Question

Consider a competitive market with aggregate demand

D(p) = { 0 if p≥80
800−10p if p<80
​and aggregate supply
S(p) = { 0 if p≤50
5p−250 if p>50
​1. Find the competitive equilibrium price p∗ and equilibrium quantity traded Q∗. The government introduces a per-unit subsidy of s=$10 per unit traded. Hence, the price paid by consumers, pD
​ , is no longer the same as the price received by producers, pS . The two prices differ by the amount of the subsidy and producers receive a higher price than consumers pay, pS−pD = s.






​

Answer 1

To find the competitive equilibrium price and quantity traded, set the quantity demanded equal to the quantity supplied and solve for p. The competitive equilibrium price is $70 and the equilibrium quantity traded is 100.

Step-by-step explanation:

To find the competitive equilibrium price and quantity traded, we need to find the price at which the quantity demanded is equal to the quantity supplied. In this case, the demand function is D(p) = 800-10p and the supply function is S(p) = 5p-250. Setting D(p) equal to S(p) and solving for p, we get: 800-10p = 5p-250. Simplifying, we find: 15p = 1050. Therefore, p = 70.

Now that we have the equilibrium price, we can substitute it back into the demand or supply function to find the equilibrium quantity traded. Using the demand function D(p) = 800-10p, we get: Q* = 800-10(70) = 800-700 = 100.

So, the competitive equilibrium price is $70 and the equilibrium quantity traded is 100.