Homework Assignment

Homework Assignment

Profit Maximization Estimation

a. Derive the profit function for the profit function.

TR = 24Q - 1.5Q2

TC = 9 + 4Q + 0.5Q2

P = TR - TC = 24Q - 1.5Q2 - 9 - 4Q - 0.5Q2

P = TR - TC = 20Q - 2Q2 - 9

Profit Function: P (Q) = 20Q - 2Q2 - 9

b. Find profit maximizing output level and Profit Amount

Output

Total Revenue

Total Cost

Profit

0

0

9

-9

1

22.5

13.5

9

2

42

19

23

3

58.5

25.5

33

4

72

33

39

5

82.5

41.5

41

6

90

51

39

7

94.5

61.5

33

8

96

73

23

9

94.5

85.5

9

10

90

99

-9

Output Level = 5 Units & Profit amount = $ 41

2. Elasticity Estimation using the Mid-Point Formula

Using,

We have,

= (3.5 + 4.42)/(222+152) x (-0.315/0.263)

= -2.497/98.31

= -0.0254

3. Demand Estimation

Q = a1P + a2Px + ...