find the market equilibrium price (p) and quantity (Q) for the given inferior good, we need to set the demand function equal to the supply function.
Given the demand function:
Qd = a – bp
and the supply function:
Qs = c + ep
At equilibrium, Qd = Qs.
So, we set the two equations equal to each other:
a – bp = c + ep
Next, we solve for p.
We can rearrange this equation to isolate terms involving p:
a – c = bp + ep
This simplifies to:
a – c = p(b + e)
Now, we can solve for p:
p = rac{a – c}{b + e}
Now that we have the equilibrium price, we need to find the equilibrium quantity (Q). We can plug the value of p back into either the demand or the supply function. Let’s use the demand function:
Q = a – b rac{a – c}{b + e}
To simplify this, we first multiply out:
Q = a – rac{b(a – c)}{b + e}
Thus, the market equilibrium price and quantity can be summarized as:
Equilibrium Price (p): rac{a – c}{b + e}
Equilibrium Quantity (Q): a – rac{b(a – c)}{b + e}