1. Consider a competitive market for good Y in which there are 10 consumers, all with...
1. Consider a competitive market for good Y in which there are 10 consumers, all with the utility function over goods X and Y given by:
u (x,y) = αln(x) + β ln(y)
The price of good X is fixed at $1. Five of the consumers have an income of $200, and the remaining 5 have an income of $400.
Operating in the market for good Y are n firms, each with the cost function c(y) = 4y2.
- Derive the Marshallian demands for goods X and Y.
- Calculate the total supply and the total demand for good Y when its price is p.
- Calculate the short-run equilibrium price for good Y. Also compute the equilibrium profit for each firm.
- In the long run, firms can enter and exit this industry for good Y. Suppose the cost of entry into this industry is F. Calculate the long-run equilibrium price for good Y and the long-run number of firms in the industry.
Homework Answers
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1. Consider a competitive market for good
Y in which there are 10 consumers, all with...
2. Suppose there are two consumers in a country: consumer 1 and consumer 2. The two...
2. Suppose there are two consumers in a country: consumer 1 and consumer 2. The two consumers have the following Cobb-Douglas utility function defined over consumption of goods X and Y: where 0 < β < 1. Each consumer has a different income, consumer 1 has income 1, while consumer 2 has income 12. For now, we will treat the income of each consumer as given. Denote aggregate income as I 12. (a) (10 points) Derive each consumer's individual Marshallian...
4. Consider an economy with 2 consumption goods and N consumers, all with the same utility...
4. Consider an economy with 2 consumption goods and N consumers, all with the same utility function: u(x1, x2) = x ma, where and a € (0,1). The goods prices are pi = 2 and P2. Among the consumers, half of them each have income yi and the rest have income y2. There are m firms operating in the competitive market for good 2. Each firm has the cost function c(q) = Bg2. First, solve for the equilibrium price P2....
1. (25 points) The market for study desks is characterized by perfect competition. Firms and consumers are price takers and in the long run there is free entry and exit of firms in this industry. Al...
1. (25 points) The market for study desks is characterized by perfect competition. Firms and consumers are price takers and in the long run there is free entry and exit of firms in this industry. All firms are identical in terms of their technological capabilities. Thus the cost function as given below for a representative firm can be assumed to function faced by each firm in the industry. The total cost and marginal cost functions t the representative firm are...
Consider a perfectly competitive market for titanium. Assume that all firms in the industry are identical and...
Consider a perfectly competitive market for titanium. Assume that all firms in the industry are identical and have the marginal cost (MC), average total cost (ATC), and average variable cost (AVC) curves shown on the following graph. Assume also that it does not matter how many firms are in the industry Tool Tip: Place the mouse cursor over orange square points on the MC curve to see coordinates. COST PER UNIT IDollars per pound) 10 MC ATC AVC 0 5...
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function...
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function u(x,y)-x"y a. Derive an expression for the Marshallian Demand functions. b. Demonstrate that the income elasticity of demand for either good is unitary 1. Explain how this relates to the fact that individuals with Cobb-Douglas preferences will always spend constant fraction α of their income on good x. Derive the indirect utility function v(pxPod) by substituting the Marshallian demands into the utility function C....
¬8) Assume a perfectly competitive industry. In the short run suppose that the market price for the good is $10. You als...
¬8) Assume a perfectly competitive industry. In the short run suppose that the market price for the good is $10. You also know that the minimum point on the average variable cost curve occurs at $6 per unit while the minimum point on the average total cost curve occurs at $11 per unit. From this information you know that in the short run, firms in this industry ____ and in the long run, holding everything else constant, there will be...
Consider the competitive market for copper. Assume that, regardless of how many firms are in the...
Consider the competitive market for copper. Assume that, regardless of how many firms are in the industry, every firm in the industry is identical and faces the marginal cost (MC), average total cost (ATC), and average variable cost (AVC) curves shown on the following graph 80 72 64 56 48 ATC 40 32 24 AVC 16 МС П 8 0 0 4 8 12 16 20 24 28 32 36 QUANTITY (Thousands of pounds) COSTS (Dollars per pound) 40 The...
1. (20p) Suppose that, in a perfectly competitive industry, the technology for making the product (by...
1. (20p) Suppose that, in a perfectly competitive industry, the technology for making the product (by any single firm) has the total cost function c(q) = 200 + 4q+ Barriers to entry and exit the market are low and an unlimited number of firms could enter this industry, all with the same total cost function. (a) Compute the long-run equilibrium price in this industry, as well as the amount of output each firm would produce at this price. Explain the...
