Question

Homework Assignment 1 You must show all your work to earn points ECON 3125 SP19 Name: 1. Use the graph below to answer the questions: 80 70 50 40 30 20 10 State the equation for the demand curve (inverse demand function) shown in the graph above using the format P.-a-bQ a. b. State the equation for the demand function implied in the graph using the format Q.-c-dP c. Find the equation for Total Revenue, where TR is a function of output (Q): d. Find the equation for Marginal Revenue, where MR is a function of output (Q): e. If MC-20, find the output level that maximizes Total Revenue: f IfMC- 20, find the output level that maximizes Total Profit: Due date: Thursday 1/31 at the time of class

Please show work!

Answer 1

1.

From the demand curve we can say that,

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

a) Px = a - bQx

By using graph data,

80 = a - b x 0

a=80

and similarly,

0 = a - 8b

a=8b

then,

80 = 8b

b = 10

The equation for demand curve is: px = 80 - 10Qx

b) px = 80 - 10Qx

10Qx = 80 - Px

Qx = 8 - 0.1Px

c) Here total revenue (TR) = (Px).(Qx)

TRx = Qx.(80 - 10Qx)

The equation for total revenue is:

TRx = 80Qx - 10Qx2

d) The marginal revenue (MR) = dTR/dQx

MR = d/dQx(80Qx - 10Qx2) = 80 - 20Qx.

This is the equation for marginal revenue.