MONOPOLISTIC COMPETITION 1. Suppose that the cost of production is given by the following function: CT = 100 + Q2 and that the demand is given by P = 80 - Q. a. Determine the level of maximization. b. Determine the value of CT and IT c. Check that the IMg = CMg
1. Suppose that the cost of production is given by the following function: CT = 100 + Q2 and that the demand is given by P = 80 - Q.
a. Determine the level of maximization.
b. Determine the value of CT and IT
c. Check that the IMg = CMg
CT (Total cost)
IMg (marginal income)
CMg (marginal cost)
Algebraically if the demand curve in the
P = a - bQ
Where a is the ordinate to the origin, b the slope and Q the quantity
So if IT = P x Q
We have that (a - bQ) Q = aQ - bQ2
IT = aQ - bQ2
And therefore the marginal income is the derivative of IT or what is equal to the variation of total income between the variation of the quantity.
Therefore the IMg = derive the quantity in the function aQ - bQ2
IMg = a - 2bQ
Consider these functions when conducting monopoly exercises.
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