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  • Visualizing Total Gains from Trade in the Bread Market Diagram (Figure 8.12)

  • Calculating Total Cost by Integrating Marginal Cost

  • Consumer Surplus

Calculating Consumer surplus Using Integration

The total consumer surplus can be precisely calculated by treating the quantity (Q) as a continuous variable, which allows for the use of integration. For any given price (P₀) and quantity (Q₀), whether at market equilibrium or not, the consumer surplus is found by integrating the individual surpluses—the difference between the inverse demand function, f(q), and the price, P₀—from zero to the total quantity sold, Q₀. The integral form is: ∫0Q0(f(q)−P0) dq\int_{0}^{Q_0} (f(q) - P_0) \,dq. This can also be expressed as F(Q0)−P0Q0F(Q_0) - P_0Q_0, where F(Q) represents the integral of the inverse demand function, f(q), from 0 to Q. This alternative method involves finding the total area under the demand curve up to the equilibrium quantity (Q∗Q^*) and then subtracting the total expenditure (P∗×Q∗P^* \times Q^*). For a more comprehensive understanding of integration, section 19.1 of 'Mathematics for Economists: An Introductory Textbook' by Pemberton and Rau is a recommended resource.

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Sociology

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Economy

CORE Econ

Introduction to Microeconomics Course

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  • Calculating Consumer surplus Using Integration

Learn After

  • Inverse Demand Function and the Law of Demand

  • Finding and Confirming the Quantity that Maximizes Consumer Surplus

  • Calculating Consumer Surplus from a Demand Function

  • A market has an inverse demand function given by P = 50 - 2Q, where P is the price and Q is the quantity. If the market price is set at P = 10, what is the total consumer surplus?

  • Interpreting the Integral for Consumer Surplus

  • Analyzing an Incorrect Consumer Surplus Calculation

  • The total consumer surplus in a market can be calculated using the mathematical expression ∫0Q0(f(q)−P0) dq\int_{0}^{Q_0} (f(q) - P_0) \,dq. Match each component of this expression to its correct economic interpretation.

  • Evaluating Calculation Methods for Consumer Surplus

  • A market is characterized by an inverse demand function given by P = 144 - Q², where P is the price and Q is the quantity. If the product is sold at a market price of $80, the correct upper limit of integration (Q₀) needed to calculate the total consumer surplus is ___.

  • Evaluating Methods for Calculating Consumer Surplus

  • Consider a market where consumer surplus is calculated using a definite integral based on the inverse demand function and the market price. True or False: If the market price of the product increases, while the demand function remains unchanged, the value of the integrand (the function being integrated) will decrease for every quantity level considered in the calculation of the new consumer surplus.

  • Suppose that for a particular good, the total area under the inverse demand curve from a quantity of 0 to 50 units is calculated to be 2,500.Thisfigurerepresentsthetotalvalueconsumersreceivefromconsumingthose50units.Ifthemarketpriceforthegoodis2,500. This figure represents the total value consumers receive from consuming those 50 units. If the market price for the good is 35 per unit and 50 units are sold, what is the total consumer surplus?