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Determining Short-Run and Long-Run Equilibrium Using Calculus
Long-Run Equilibrium in a Competitive Industry
Consider a perfectly competitive industry where all potential firms are identical. The market demand is given by the function Q_D = 5000 - 100P, and the total cost function for a single firm is TC(q) = 200 + 2q + 0.5q². Based on this information, analyze the market to determine the long-run equilibrium price, the quantity produced by each firm, and the total number of firms that will operate in the industry.
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Market Equilibrium Analysis
Short-Run vs. Long-Run Market Equilibrium
A perfectly competitive market consists of 10 identical firms. The total cost function for each firm is TC = 25 + q², where q is the quantity produced by a single firm. The market demand function is given by Q = 150 - P. What is the short-run equilibrium price in this market?
A perfectly competitive market has a demand function given by Q = 240 - 5P. All potential firms in this market are identical, each with a total cost function of TC = 16 + 4q + q², where q is the quantity produced by a single firm. Assuming firms can freely enter and exit the market, how many firms will operate in the long-run equilibrium?
Comparative Equilibrium Analysis in a Competitive Market
You are given the total cost function for a typical firm in a perfectly competitive market and the market demand function. Arrange the following steps in the correct logical order to determine the number of firms operating in the long-run equilibrium.
In a perfectly competitive market comprised of identical firms, if the current market price is greater than the minimum average total cost for each firm, it is true that in the long run, new firms will enter the market, causing the short-run market supply curve to shift to the left.
Long-Run Equilibrium in a Competitive Industry
A perfectly competitive market is composed of numerous identical firms. Match each economic condition with its correct mathematical or graphical representation. Assume P is price, MC is marginal cost, ATC is average total cost, and AVC is average variable cost.
Firm's Output in Long-Run Equilibrium