4. The demand for tickets to an Ethiopian Camparada film is given by D(p)= 200,000-
10,000p, where p is the price of tickets. If the price of tickets is 12 birr, calculate price
elasticity of demand for tickets and draw the demand curve
5. Given market demand Qd = 50 - P, and market supply P = Qs + 5
A) Find the market equilibrium price and quantity?
B) What would be the state of the market if market price was fixed at Birr 25 per unit?
�
4. To calculate the price elasticity of demand for tickets, we can use the formula:
E = (dQ/dP) * (P/Q)
First, calculate dQ/dP by taking the derivative of the demand function, D(p). Since the derivative of a constant term is 0, we only need to differentiate -10,000p:
dQ/dP = -10,000
Next, substitute the given price P = 12 birr into the demand function to find the quantity Q:
Q = D(12) = 200,000 - 10,000(12) = 200,000 - 120,000 = 80,000
Now substitute the values into the price elasticity of demand formula:
E = (-10,000) * (12/80,000) = -1.5
The price elasticity of demand for tickets is -1.5. Since it is negative, the demand for tickets is elastic.
To draw the demand curve, we can plot the price (p) on the x-axis and the quantity (Q) on the y-axis. The demand function is D(p) = 200,000 - 10,000p.
X-axis: Price (p)
Y-axis: Quantity (Q)
- Start by setting p = 0 and solve for Q:
Q = D(0) = 200,000 - 10,000(0) = 200,000
Plot the point (0, 200,000) on the graph.
- Then, set Q = 0 and solve for p:
0 = 200,000 - 10,000p
10,000p = 200,000
p = 20
Plot the point (20, 0) on the graph.
- Connect the two points with a straight line. This line represents the demand curve.
5.
A) To find the market equilibrium price and quantity, we need to find the intersection point of the demand and supply curves.
Start by equating the demand and supply equations:
Qd = Qs + 5
Substitute the given demand equation Qd = 50 - P:
50 - P = Qs + 5
Next, rearrange the equation to isolate P:
P = 55 - Qs
Substitute the supply equation P = Qs + 5 into the equation above:
P = 55 - (P - 5)
Simplify:
P = 60 - P
2P = 60
P = 30
Now substitute the value of P into either the supply or demand equation to find the quantity (Q):
Qd = 50 - P = 50 - 30 = 20
The market equilibrium price is Birr 30 per unit and the equilibrium quantity is 20 units.
B) If the market price was fixed at Birr 25 per unit, we can substitute this value into the supply equation to find the quantity supplied (Qs):
P = Qs + 5
25 = Qs + 5
Qs = 25 - 5 = 20
Since the quantity supplied (20) is less than the quantity demanded (Qd = 50 - P = 50 - 25 = 25), there would be a shortage in the market.
4. To calculate the price elasticity of demand for tickets, we can use the formula:
E = (ΔQ / Q) / (ΔP / P)
where E is the price elasticity of demand, ΔQ is the change in quantity demanded, Q is the initial quantity demanded, ΔP is the change in price, and P is the initial price.
In this case, the price is given as 12 birr. Let's calculate the price elasticity of demand at that price.
ΔP = 0 (since there is no change in price)
P = 12 birr (initial price)
To calculate ΔQ, we can substitute the price into the demand equation:
D(P) = 200,000 - 10,000P
D(12) = 200,000 - 10,000(12)
D(12) = 200,000 - 120,000
D(12) = 80,000
ΔQ = D(12) - D(0)
ΔQ = 80,000 - 200,000
ΔQ = -120,000
Now we can calculate the price elasticity of demand:
E = (ΔQ / Q) / (ΔP / P)
E = (-120,000 / 80,000) / (0 / 12)
E = -1.5 / 0
E = undefined (since we are dividing by zero)
Therefore, the price elasticity of demand for tickets at a price of 12 birr is undefined.
To draw the demand curve, we can plot different price-quantity combinations using the demand equation D(p) = 200,000 - 10,000p.
Price (birr) | Quantity Demanded
-------------------------------
0 | 200,000
1 | 190,000
2 | 180,000
... | ...
10 | 100,000
11 | 90,000
12 | 80,000
13 | 70,000
... | ...
20 | 0
Plotting these points on a graph will give you the demand curve. The price (p) is on the x-axis and the quantity demanded (Q) is on the y-axis.
5. A) To find the market equilibrium price and quantity, we need to set the quantity demanded equal to the quantity supplied.
Quantity Demanded (Qd) = Quantity Supplied (Qs)
Qd = 50 - P
Qs = P - 5
Setting these two equations equal to each other:
50 - P = P - 5
Simplifying:
55 = 2P
Solving for P:
P = 27.5
We have found the market equilibrium price.
Now, substitute the equilibrium price back into either the quantity demanded or quantity supplied equation to find the equilibrium quantity:
Qd = 50 - P
Qd = 50 - 27.5
Qd = 22.5
Therefore, the market equilibrium price is 27.5 birr and the market equilibrium quantity is 22.5 units.
B) If the market price is fixed at 25 birr per unit, it will be higher than the equilibrium price. This means the quantity supplied will exceed the quantity demanded, leading to a surplus in the market.