Question

Given the following function: Q_D = 200 - 5.25P

7.1 Derive the Regular Demand Function

7.2 Derive the Inverse Demand Function

7.3 Derive the Price and Quantity which maximizes TR.

7.4 Suppose the Supply Curve is given as Q_s = 25; derive the price and quantity equilibrium.

7.5 Use the price and quantity which maximizes TR and the Price and Quantity equilibrium, drive the mid-point (Arc) elasticity and interpret the result.

Answer 1

7.1. Regular demand function is Qd = 200 - (21/4)P

7.2 Inverse demand function is (21/4)P = 200 - Qd or P = 800/21 - (4/21)Qd

7.3 Total revenue is TR = PQ = (800/21 - (4/21)Q)Q. This becomes 800Q/21 - (4/21)Q^2. Place its derivative equal to 0 and see that 800/21 - (8/21)Q = 0 or Q = 100 units. At this quantity, price is P = 800/21 - 400/21 = 400/21 or 19.05

7.4. Use Qd = Qs and get 200 - 5.25P = 25. This gives P = (200 - 25)/5.25 = 100/3 or 33.33 and quantity = 25 units.

7.5. P1 = 19.05, P2 = 33.33. Q1 = 100, Q2 = 25. Use Ed = (Q2 – Q1) / [(Q2 + Q1)/2] / (P2 – P1) / [(P2 + P1)/2] and see that ed = -2.20

Q1	Q2	P1	P2	Q2-Q1	(Q2+Q1)/2	%Q	P2-P1	(P1+P2)/2	%P	Ed
100.00	25.00	19.05	33.33	-75.00	62.50	-120.00	14.28	26.19	54.54	-2.20