A good's Demand Curve is: Qd = 10 - P, and its Supply Curve is: Qs = 4P.

Consumer surplus is

Question

A good's Demand Curve is: Qd = 10 - P, and its Supply Curve is: Qs = 4P.

Consumer surplus is

BlackTom AI · Accepted Answer

We start by identifying the market equilibrium to anchor the consumer surplus calculation. The demand is Qd = 10 - P and the supply is Qs = 4P. Setting Qd = Qs gives 10 - P = 4P, so 5P = 10 and P* = 2. Substituting back into either equation yields Q* = Qd = 10 - 2 = 8 (or Qs = 4*2 = 8). Next, determine the maximum price consumers are willing to pay for the first unit, which occurs where quantity demanded drops to zero. From the demand equation, Qd = 0 implies 0 = 10 - P, so Pmax = 10. Consumer surplus is the area of the triangle between the demand curve, the price line, and the vertical axis, calculated as CS = 0.5 * (Pmax - P*) * Q*. Here, Pmax = 10, P* = 2, and Q* = 8, giving CS = 0.5 * (10 - 2) * 8 = 0.5 * 8 * 8 = 32.

Option-by-option analysis:
- $64: If CS were 64, the triangular area would imply a combination of price gap and quantity that exceed the computed equilibrium values (P* = 2 and Q* = 8) and the maximum willingness to pay of 10, making this value inconsistent with the demand schedule. This would require either a larger price gap (Pmax - P*) or a larger Q than supported by the curves, which is not possible here.
- $16: A CS of 16 would correspond to a smaller price gap or quantity than the equilibrium calculation yields. Given Pmax = 10 and P* = 2, the product 0.5*(Pmax - P*)*Q would not align with the 16 value when Q* is 8; specifically, it would require a smaller Q or a smaller Pmax - P* than is given by the demand function.
- $8: This option represents an even smaller triangle area, which again does not fit the combination of P*, Q*, and Pmax derived from the demand curve. The numbers do not multiply to 8 under the LHS terms with the given Pmax and P*.
- $32: This value matches the computed consumer surplus given the equilibrium price and quantity and the intercept of the demand curve. Since CS = 0.5 * (Pmax - P*) * Q* with Pmax = 10, P* = 2, Q* = 8, the result 32 aligns with the standard CS formula for linear demand.

Overall, the reasoning shows how the equilibrium and the demand intercept determine the CS, and how the other listed values fail to fit the same calculation.

ECON1-TTh Chapter7 Assignment

A good's Demand Curve is: Qd = 10 - P, and its Supply Curve is: Qs = 4P. Consumer surplus is

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