ECON 2300 Lecture Notes - Lecture 10: Demand Curve, Marginal Cost, Inverse Demand Function

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amaranthhamster412

9 Jan 2017

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Suppose that the inverse demand curve is d(p) = a bp. The follower has a cost function c2(y2) = y2 2/2, and the leader has a cost function c1(y1) = cy1. For any price p the follower wants to operate where price equals marginal cost. If the cost function is c2(y2) = y2 2/2, it can be shown that the marginal cost curve is. Setting price equal to marginal cost gives us p = y2. Solving for the follower"s supply curve gives y2 = s(p) = p. The demand curve facing the leader the residual demand curve is. R(p) = d(p) s(p) = a bp p = a (b + 1)p. From now on this is just like an ordinary monopoly problem. Solving for p as a function of the leader"s output y1, we have p = a b + 1 1 b + 1y1. This is the inverse demand function facing the leader.

Related Questions

Now, suppose the inverse market demand function for a two-firm Stackelberg model is given by P=49-Q where Q=q1+q2 is the total output produced in the market, P is the market price, q1 is the quantity of output produced by firm 1, q2 is the quantity of output produced by firm 2. The firm is the leader and firm 2 is a follower. The marginal costs of the two firms are MC1=2 and MC2=3.

1. What is the follower’s reaction function?

2. Determine the equilibrium output level for both the leader and the follower.

3. Determine the equilibrium market price.

4. Determine the profits of the leader and the follower assuming there are no fixed costs.

upstairsatom

Now, suppose the inverse market demand function for a two-firm Stackelberg model is given by P=49-Q where Q=q1+q2 is the total output produced in the market, P is the market price, q1 is the quantity of output produced by firm 1, q2 is the quantity of output produced by firm 2. Firm 1 is the leader and firm 2 is the follower. The marginal costs of the two firms are MC1=2 and MC2=3.

1. What is the follower’s reaction function?

2. Determine the equilibrium output level for both the leader and the follower.

3. Determine the equilibrium market price.

4. Determine the profits of the leader and the follower assuming there are no fixed costs.

upstairsatom

I just need part 3 for this problem!! Thank you!!

Part 1 Suppose the inverse market demand function for a two-firm Cournot model is given by P=49-Q where Q=q_1+q_2 is the total output produced in the market, P is the market price, q_1 is the quantity of output produced by firm 1, q_2 is the quantity of output produced by firm 2. The marginal costs of the two firms are MC1=2 and MC2=3. For a linear inverse demand function P=a+bq, the marginal revenue is given by MR=a+2bq.

1. Find the marginal revenue MR1 of firm 1 as a function of q_1 and q_2.

2. Setting MR1=MC1, determine the reaction function of firm 1.

3. Find the marginal revenue MR2 of firm 2 as a function of q_1 and q_2.

4. Setting MR2=MC2, determine the reaction function of firm 2.

5. What quantity of output will each firm produce? That is, use the two reactions functions to find q_1 and q_2.

6. What is the market price P.

7. Determine the profits of each firm assuming there are no fixed costs.

Part 2 Now, suppose the inverse market demand function for a two-firm Stackelberg model is given by P=49-Q where Q=q_1+q_2 is the total output produced in the market, P is the market price, q_1 is the quantity of output produced by firm 1, q_2 is the quantity of output produced by firm 2. Firm is leader and firm 2 is follower. The marginal costs of the two firms are MC1=2 and MC2=3.

1. What is the follower’s reaction function?

2. Determine the equilibrium output level for both the leader and the follower.

3. Determine the equilibrium market price.

4. Determine the profits of the leader and the follower assuming there are no fixed costs.

Part 3 Use information from parts 1 & 2 to compare the output levels and profits in settings characterized by Cournot and Stackelberg.

upstairsatom

ECON 2300 Lecture Notes - Lecture 10: Demand Curve, Marginal Cost, Inverse Demand Function

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