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. 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?
�
1 answer
1 answer