1. To find the price elasticity of demand at the equilibrium point, we need to determine the equilibrium price (P) and quantity (Q) by setting the demand equal to the supply:

Qd = Qs

80 - 2P = -20 + 8P

Rearranging the equation:

10P = 100

P = 10

Substituting this equilibrium price back into the demand equation to find the equilibrium quantity:

Q = 80 - 2P = 80 - 2(10) = 60

Now, we can calculate the price elasticity of demand (PED) at the equilibrium point using the following formula:

PED = (% change in quantity demanded) / (% change in price)

At the equilibrium point, the percentage change in quantity demanded and price will be the same because we are calculating the elasticity at the equilibrium:

PED = (% change in Q) / (% change in P) = (0) / (0) = undefined

Since the denominator is zero, the price elasticity of demand at the equilibrium point is undefined.

2. a) To find the market clearing price and quantity, we set the demand equal to the supply:

Qd = Qs

30 - 2P = -6 + P

3P = 36

P = 12

Substituting this equilibrium price back into either the demand or supply equation to find the equilibrium quantity:

Q = 30 - 2P = 30 - 2(12) = 6

Therefore, the market clearing price is 12 and the quantity is 6.

b) To calculate the price elasticity of demand, we use the formula:

PED = (% change in quantity demanded) / (% change in price)

The demand function given is Qx = 30 - 2P. Taking the derivative of Qx with respect to P, we get:

dQx/dP = -2

The price elasticity of demand is the absolute value of this derivative multiplied by the price and divided by the quantity:

PED = |-2| * P / Q = 2 * 12 / 6 = 4

Therefore, the price elasticity of demand is 4.

3. a) To find the market equilibrium price and quantity, we set the demand equal to the supply:

Qd = Qs

50 - P = Qs + 5

Rearranging the equation:

P = Qs + 5

Substituting this into the demand equation:

50 - (Qs + 5) = Qs

45 = 2Qs

Qs = 22.5

Substituting Qs back into the supply equation to find the equilibrium price:

P = Qs + 5 = 22.5 + 5 = 27.5

Therefore, the market equilibrium price is Birr 27.5 per unit, and the quantity is 22.5 units.

b) If the market price was fixed at Birr 25 per unit, it would be below the equilibrium price. This means there would be excess demand in the market, as the quantity demanded at that price (Qd = 50 - 25 = 25) is greater than the quantity supplied (Qs = 25 - 5 = 20). This could lead to shortages and potential upward pressure on prices.

c) To calculate the price elasticity of demand at the equilibrium point, we use the formula:

PED = (% change in quantity demanded) / (% change in price)

At the equilibrium point, the percentage change in quantity demanded and price will be the same, as we are calculating the elasticity at the equilibrium:

PED = (% change in Q) / (% change in P) = (0) / (0) = undefined

Since the denominator is zero, the price elasticity of demand at the equilibrium point is undefined.