EC2100: The table below represents the production function for a small catering company specializing in barbecued pork: Applied Microeconomics for Business Assignment, NUI, Ireland
University | National University of Ireland (NUI) |
Subject | EC2100 Applied Microeconomics for Business |
1. The table below represents the production function for a small catering company specializing in barbecued pork. The numbers in each cell represent the number of customers that can be served with various combinations of labor and capital.
a. Suppose that the company employs 5 units of capital and 3 workers. What is the marginal product of an additional worker?
b. Suppose the level of capital is fixed at 5 units. Does this production function satisfy the principle of diminishing marginal returns at this level of output? Explain your answer carefully.
c. Suppose the company employs 5 units of capital and 3 workers and is considering buying another unit of capital or hiring another worker. A unit of capital costs €8 while the additional worker costs €7. Should the company hire the extra worker or buy a unit of capital? Explain your answer carefully.
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2. Suppose that a firm’s production function is q =LK.
a. Show that the Marginal Rate of Technical Substitution for this firm is equal to K/L. Hint: use the note on differentiation.
b. Suppose that a unit of labor costs €1 while a unit of capital costs €9. Find the cost minimizing level of labor and capital if the firm wants to produce 144 units of output. What is the total and average cost to the firm of producing 144 units of output?
c. Suppose that the price of capital and price of labor remain as they were originally (€9 and €1) but the firm wants to produce 225 units instead of 144. Find the cost minimizing level of labor and capital. What is the total and average cost to the firm of 225 units?
d. What kind of returns to scale – increasing, constant or decreasing – does this production function exhibit? Explain clearly.
e. Compare the average cost of producing 144 units and the average cost of producing 225 units. Relate this comparison to the kind of returns to scale that the production function exhibits.
3. The market demand and supply functions for a good are as follows:
QD = 100 – 2P and QS = 10 + 3P
The equilibrium quantity and price are 64 and €18 respectively.
a. Calculate the point elasticity of demand and supply at the equilibrium price and quantity.
b. Suppose the government imposes a tax of €5 per unit. Calculate the new equilibrium price and quantity.
c. What percentage of the tax is paid for by consumers?
d. How, if at all, does your answer in part c relate to your answers in part a?
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4. Suppose that the inverse demand for a product is represented by the
equation P = 120 – 10Q, where P is the price in Euros and Q is the annual output. Suppose that only one firm produces this product and that the marginal and average cost is €20.
a. What is the monopolist’s profit maximizing price and output assuming that it has to charge a single price to each consumer?
b. Why is marginal revenue less than price for a monopolist? Verify that marginal revenue is less than price at the profit maximizing price that you found in part (a)
c. Suppose that the firm learns that there is a pricing scheme called a two-part tariff. Calculate the optimal two-part tariff for this firm.
d. Why is deadweight loss lower under a two-part tariff than the situation where the firm must charge the same single price to every customer as in part a of this question?
e. Suppose that the monopolist learns that there is a second group of people who are also interested in buying its product. The inverse demand for the second group is given by P = 60 – 2Q. Suppose that the firm can separate the two groups of consumers perfectly but that it cannot use a two-part tariff. Calculate the optimal prices it should charge to each group of customers.
f. A profit maximizing monopolist that is able to practice price discrimination between 2 groups should set prices according to the following formula: (P1/P2) = (1 + 1/E2)/(1 + 1/E1) where E2 and E1 refer to the elasticity of demand in the second and first market respectively. Verify that your answers in part (a) and part (e) satisfy this formula (You need to calculate the elasticity in each market to do this. Hint: you need to rewrite the inverse demand equations as demand equations.)
5. A good can be produced at a constant average (and marginal) cost of AC = MC = €5. The market demand curve given by Q = 53 – P.
a. Suppose there are two firms in the market. Let Q1 be the output of the first firm and Q2 be the output of the second. Suppose (as in the Cournot model) that each firm chooses its profit-maximizing level of output on the assumption that its competitor’s output is fixed. What is a reaction function in this model?. Calculate the Cornet equilibrium (the values of Q1 and Q2 for which each firm is doing as well as it can, given its competitor’s output). What are the resulting market price and profits of each firm?
b. Suppose in part (a) of this question that the two firms decided to form a cartel and divide the market equally between them. How many units of output would each firm produce? What are the resulting market price and profits of each firm?
c. In practice what factors inhibit the formation and maintenance of cartels?
6. Some concepts in behavioral economics such as framing and self-control problems cast doubt on how rational people are in practice.
Explain clearly what each of these concepts means. Give an example from either an experiment or the real world of each concept. Discuss how the concepts of framing and self-control might have a role to play in the design and introduction of policies to increase savings in a country.
7. Suppose the iPad made by Apple is the only tablet on the market and Amazon are considering entering the market for tablets with their own product. If Amazon does not enter the market Apple will earn profits of €2 billion. If Amazon does enter the market, Apple faces a choice of cutting its prices or not. If Apple cuts its prices its profits will fall to €0.8 billion and Amazon will lose €0.5 billion. If Apple does not cut its prices, it will earn profits of €1 billion while Amazon will earn profits of €0.5 billion.
a. Set up the extensive form (decision tree) of this game.
b. Apple hears that Amazon is considering entering the market and announces that it will cut its prices. Should Amazon enter this market? Explain your reasoning carefully.
c. Generally speaking, what does the concept of a credible threat refer to?
d. Why might Apple do something to reduce its profits as a monopolist from €2billion to €1.2 billion? Give an example of how it might reduce its profits.
8. Two firms, A and B, are situated next to a lake, and it costs each firm
€1,500 per period to use filters that avoid polluting the lake. However, each firm must use the lake’s water in production, so it is also costly to have a polluted lake. The cost to each firm of dealing with water from a polluted lake is €1,000 times the number of polluting firms. Assume that the firms do not communicate with each other. Each form is facing a choice of either buying a filter or not.
a. Write out this situation in normal form (i.e. matrix form).
b. Does either firm have a dominant strategy? Explain your answer carefully.
c. What is the Nash equilibrium of this game if it is played once?
d. Is this game an example of a Prisoner’s Dilemma game? Explain your answer
carefully.
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