a. In perfect competition, if the total cost is given, take the derivative of the total cost and find the marginal cost. The equilibrium quantity is determine by the intersection of the price and the marginal cost. Set the market price equal to the marginal cost and solve for the equilibrium quantity. The equilibrium profit maximizing quantity is equal to 5.

• TC = 100 + 10Q + 5Q2
• MC = 10 + 10Q
• P = 60
• 60 = 10 + 10Q
• 10Q = 50
• Q = 5

b. The total revenue is equal the market price multiplied by the profit maximizing quantity. The total revenue is equal to $300.

• TR = P * Q
• TR = $60 * 5 = $300

We can then find out total cost by plugging the equilibrium output into the cost function. The profit is equal to the total revenue minus the total cost. The profit is equal to $25.

• TC = 100 + 10(5) + 5(5^2) = $100 + $50 + $125 = $275
• Profit = $300 - $275 = $25

c. The average total cost is equal to the total cost divided by the output. The average total cost is equal to $55.

• ATC = $275/5 = $55

d. In a perfectly competitive market, firms enter until there is zero economic profit because there are no barriers to entry. Since they have the same cost function and the price is the same, entry will always be profitable. Therefore, the market is in short run equilibrium but it is not in long run equilibrium until there is zero economic profit.