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Question 2. (a) Suppose there is a firm producing two goods. The profit function π is...
Question 2 (60 points) Consider two following Cournot competition between two firms, Firm 1 and Firm...
Question 2 (60 points) Consider two following Cournot competition between two firms, Firm 1 and Firm 2. The firms face an inverse demand function P = 600-Q where Q = 91 + 92 is the total output. Each unit produced costs c-$60. Therefore the profit of each farmer is given by π1 (J1.qz) = (600-91-J2)a1-6091 712 (41,42) (600 q1 q2)42-6092 Each firm. i simultaneusly chooses own qi to maximize own profits πί. a) (15 points) Find the Cournot NE quantities...
3. A firm produces two goods in pure competition and has the following total revenue and total cost function. TR(X1,X2) = 18x1 + 15x2 (a) Maximize profits for the firm, using matrix inversion to...
3. A firm produces two goods in pure competition and has the following total revenue and total cost function. TR(X1,X2) = 18x1 + 15x2 (a) Maximize profits for the firm, using matrix inversion to solve the first-order conditions. 13) Answer: 3 (. Refar to the fim in Question 3(0) use the Hessian to check the second conditions for profit maximization. 13] Answer:
3. A firm produces two goods in pure competition and has the following total revenue and total cost...
6. The profit function of a firm is (x,y) = px +qy-ar? - By?, where p...
6. The profit function of a firm is (x,y) = px +qy-ar? - By?, where p and q are the prices per unit and ar? + By are the costs of producing and selling x units of the first good and y units of the other. The constants are all positive. (a) Find the values of x and y that maximize profits. Denote them by x* and y'. Verify that the second-order conditions are satisfied. (1) Define (p, q) =...
Suppose two firms (Firm 1 and Firm 2) are producing a product. The total demand is:...
Suppose two firms (Firm 1 and Firm 2) are producing a product. The total demand is: Q = 110 –10P, where Q = Q1 + Q2. Each of the two firms has the cost function TC = 5Q. Based on the information given, calculate the equilibrium P, Q, Q1, Q2, Profit1 and Profit2 under monopoly (collusion), Cournot, and Stackelberg. For the Stackelberg model, assume that Firm 1 is the leader and Firm 2 is the follower. Show all your workings...
A firm is selling two goods, A and B, with a total profit function: TP=-16 +...
A firm is selling two goods, A and B, with a total profit function: TP=-16 + 598.8A- 0.3A^2 + 498.5B - 0.2B^2 -0.2AB Find the values of A and B that will maximise profit. Prove that profit is a maximum.
In order to maximize profit, a firm producing two goods that are related in consumption should...
In order to maximize profit, a firm producing two goods that are related in consumption should choose the levels of output at which a. total marginal revenue equals total marginal cost. b. total marginal revenue equals the marginal cost of each good. c. the marginal revenue of each good equals total marginal cost. d. marginal revenue equals marginal cost for each good simultaneously.
Question 2: A monopolistic firm produces goods in a market where the demand function is P...
Question 2: A monopolistic firm produces goods in a market where the demand function is P = 43 - 0.3Q and the corresponding total cost function is TC =0.0103 – 0.4Q2 +3Q (a) What can you say about the fixed costs of this firm? (b What can you say about the variable costs of this firm? (c) Find the (non-zero) output for which average cost is equal to marginal cost, and explain the significance of this value. (d Find the...
Suppose that the profit of a car producing firm is given by: ? = ?? −...
Suppose that the profit of a car producing firm is given by: ? = ?? − ?(?) And that the cost function is given by: ?(?) = 4? where ? is profits, ? is the price and ? is quantity produced. By setting profits equal to a constant level, ?, derive an expression for the isoprofit curve of this firm which expresses ? as a function of ? (for a given level of profits, ?). c) Let the demand curve...
Exercise 11.3 Consider the following duopoly model. There are two firms sup- plying a market where...
Exercise 11.3 Consider the following duopoly model. There are two firms sup- plying a market where demand is given by p(Q)- a-bQ. Firm i produces qi units of output and so the total level of production is q1q2. Both firms face the same constant marginal cost, so the cost of producing qi for firm i įs cqỉ. Thus the profit functions of firms 1 and 2 respectively, are given by: (a) Suppose that each firm takes the output of the...
5. Suppose a firm offers two software products: Wordy -- a document creator, and Excello, a...
5. Suppose a firm offers two software products: Wordy -- a document creator, and Excello, a spreadsheet app. They know there are two types of consumers overall, English types and Quant types, each with a different valuation (demand) for each product. Use the following table to answer questions below. Assume the cost of producing Wordy is a constant MC = $100, the cost of producing Excello is a constant MC = $150 and that each consumer will purchase each good...
Question 2 (60 points) Consider two following Cournot competition between two firms, Firm 1 and Firm 2. The firms face an inverse demand function P = 600-Q where Q = 91 + 92 is the total output. Each unit produced costs c-$60. Therefore the profit of each farmer is given by π1 (J1.qz) = (600-91-J2)a1-6091 712 (41,42) (600 q1 q2)42-6092 Each firm. i simultaneusly chooses own qi to maximize own profits πί. a) (15 points) Find the Cournot NE quantities...
3. A firm produces two goods in pure competition and has the following total revenue and total cost function. TR(X1,X2) = 18x1 + 15x2 (a) Maximize profits for the firm, using matrix inversion to solve the first-order conditions. 13) Answer: 3 (. Refar to the fim in Question 3(0) use the Hessian to check the second conditions for profit maximization. 13] Answer:
3. A firm produces two goods in pure competition and has the following total revenue and total cost...
6. The profit function of a firm is (x,y) = px +qy-ar? - By?, where p and q are the prices per unit and ar? + By are the costs of producing and selling x units of the first good and y units of the other. The constants are all positive. (a) Find the values of x and y that maximize profits. Denote them by x* and y'. Verify that the second-order conditions are satisfied. (1) Define (p, q) =...
Question 2: A monopolistic firm produces goods in a market where the demand function is P = 43 - 0.3Q and the corresponding total cost function is TC =0.0103 – 0.4Q2 +3Q (a) What can you say about the fixed costs of this firm? (b What can you say about the variable costs of this firm? (c) Find the (non-zero) output for which average cost is equal to marginal cost, and explain the significance of this value. (d Find the...
Exercise 11.3 Consider the following duopoly model. There are two firms sup- plying a market where demand is given by p(Q)- a-bQ. Firm i produces qi units of output and so the total level of production is q1q2. Both firms face the same constant marginal cost, so the cost of producing qi for firm i įs cqỉ. Thus the profit functions of firms 1 and 2 respectively, are given by: (a) Suppose that each firm takes the output of the...
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