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Exercises · Q10

Q.A linear supply function is given as P=20+0.5QP = 20 + 0.5Q. Find

(a) the slope,
(b) the Y-intercept and its meaning, and
(c) the quantity supplied when price is Rs. 50.
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Step 1 — Slope. Comparing P=20+0.5QP = 20 + 0.5Q with the general linear form P=c+dQP = c + dQ, the slope is d=0.5d = 0.5 — positive, confirming this is an upward-sloping (normal) supply line.

Step 2 — Y-intercept. Setting Q=0Q = 0: P=20+0.5(0)=20P = 20 + 0.5(0) = 20. Economically, this is the minimum price sellers require before they are willing to supply any quantity at all.

Step 3 — Quantity at P = Rs. 50. Substitute P=50P = 50: 50=20+0.5Q⇒0.5Q=30⇒Q=6050 = 20 + 0.5Q \Rightarrow 0.5Q = 30 \Rightarrow Q = 60.

Step 4 — Independent check (dual-solve). Substitute Q=60Q = 60 back into the original equation: P=20+0.5(60)=20+30=50P = 20 + 0.5(60) = 20 + 30 = 50. ✓ Confirms the answer. …

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