Question

Question 2: Working with Marginal Benefits and Costs Suppose the total benefit derived from a continuous decisions, Q, ís B(Q) = 200-202 and the total cost from deciding Q is C(O) 4+2Q. The marginal benefit (MB) and marginal cost (MC) is the first order derivative of these functions. MBO) 20-4 and MC(O) 4+40 (1) (4 points, 2 each) What is the total benefit when Q-2? Q-10? (2) (4 points, 2 each) What is the marginal benefit when Q-2? Q-10? (3) (4 points) What level of Q maximizes total benefit? (hint: recall our first order condition for maximization. The first derivative is given as the MB function). 4) (4 points, 2 each) What is total cost when Q-2? Q-10? (5) (4 points, 2 each) What is marginal cost when Q-2? Q-10? (6) (4 points) What level of Q minimizes total cost? (7) (6 points) What level of Q maximizes net benefit - that is Total Benefit- Total Cost?

Answer 1

Totally benefit = B(Q) = 20Q -2 Q^2 ,total cost = C(Q) = 4Q + 2Q^2 ( in question Total cost is given as 4+2Q^2 but taken into consideration what marginal cost is given the actual total cost is = 4Q+2Q^2)

1. With Q = 2

Total benefit = 20×2- 2×2×2

= 40-8= 32

With Q = 10

Total benefit = 20×10-2×10×10

= 200-200 = 0

2. Marginal benefit = 20-4Q

With Q = 2

Marginal benefit = 20-4×2

= 20-8= 12

With Q= 10

Marginal benefit = 20-4×10

20-40= -20

3. Level of Q that maximises total benefit is when marginal benefit = marginal cost

i.e 20-4Q = 4+4Q

20-4= 8Q

8Q= 16

Q= 2

Output level Q= 2 maximises total benefit.

4.Total cost = 4Q+2Q^2

With Q =2

Total cost = 4×2+2×2×2

=8+8=16

With Q=10

Total cost = 4×10+2×10×10

= 40+200=240

5. Marginal cost = 4+4Q

With Q = 2

Marginal cost = 4+4×2

= 4+8=12

With Q= 10

Marginal cost = 4+4×10

= 4+40=44

7.Total benefit - Total cost

= 20Q-2Q^2- (4Q+2Q^2)

= 16Q- 4Q^2

For maximisation of this benefit we take first order derivative

= 16-8Q

Putting it equal to 0

8Q= 16

Q =2

Taking second order derivative we get = -8

So this is the point of Maxima

=> Output level Q = 2 maximises total benefit - Total cost