ECON 1 Chapter Notes - Chapter 5: Average Variable Cost, Marginal Revenue, Marginal Cost

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In a competitive market, production is divided across firms in just such a way that total costs of production are minimized. Resources move across industries in just such a way that total value of production is maximized. In perfect competitive industry, firms don"t have much influence over the price of their product under the following conditions: The product being sold is similar across sellers. There are many buyers and sellers, each small relative to the total market. Total revenue is the price times quantity sold: tr = p * q. Total cost is the cost of producing a given quantity of output. Fixed costs are costs that do not vary with output. Variable costs are costs that do vary with output. Marginal revenue mr is the change in total revenue from selling an additional unit. For a firm in a competitive industry, mr = price. Marginal cost mc is the change in total cost from producing an additional unit.

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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

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.

upstairsatom

Suppose the inverse market demand function for a two-firm Cournot 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 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 q1 and q2.

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

3. Find the marginal revenue MR2 of firm 2 as a function of q1 and q2.

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 reaction functions to find q1 and q2.

6. What is the market price P.

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

upstairsatom

ECON 1 Chapter Notes - Chapter 5: Average Variable Cost, Marginal Revenue, Marginal Cost

ECON 1 Full Course Notes

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