P=100-30+4A1/2 and TC=4Q2+10Q+A Where p= Price ,Q=quantity , A=advertising
a) Find the equilibrium of quantity and advertisement price
b) Compute the degree of monopoly power
P=100-30+4A1/2 and TC=4Q2+10Q+A Where p= Price ,Q=quantity , A=advertising
a) Find the equilibrium of quantity and advertisement price
b) Compute the degree of monopoly power
that is good question
very difficult to view.
To find the equilibrium quantity and advertisement price, we need to find the point where quantity demanded equals quantity supplied.
a) Equilibrium Quantity:
We can set the quantity demanded equal to the quantity supplied and solve for Q.
Quantity Demanded (Qd) = Quantity Supplied (Qs)
Quantity Demanded: Qd = P = 100 - 30 + 4A(1/2) = 70 + 4A(1/2)
Quantity Supplied: Qs = Q
Setting Qd equal to Qs:
70 + 4A(1/2) = Q
b) Equilibrium Price:
To find the equilibrium price, substitute the equilibrium quantity (Q) into the demand equation.
P = 100 - 30 + 4A(1/2)
P = 70 + 4A(1/2)
P = 70 + 2A
Therefore, the equilibrium quantity is Q = 70 + 4A(1/2) and the equilibrium price is P = 70 + 2A.
b) Degree of Monopoly Power:
To compute the degree of monopoly power, we need to calculate the Lerner Index, which measures the extent to which a firm can set prices above marginal cost.
Lerner Index = (P - MC) / P
In this case, the marginal cost (MC) is represented by the total cost (TC) equation:
TC = 4Q^2 + 10Q + A
To calculate the degree of monopoly power, we need to determine the marginal cost when the firm produces at the equilibrium quantity.
First, calculate the derivative of the total cost equation with respect to quantity (Q):
dTC/dQ = 8Q + 10
Then, substitute the equilibrium quantity (Q) into the derivative equation to find the marginal cost (MC):
MC = 8(70 + 4A(1/2)) + 10
Now, substitute the equilibrium price (P) into the Lerner Index equation and calculate the degree of monopoly power:
Lerner Index = (70 + 2A - (8(70 + 4A(1/2)) + 10)) / (70 + 2A)
This calculation will give you the degree of monopoly power.