Firm 1 produces cars and the total cost of producing q cars is given as C(q) = 2

Question

Firm 1 produces cars and the total cost of producing q cars is given as C(q) = 2q2 + 5q. Assuming the firm operates in a perfectly competitive market.Write down the profit function of the firm and solve for the first order condition. What is the supply curve of the firm? Suppose firm 2 also produces cars at a cost of C(q) = 3q2. What is the supply curve of this firm? Solve for the aggregate supply curve of cars, Illustrate this in a diagram. Is it efficient if both firms produce 10 cars? Why or why not? Suppose there are 2 consumers. Both consumers have individual demand functions of p = 20 ? 2qi for cars. What is the aggregate demand curve? Illustrate in a diagram. What is the market equilibrium (where price equals demand). What is the equilibrium quantity and price? How much does each firm produce and how much does each consumer consume at the equilibrium. What is the marginal cost of each .firm at the equilibrium? What is the marginal willingness to pay of each consumer at the equilibrium? Is the equilibrium Pareto optimal?

Explanation / Answer

Profit function: quantity*(price-cost) A. q*(y-2q^2-5q)=yq-2q^3-5q^2 take the derivative and set = to 0 y-6q^2-10q=0 y=6q^2+10q B. q*(y-3q^2)=qy-3q^3 take the derivative and set = to 0 y-9q^2=0 y=9q^2 C. I'm not drawing it, sorry. You can just add and get y=15q^2+10q

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