Part 1. 1. Use the figure above to answer this question. Consider a perfectly competitive market experiencing good time...
Part 1.
1. Use the figure above to answer this question.
Consider a perfectly competitive market experiencing good times.
Figure ________ shows a firm maximizing profit in the LONG RUN
because it produces ________ units and makes an economic profit of
________.
A) A; 100; $2 per unit
B) A; 90; $3 per unit
C) B; 100; $0 per unit
D) C; 100; $3 per unit
Part 2.
2. The figure above shows a firm's demand and marginal
revenue curves...
4. Consider an economy with 24 firms in the short run. The market demand function is...
4. Consider an economy with 24 firms in the short run. The market demand function is given by p= 50 – 2Q. A firm's cost function is C(q) = 3+q?. (a) [10 pts) Derive the equilibrium price in the short run. ts] Firms face a cost of 6 to enter this industry. Calculate the equilibrium price and number of firms in the long run.
2. Suppose there are two consumers in a country: consumer 1 and consumer 2. The two consumers have the following Cobb-Douglas utility function defined over consumption of goods X and Y: where 0 < β < 1. Each consumer has a different income, consumer 1 has income 1, while consumer 2 has income 12. For now, we will treat the income of each consumer as given. Denote aggregate income as I 12. (a) (10 points) Derive each consumer's individual Marshallian...
4. Consider an economy with 2 consumption goods and N consumers, all with the same utility function: u(x1, x2) = x ma, where and a € (0,1). The goods prices are pi = 2 and P2. Among the consumers, half of them each have income yi and the rest have income y2. There are m firms operating in the competitive market for good 2. Each firm has the cost function c(q) = Bg2. First, solve for the equilibrium price P2....
1. (25 points) The market for study desks is characterized by perfect competition. Firms and consumers are price takers and in the long run there is free entry and exit of firms in this industry. All firms are identical in terms of their technological capabilities. Thus the cost function as given below for a representative firm can be assumed to function faced by each firm in the industry. The total cost and marginal cost functions t the representative firm are...
Consider a perfectly competitive market for titanium. Assume that all firms in the industry are identical and have the marginal cost (MC), average total cost (ATC), and average variable cost (AVC) curves shown on the following graph. Assume also that it does not matter how many firms are in the industry Tool Tip: Place the mouse cursor over orange square points on the MC curve to see coordinates. COST PER UNIT IDollars per pound) 10 MC ATC AVC 0 5...
Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function u(x,y)-x"y a. Derive an expression for the Marshallian Demand functions. b. Demonstrate that the income elasticity of demand for either good is unitary 1. Explain how this relates to the fact that individuals with Cobb-Douglas preferences will always spend constant fraction α of their income on good x. Derive the indirect utility function v(pxPod) by substituting the Marshallian demands into the utility function C....
Consider the competitive market for copper. Assume that, regardless of how many firms are in the industry, every firm in the industry is identical and faces the marginal cost (MC), average total cost (ATC), and average variable cost (AVC) curves shown on the following graph 80 72 64 56 48 ATC 40 32 24 AVC 16 МС П 8 0 0 4 8 12 16 20 24 28 32 36 QUANTITY (Thousands of pounds) COSTS (Dollars per pound) 40 The...
1. (20p) Suppose that, in a perfectly competitive industry, the technology for making the product (by any single firm) has the total cost function c(q) = 200 + 4q+ Barriers to entry and exit the market are low and an unlimited number of firms could enter this industry, all with the same total cost function. (a) Compute the long-run equilibrium price in this industry, as well as the amount of output each firm would produce at this price. Explain the...
Part 1.
1. Use the figure above to answer this question.
Consider a perfectly competitive market experiencing good times.
Figure ________ shows a firm maximizing profit in the LONG RUN
because it produces ________ units and makes an economic profit of
________.
A) A; 100; $2 per unit
B) A; 90; $3 per unit
C) B; 100; $0 per unit
D) C; 100; $3 per unit
Part 2.
2. The figure above shows a firm's demand and marginal
revenue curves...
4. Consider an economy with 24 firms in the short run. The market demand function is given by p= 50 – 2Q. A firm's cost function is C(q) = 3+q?. (a) [10 pts) Derive the equilibrium price in the short run. ts] Firms face a cost of 6 to enter this industry. Calculate the equilibrium price and number of firms in the long run.
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