The market demand in a Bertrand duopoly is P = 15 - 4Q, and the marginal costs are $3. Fixed costs are zero for both firms. Which of the following statement(s) is/are true?
a.P = $3.
b.P = $10.
c. P = $15.
d. None of the statements associated with this question are correct.
I choose A as my answer because fixed cost was zero. If I'm wrong, can you please explain to me how to solve this...
To determine the equilibrium price in a Bertrand duopoly, we need to find the point where both firms have the same price and there is no incentive for either firm to deviate from this price. This occurs when the marginal cost of producing an additional unit is equal to the price.
In this case, the marginal cost is given as $3. To find the equilibrium price, we set this equal to the market demand equation P = 15 - 4Q:
3 = 15 - 4Q
Rearranging the equation, we have:
4Q = 15 - 3
4Q = 12
Q = 3
Substituting the value of Q back into the demand equation, we can find the equilibrium price:
P = 15 - 4(3)
P = 15 - 12
P = 3
So the correct answer is a: P = $3.
To solve this question, we first need to understand the concept of a Bertrand Duopoly. In a Bertrand duopoly, two firms compete by setting prices for their products.
In this case, the market demand is given by the equation P = 15 - 4Q, where P represents the price and Q represents the quantity demanded in the market.
To find the equilibrium price, we need to find the point where both firms' marginal costs are equal to the market demand. In this case, the marginal cost of each firm is $3.
Setting the marginal cost equal to the market demand equation, we have:
3 = 15 - 4Q
Rearranging the equation, we get:
4Q = 15 - 3
4Q = 12
Q = 12/4
Q = 3
Once we know Q, we can substitute it back into the market demand equation to find the equilibrium price:
P = 15 - 4(3)
P = 15 - 12
P = 3
Therefore, the equilibrium price in this Bertrand duopoly is P = $3.
So, statement a, "P = $3," is correct.