Determining Short-Run and Long-Run Equilibrium Using Calculus
This node outlines a method for finding the market equilibrium price and quantity in both the short and long run within a market of identical firms. The process involves applying calculus to derive the market supply curve from the firms' shared cost function. This derivation is performed under two conditions: a short-run scenario with a fixed number of firms, and a long-run scenario where firms can enter and exit the market. [3]
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Introduction to Microeconomics Course
The Economy 2.0 Microeconomics @ CORE Econ
Ch.8 Supply and demand: Markets with many buyers and sellers - The Economy 2.0 Microeconomics @ CORE Econ
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The Market Supply Curve for Bread (Figure 8.9)
Approximating the Market Supply Curve with a Smooth Curve
Visual Representation of Individual vs. Market Supply Curves with Identical Firms
Aggregation Flattens the Market Supply Curve
Determining Short-Run and Long-Run Equilibrium Using Calculus
A market for a particular good consists of 40 identical firms. The supply function for a single firm is given by the equation q = 2P - 8, where 'q' is the quantity supplied by the firm and 'P' is the market price. What is the market supply function (Q) for this good?
A market consists of two types of firms. There are 10 firms of 'Type A', each with an individual supply function of q_A = P - 5. There are also 20 firms of 'Type B', each with an individual supply function of q_B = 2P - 10. Assuming the market price (P) is high enough for both types of firms to produce a positive quantity, what is the total market supply function (Q)?
A market consists of only two firms, Firm 1 and Firm 2. The quantity supplied by Firm 1 is given by
q₁ = P - 8, and the quantity supplied by Firm 2 is given byq₂ = 2P - 20. Which equation represents the market supply function (Q) when the market price (P) is between $8 and $10?In a competitive market with 50 identical firms, the total market supply is described by the function Q = 100P - 500, where Q is the total quantity supplied and P is the price. What is the supply function (q) for a single, individual firm in this market?
Individual vs. Market Supply Responsiveness
Local Coffee Market Supply Analysis
A market contains two firms. Firm 1 will begin to supply goods only if the price is above $5. Firm 2 will begin to supply goods only if the price is above $10. Both firms have individual supply curves that slope upwards. If the market supply curve is drawn with price (P) on the vertical axis and quantity (Q) on the horizontal axis, which statement best describes its shape?
Limitations of the Short-Run Market Supply Model
Deconstructing a Market Supply Function
A market for a specific product consists of only two producers, Firm A and Firm B. Their individual supply schedules, showing the quantity each is willing to supply at different prices, are given below.
Firm A Supply:
Price Quantity $5 0 $10 10 $15 20 Firm B Supply:
Price Quantity $5 5 $10 15 $15 25 Which of the following tables correctly represents the total market supply schedule?
A market for a particular good consists of 40 identical firms. The supply function for a single firm is given by the equation q = 2P - 8, where 'q' is the quantity supplied by the firm and 'P' is the market price. What is the market supply function (Q) for this good?
Deriving Market Supply with Heterogeneous Firms
A competitive market for widgets has 50 identical firms. The total market supply is described by the equation Q = 100P - 500, where Q is the total quantity supplied and P is the price. Assuming all firms have the same supply function, what is the supply equation (q) for a single firm?
Relationship Between Individual and Market Supply Elasticity
A market for a product consists of two firms, Firm 1 and Firm 2. Their individual supply functions are as follows:
- Firm 1: q₁ = P - 10, for any price (P) greater than or equal to $10.
- Firm 2: q₂ = 2P - 40, for any price (P) greater than or equal to $20.
Which of the following equations correctly describes the total market supply function (Q)?
Critique of a Market Supply Derivation
Evaluating a Market Strategy
Deriving a Kinked Market Supply Curve
In a market where 20 identical firms are producing a good, the market price must rise by $0.50 to increase the total quantity supplied by 100 units. If 20 more identical firms enter this market, it is true that the market price would now need to rise by $1.00 to achieve the same 100-unit increase in total quantity supplied.
Consider three different markets for the same product, each with different firm compositions. Match each market description to the most likely characteristic of its short-run market supply curve. Assume all individual firms have upward-sloping supply curves.
Sources of Variation in Marginal Costs Among Firms
Dual Interpretation of the Market Supply Curve
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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