# Take‑home: Demand increase (read from your graph) Below I extract the linear equations from the picture, then compute the initial and new equilibria and all surplus measures. I also decompose where gains and losses in CS and PS come from. ## 1) Read the functions from the graph Rule: For a straight line, use two points to get the slope, then write P = a + bQ. - Supply S goes through (Q=0, P=0) and (Q=30, P=15). - Slope b = ΔP/ΔQ = 15/30 = 0.5 - Supply: S: P = 0.5Q - Initial demand D1 goes through (0, 15) and (15, 0). - Slope = (0 − 15)/(15 − 0) = −1 - Demand (initial): D1: P = 15 − Q - New demand D2 goes through (0, 15) and (30, 0). - Slope = (0 − 15)/(30 − 0) = −0.5 - Demand (after increase): D2: P = 15 − 0.5Q Interpretation of axes: Price on the vertical axis (0 to 15); Quantity on the horizontal axis (0 to 30). ## 2) A factor that increased D Any standard shifter works; for example: an increase in consumers’ income if the good is normal. Others you could cite: more buyers (population growth), a rise in the price of a substitute, a fall in the price of a complement, a positive taste/advertising shock, or expectations of higher future prices. ## 3) Solve the equilibria Rule: Competitive equilibrium is where Demand = Supply. - Initial equilibrium (D1 with S): - 15 − Q = 0.5Q ⇒ 15 = 1.5Q ⇒ Q₁ᵉ = 10 - Plug back: P₁ᵉ = 0.5(10) = 5 - New equilibrium (D2 with S): - 15 − 0.5Q = 0.5Q ⇒ 15 = Q ⇒ Q₂ᵉ = 15 - Plug back: P₂ᵉ = 0.5(15) = 7.5 ## 4) Surplus formulas (then compute) Rules for linear curves at competitive equilibrium: - Consumer Surplus: CS = 1/2 × (Pmax − Pe) × Qe - Producer Surplus: PS = 1/2 × (Pe − Pmin) × Qe - Total Surplus: TS = CS + PS Here, Pmax (demand intercept) = 15; Pmin (supply intercept) = 0. - Initial surpluses (at Pe = 5, Qe = 10) - CS₁ = 1/2 × (15 − 5) × 10 = 1/2 × 10 × 10 = 50 - PS₁ = 1/2 × (5 − 0) × 10 = 1/2 × 5 × 10 = 25 - TS₁ = 50 + 25 = 75 - New surpluses (at Pe = 7.5, Qe = 15) - CS₂ = 1/2 × (15 − 7.5) × 15 = 1/2 × 7.5 × 15 = 56.25 - PS₂ = 1/2 × (7.5 − 0) × 15 = 1/2 × 7.5 × 15 = 56.25 - TS₂ = 56.25 + 56.25 = 112.5 - Changes - ΔCS = CS₂ − CS₁ = 56.25 − 50 = +6.25 - ΔPS = PS₂ − PS₁ = 56.25 − 25 = +31.25 - ΔTS = TS₂ − TS₁ = 112.5 − 75 = +37.5 ## 5) Decomposing the gains and losses (how the numbers arise) Use rectangles and triangles from your graph. - Consumer Surplus - Loss from higher price on the original 10 units: - Rectangle = (P₂ᵉ − P₁ᵉ) × Q₁ᵉ = (7.5 − 5) × 10 = 25 - Gains: 1) Higher willingness to pay on the first 10 units after the shift (area between D2 and D1 up to Q = 10): - Triangle = 1/2 × base 10 × height 5 = 25 2) Surplus from the 5 extra units (Q = 10 to 15) whose value exceeds P₂ᵉ: - Triangle = 1/2 × base 5 × height (value at Q=10 on D2 − P₂ᵉ) = 1/2 × 5 × (10 − 7.5) = 6.25 - Net: −25 + 25 + 6.25 = +6.25 (matches ΔCS) - Producer Surplus - Gain from the higher price on the original 10 units: - Rectangle = (P₂ᵉ − P₁ᵉ) × Q₁ᵉ = 25 - Gain from producing the extra 5 units (moving up the supply curve from Q=10 to 15): - Triangle = 1/2 × base 5 × height (7.5 − 5) = 6.25 - Net: 25 + 6.25 = +31.25 (matches ΔPS) - Total Surplus - TS rises by the sum of the two triangles representing new mutually beneficial trades: - 25 (between D2 and D1 for Q ≤ 10) + 12.5 (between D2 and S from Q=10 to 15) = 37.5 - Note: the latter 12.5 is 1/2 × 5 × 5 because [D2 − S] falls from 5 at Q=10 to 0 at Q=15. ## 6) Deadweight loss (DWL) Rule: DWL arises only when quantity is away from competitive equilibrium due to a tax, price control, quota, etc. - Here both before and after the shift, the market clears at the competitive equilibrium on the relevant demand curve and the supply curve. - Therefore DWL = 0 in both cases. The increase in D raises TS; it does not create inefficiency. ## 7) Final answers - Supply: P = 0.5Q - Demand (initial): P = 15 − Q - Demand (new): P = 15 − 0.5Q - Initial equilibrium: P₁ᵉ = 5, Q₁ᵉ = 10; CS₁ = 50; PS₁ = 25; TS₁ = 75 - New equilibrium: P₂ᵉ = 7.5, Q₂ᵉ = 15; CS₂ = 56.25; PS₂ = 56.25; TS₂ = 112.5 - Changes: ΔCS = +6.25; ΔPS = +31.25; ΔTS = +37.5 - DWL: 0 These values match the shading in your sketch: consumers lose a price‑rise rectangle (25) but gain more from the rightward shift and extra units (31.25 total), and producers gain both from the higher price and from selling more units.