Can someone please help me with a hint to solve this problem?? I'm struggling really hard with this.
Thanks!!!
"Consider an oligopolistic market with two firms. Each of them produces using a cost function given by c(q)=q^2.
The aggregate demand in the market is given by 1000−p.
Suppose that, in order to increase production, the government gives the firms a $100 per-unit produced subsidy. The cost of the subsidy is financed with an identical lump-sum tax on consumers.
What is the total level of production and the equilibrium price in the market?"
I think that first of all you need to calculate the oligopoly equilibrium (without the tax), and you'll get Q=400 and P=600 right???
Then the inclusión of the tax (for consumers) and the subsidy (for producers) increase/reduce the Price/cost; so the answer should be P=660 and Q=440; but not sure.
Am I right?????
Can someone please help me with a hint to solve this problem?? I'm struggling really hard with this.
Thanks!!!
"Consider an oligopolistic market with two firms. Each of them produces using a cost function given by c(q)=q^2.
The aggregate demand in the market is given by 1000−p.
Suppose that, in order to increase production, the government gives the firms a $100 per-unit produced subsidy. The cost of the subsidy is financed with an identical lump-sum tax on consumers.
What is the total level of production and the equilibrium price in the market?"
I think that first of all you need to calculate the oligopoly equilibrium (without the tax), and you'll get Q=400 and P=600 right???
But the subsidy (for producers)reduces the cost; so the answer for the new Q should be Q=440.
My question is about the Price; because a lum-sum tax does not affect the inverse demand function, then:
P = 1000 - Q = 1000-440 = 560.
It's that correct??
YES
To solve this problem, you can use the concept of Cournot competition to determine the equilibrium quantity produced by each firm. Here's how:
1. Start by finding the individual firm's profit-maximizing quantity. In an oligopolistic market with two firms, each firm assumes that its competitor's quantity will remain fixed. So, the firm solves for its profit-maximizing quantity by taking the derivative of its profit function with respect to its quantity, setting it equal to zero, and solving for quantity.
2. In this case, the cost function for each firm is given by c(q) = q^2.
To find the equilibrium quantity produced by each firm, differentiate the total profit function with respect to Q1 (quantity produced by firm 1) and set it equal to zero:
Π1 = (P - c(q1)) * q1
Π1 = (P - q1^2) * q1
dΠ1/dQ1 = P - 3q1^2 = 0
Solving for q1, we get:
P = 3q1^2
3. Now, we can find the equilibrium quantity produced by each firm. Since both firms are identical, the total quantity produced in the market, Q, is the sum of the individual quantities produced by each firm (Q = q1 + q2).
4. The total demand in the market is given by 1000 - p, where p is the equilibrium price. Because each firm assumes that its competitor's quantity will remain fixed, the total quantity in the market is equal to the sum of the individual quantities produced by each firm (Q = q1 + q2). Therefore, we can express the total demand as (1000 - p) = Q.
5. Equating the total demand and the total quantity produced (Q = 1000 - p), we can solve for the equilibrium price, p, and substitute it back into the equation for equilibrium quantity (Q = q1 + q2).
6. However, in this problem, the government provides a $100 per-unit subsidy to the firms, which reduces their cost of production. To account for this subsidy, the firms' costs become c(q) = (q - 100)^2.
7. Also, the subsidy is financed with an identical lump-sum tax on consumers, which increases their price by the same amount it reduces the firms' cost. Therefore, the subsidy and tax cancel each other out, and the equilibrium price remains the same as without the tax.
So, the total level of production and the equilibrium price in the market should be:
Total production: Q = q1 + q2 = (600 - P) / 3
Equilibrium price: P = 600
Therefore, the total level of production is Q = (600 - 600) / 3 = 0, and the equilibrium price in the market is P = 600.
Note: It is crucial to understand the concept of Cournot competition and the behavior of firms in an oligopolistic market to solve this problem effectively.