Suppose that the market demand curve for bean sprouts is given by P = 1,660 - 4Q, where P is the price and Q is total industry output. Suppose that the industry has two firms, a Stackleberg leader and a follower. Each firm has a constant marginal cost of $60 per unit of output. In equilibrium, total output by the two firms will be:.a. 200. b. 400. c. 50. d. 100. e. 300.

In equilibrium, total output by the two firms will be option e= 300.  

Q = +

Q = 100 + 200

Q = 300

Explanation:

Data Given:

Market Demand Curve = P = 1660-4Q

where, P = price and Q = total industry output

Each firm's marginal cost = $60 per unit of output

So, we know that Q =   +

where being the individual firm output.

Solution:

P = 1660-4Q

P = 1660- 4( + )

P = 1660 - 4 - 4

Including the marginal cost of firm 1 and multiplying the whole equation by

Let's suppose new equation is X

X =  1660 - 4 - 4 - 60

Taking the derivative w.r.t to , we will get:

= 1660 - 8 - 4 - 60 = 0

Making rearrangements into the equation:

8 + = 1660 - 60

8 + = 1600

Dividing the whole equation by 4

2 + = 400

Solving for

2 = 400 -

= 200 - 0.5  

Including the marginal cost of firm 1 and multiplying the whole equation by

P = 1660 - 4 - 4

Let's suppose new equation is Y

Y =  1660 - 4 -4 - 60

Pugging in the value of

Y =  1660 - 4(200 - 0.5 ) -4 - 60

Y =  1660 - 800 +2 -4 - 60

Y =  1600 - 800 -2

Taking the derivative w.r.t

= 1600 - 800 - 4 = 0

Solving for

4 = 800

= 200

= 200 - 0.5

Plugging in the value of to get the value of

= 200 - 0.5 (200)

= 200 - 100

= 100

Q = +

Q = 100 + 200

Q = 300

Hence, in equilibrium, total output by the two firms will be option

e= 300.