BENEDICTINE COLLEGE

Managerial Economics

Instructor: Shu Yan Fei

Assignment One

Student Name: Peng TangBin

October 9, 2009

The demand curve for product X is given as Q = 2000 – 20P.

a. How many units will be sold at $ 10 ?
b. At what price would 2,000 units be sold ? 0 units ? 1,500?
c. Write equations for total revenue and marginal revenue (in term of Q).
d. What will be the total revenue at a price of $70? What will be the marginal revenue ?
e. What is the point elasticity at price of $70 ?
f. If price were to decrease to $60, what would total revenue, marginal revenue and point elasticity be now?
g. At what price would elasticity be unitary?

a. when P = $10, Q = 2000 – 20p. Q = 2000 – 20*10 =2000 – 200 = 1,800

b. Q = 2000 – 20P 1. when Q = 2,000 , P= [pic][pic]= 100 – 0.05Q = 100 – 0.05*2,000 = 100 – 100 = 0 2. when Q= 0 , P= [pic][pic]= 100 – 0.05Q = 100 – 0.05*0 = 100

3. when Q = 1,500 , P= [pic][pic]= 100 – 0.05Q = 100 – 0.05*1,500 = 100 – 75 = 25

c. Q = 2000 – 20P P = [pic][pic]= 100 – 0.05Q TR = P*Q = ( 100 – 0.05Q )* Q = 100Q – 0.05Q[pic] MR = [pic] = 100 – 2*0.05*Q = 100 – 0.1Q Where TR = total revenue, MR = mariginal revenue Demand curve: P = a – bQ Total revenue: PQ = aQ - bQ[pic] Marginal revenue: MR = [pic] = a – 2bQ

d. when P = $70, Q = 2,000 – 20P = 2,000 – 20*70 =2,000 – 1,400 = 600 TR = 100Q – 0.05*Q[pic] = 100 *600– 0.05*600[pic]=60,000 – 18,000 = 42,000 MR = 100 – 0.1Q = 100 – 0.1*600 = 100 – 60 = 40

e. Ed=( △Qd/Qd)/( △P/P) = (△Qd/△P)*(P/Qd) Q = 2000 – 20P When P[pic] = $10, Qd[pic] =1,800 P[pic]= $70, Qd[pic] = 600 △ Qd =Qd[pic] -Qd[pic] = 1,800 – 600 = 1,200 △ P = P[pic] - P[pic] = 70 -10 = 60 Ed = [pic]* [pic] = [pic]*[pic] = 2.33

f. If P[pic] =$60, Q[pic] = 2000