Can someone please help me with a hint to solve this problem?? I'm struggling really hard with this.
"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
how about this one?
Suppose that firms are NOT owned by consumers.
Let s denote the size of the per-unit subsidy/tax given to the firms. Let positive values of s denote subsidies, and negative values of s denote taxes.
QUESTION: What is the value of s that maximizes total consumer well-being? (Note: Don't forget to add the sign in entering your answer, if necessary).
?
I think that is 250
Wrong values: 250,-250,-300,-500
Aldo 125. Answer should be positive
Also sorry. 125 is wrong
To solve this problem, you are on the right track in calculating the oligopoly equilibrium without the tax. Given the cost function c(q) = q^2, you correctly found that the equilibrium quantity without the tax, Q, is equal to 400.
However, to find the equilibrium price without the tax, you need to determine the aggregate demand function in the market. The problem states that the aggregate demand function is given by 1000 - p, where p represents the price. To find the equilibrium price, you need to set the quantity Q equal to the aggregate demand and solve for p.
So, setting Q = 1000 - p, we have:
400 = 1000 - p
Solving for p, we find that the equilibrium price without the tax is 600.
Now, let's consider the effect of the subsidy on production. The subsidy of $100 per unit produced reduces the cost for each firm, meaning their new cost function is c(q) = (q - 100)^2. To find the new total level of production, we can determine the quantity that minimizes the total cost of production. Taking the derivative of the cost function and setting it to zero, we find:
2(q - 100) = 0
Solving for q, we obtain q = 100. Thus, the new total level of production, Q_new, is 100.
Regarding the equilibrium price with the subsidy, you correctly state that a lump-sum tax does not affect the inverse demand function. So, the price (P_new) with the subsidy remains 600, as calculated previously.
To summarize, the total level of production with the subsidy is 100, and the equilibrium price remains 600.