Question

1. Use the graph below to answer the questions: 80 70 60 50 40 30 20 10 ㄒ ㄧ -- 4 State the equation for the demand curve (inverse demand function) shown in the graph above using the format Px- a - bQx: a. b. State the equation for the demand function implied in the graph using the format Qx-c - dPx c. Find the equation for Total Revenue, where TR is a function of output (Qx) d. Find the equation for Marginal Revenue, where MR is a function of output (Qx):

Answer 1

From demand curve,

When Q = 0, P = 80 (Vertical intercept) and when P = 0, Q = 8 (Horizontal intercept).

(a) Px = a - bQx

Using above data,

80 = a - b x 0

a = 80

Also,

0 = a - 8b

a = 8b

80 = 8b

b = 10

Demand equation: Px = 80 - 10Qx

(b) Px = 80 - 10Qx

10Qx = 80 - Px

Qx = 8 - 0.1Px

(c)

Total revenue (TR) = (Px).(Qx)

TRx = Qx.(80 - 10Qx)

TRx = 80Qx - 10Qx²

(d)

Marginal revenue (MR) = dTR/dQx

MR = d/dQx(80Qx - 10Qx²) = 80 - 20Qx