Economics Assignment: Market Demand and Total Cost Function

This economics assignment deals with market demand function and total cost function of firm 's' and firm 't'. It includes profit maximization condition, reaction function and optimal output for both firms.

Running head: ECONOMICS ASSIGNMENT
Economics Assignment
Name of the Student
Name of the University
Course ID

1ECONOMICS ASSIGNMENT
Given market demand function
P=2000−2 QS −3Qt
The respective total cost function of firm ‘s’ and firm ‘t’ are given as
TCS=10000+ 4 QS + 0.45QS
2
TC t=60,000+ 2Qt + 0.25Qt
2
For firm s,
Total revenue is given as
TRS=QS × P
¿ QS × ( 2000−2 QS −3 Qt )
¿ 2000 QS −2QS
2 −3 Qt QS
From the total revenue, marginal revenue for firm s is obtained as
MRs= d ( TRs )
d Qs
¿ ∂ ¿ ¿
¿ 2000−4 Qs−3 Qt
From the given total cost function, the marginal cost for firm s is obtained as
MCs =d ( TCs )
d Qs

2ECONOMICS ASSIGNMENT
¿ ∂(10000+4 QS +0.45 QS
2 )
∂ Qs
¿ 4 +0.90 Qs
Profit maximization condition of firm s requires,
MRs=MCs
¿ , 2000−4 Qs −3 Qt=4+ 0.90Qs
¿ , 2000−4 Qs −3 Qt−4−0.90 Qs=0
¿ , 1996−4.90 Qs−3 Qt =0
¿ , 4.90 Qs =1996−3 Qt
¿ , Qs= 1996−3 Qt
4.90
¿ , Qs=407.35−0.61Qt
The reaction function of firm s thus is given as
Qs =407.35−0.61Qt
Qs =407.35−0.61Qt ………………………………………………………………..(i)

3ECONOMICS ASSIGNMENT
For firm t,
Total revenue is given as
TRt =Qt × P
¿ Qt × ( 2000−2 QS −3Qt )
¿ 2000 Qt −2Qt QS−3 Qt
2
From the total revenue, marginal revenue for firm t is obtained as
MRt= d ( TRt )
d Qt
¿ ∂(2000 Qt −2Qt QS−3 Qt
2 )
∂ Qt

4ECONOMICS ASSIGNMENT
¿ 2000−2Qs−6 Qt
From the given total cost function, the marginal cost for firm t is obtained as
MCt = d ( TCt )
d Qt
¿ ∂(60,000+2 Qt +0.25 Qt
2 )
∂Qt
¿ 2+0.50 Qt
Profit maximization condition of firm t requires,
MRt=MCt
¿ , 2000−2 Qs −6 Qt =2+ 0.50 Qt
¿ , 2000−2 Qs −6 Qt −2−0.50 Qt =0
¿ , 1998−2 Qs −6.50 Qt=0
¿ , 6.50 Qt=1998−2 Qs
¿ , Qt =1998−2Qs
6.50
¿ , Qt =307.38−0.31 Qs
The reaction function of firm t thus is given as
Qt =307.38−0.31Qs…………………………………………………………………………(ii)

5ECONOMICS ASSIGNMENT
Putting the value of Qt in equation (i), optimal output for firm s is obtained as
Qs =407.35−0.61Qt
¿ , Qs=407.35−0.61 ( 307.38−0.31 Qs )
¿ , Qs=407.35−187.50+0.19 Qs
¿ , Qs−0.19Qs=219.85
¿ , 0.81 Qs=219.85
¿ , Qs= 219.85
0.81
¿ , Qs=271.12
Using the value of Qs, the optimal output for firm t is obtained as

6ECONOMICS ASSIGNMENT
Qt =307.38−0.31Qs
¿ 307.38− ( 0.31× 271.12 )
¿ 307.38−84.05
¿ 223.33
After obtaining the profit maximizing output for firm s and firm t, the profit-maximizing price is
obtained as
P=2000−2 QS −3Qt
¿ 2000− ( 2× 271.12 ) − ( 3 ×223.33 )
¿ 2000−542.24−670
¿ 787.76

7ECONOMICS ASSIGNMENT