Learn Before
Finding and Confirming the Quantity that Maximizes Total Surplus
To determine the quantity () that maximizes total surplus, calculus is used. The first step involves taking the derivative of the total surplus function, N(Q), with respect to quantity (Q) and setting it to zero. The quantity that solves this equation is the potential point of maximum surplus. To confirm that this quantity indeed maximizes the total surplus, the second-order condition must be checked. This involves examining the second derivative of the total surplus function, N(Q). Given that the integral of the inverse demand function (F) is concave (its second derivative is negative) and the cost function (C) is convex (its second derivative is positive), it can be concluded that the second derivative of the total surplus function N(Q) is negative. A negative second derivative confirms that corresponds to a maximum point.
0
1
Tags
Social Science
Empirical Science
Science
CORE Econ
Economics
Economy
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
Related
Finding and Confirming the Quantity that Maximizes Consumer Surplus
Condition for Maximizing Producer Surplus: Price Equals Marginal Cost
Finding and Confirming the Quantity that Maximizes Total Surplus
In a competitive market for a good, the demand curve represents buyers' marginal willingness to pay, and the supply curve represents sellers' marginal cost. If the current quantity of the good being produced and sold is less than the market equilibrium quantity, why is the total surplus (the combined economic gain for all buyers and sellers) not at its maximum?
Optimizing Production in a Widget Market
Impact of Price Controls on Market Efficiency
Analyzing Market Inefficiency
In a standard competitive market model where the demand curve slopes down and the supply curve slopes up, match each production quantity scenario with its corresponding effect on the total gains from trade (the sum of consumer and producer surplus).
In a market, if the goal is to maximize the total gains from trade (the sum of all participants' economic well-being), the production level should be set to the point that maximizes only the producers' surplus.
In a market, the total gains from trade, represented by the sum of consumer and producer surplus, are maximized when the quantity produced and consumed is such that the value to the marginal buyer is exactly equal to the __________ of the marginal seller.
Consider a market with a downward-sloping demand curve (representing buyers' value) and an upward-sloping supply curve (representing sellers' cost). Arrange the following market outcomes in order from the one that generates the LEAST total gains from trade (sum of consumer and producer surplus) to the one that generates the MOST.
Evaluating a Price Control Policy
Consider a market where the value of a good to buyers decreases as more is consumed, and the cost to sellers increases as more is produced. If the current level of production is at a point where the value of the last unit to a buyer is significantly higher than the cost of producing it for a seller, which statement best analyzes the total gains from trade (the sum of all participants' economic well-being)?
Learn After
Algebraic Proof that Competitive Equilibrium Maximizes Total Surplus
Verifying a Surplus Maximum
An economist has determined the quantity, Q*, that satisfies the first-order condition for maximizing total surplus (i.e., where the first derivative of the total surplus function with respect to quantity is zero). To confirm that Q* truly represents a maximum rather than a minimum, what additional condition must be met, and why is it typically satisfied in this economic context?
Calculating the Surplus-Maximizing Quantity
The Rationale Behind the Second-Order Condition for Surplus Maximization
If an economist determines that at a specific quantity, Q', the first derivative of the total surplus function with respect to quantity is equal to zero, it is guaranteed that Q' is the quantity that maximizes total surplus.
Match each mathematical expression from the calculus-based method of finding the surplus-maximizing quantity with its correct economic interpretation or condition.
A microeconomist wants to use calculus to find and verify the exact quantity of a good that maximizes total surplus. Arrange the following steps into the correct logical sequence they should follow.
Analyzing Second-Order Conditions for Surplus Maximization
Consider a market where, at the current production level of 500 units, the value to the consumer of the 500th unit is $40, and the cost to the producer of making that 500th unit is $30. Assuming the standard conditions required for a unique surplus-maximizing quantity are met, what does this situation imply about the total surplus?
An economist is analyzing a market and identifies a quantity, Q', where the value of the last unit to the consumer is exactly equal to the cost of producing it. However, a further analysis reveals that for quantities immediately greater than Q', the cost of producing an additional unit is less than the value consumers place on it. Based on this information, what can be concluded about the total surplus at quantity Q'?