Copy and paste the following data into Excel: P Q $52.50 1130 $50.75 1145 $49.80
ID: 1165021 • Letter: C
Question
Copy and paste the following data into Excel:
P
Q
$52.50
1130
$50.75
1145
$49.80
1165
$49.15
1170
$48.85
1210
e. Use your first demand function to determine an equation for TR and MR as a function of Q, and create a graph of P and MR on the vertical and Q on the horizontal axis.
f. What is the total-revenue maximizing price and quantity, and how much revenue is earned there? Compare that to the TR when P = $52.50 and P = $51.00.
****
c) At P= $49.80 e= .32314,
d) I would recomend to increase the price because in this case demand is inelastic.
P
Q
$52.50
1130
$50.75
1145
$49.80
1165
$49.15
1170
$48.85
1210
Explanation / Answer
Part e
Demand function => P = a - bQ
Total Revenue = PQ = (a-bQ) Q = aQ - b Q2 = TR
If P = 52.50 , Q = 1130
52.50 = a - 1130 b ...................... eq (1)
If P = 50.75 , Q = 1145
50.75 = a - 1145b ...................... eq (2)
From eq (1), we have
a = 52.50 + 1130 b ..................eq(3)
Substituting above value of a in eq(2)
50.75 = (52.50 + 1130 b) - 1145b
50.75 = 52.50 - 15 b
15 b = 52.50 - 50.75 = 1.75
b = 1.75 / 15
b = 0.116
Substituting value of b in eq (3)
a = 52.50 + 1130 (0.116) = 183.58
P = a - bQ = 183.58 - (0.116 ) Q
TR = PQ = 183.58Q - (0.116) Q2
MR = dTR/ dQ = 183.58 - (0.116) Q
Part f
MR = 0
183.58 - (0.116) Q = 0
Q = 183.58/0.116
Q = 1582.5862
P = a - bQ = 183.58 - (0.116 * 1582.5862) = 183.58 - 183.579 = 0.001