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Perform the hypothesis of the following scenarios.
The graduate record exam is standardized test recquired to be admitted to many graduate schools in the United States. A high score in GRE makes admissions more likely. According th the educational testing service, the mean score for takers of GRE who do not have training courses is 555 with standard deviation of 139. Brain Philippine offers expensive GRE training courses, claiming their graduates score better than those who have not talen any training courses. To test the company's claim, a statisticiam randomly selected 30 graduates of BP and asked their GRE scores. They recorded a mean score of 560 in GRE. Is the company's claim true, using a 95% confidence level?
A locomotive producer’s demand function is P1 = 18 – 0.6Q for price increases and
P2 = 20 - 0.8Q for price decreases. The marginal cost is constant and equal to 5.
a. What price is the firm now charging and how much output is being produced?
b. If marginal cost increase to 6, how much would the firm produce?
c. If marginal cost decreases to 3, how much would the firm produce?
EnviroWest can produce recycle paper at a constant marginal cost of $1.5 per pound. Currently, the firm is selling 500,000 pounds each year at $2.00 per pound. This is the price charged by all other firms in the industry. Managers of EnviroWest are considering increasing the price to $2.5 per pound. Demand elasticity is constant and equals –0.6 if the price increase is matched by competitors and –4.0 if it is not matched. Management believes there is a 60 percent chance that other firms will follow EnviroWest's lead and increase their prices.
a/ If managers are risk neutral, should the proposed price change be implemented? Explain
b/ Write equation for the expected profit as a function of the probability that the price increase will be matched by the other firms.
Unique Motor Inc. manufactures motorcycles that are sold in a monopolistically competitive market. The firm’s demand curve is
P = 5,000 – 2Q
Where P is price and Q is quantity and the average cost (AC) function is
AC = 6,000 – 4Q + 0.001Q2
All firms in the industry have the same demand and average cost functions. If the entry or exit of firms in the industry results in the demand curve shifting in a parallel manner, what is the long-run equilibrium price and quantity produced for Unique( and, of course, for each of the other firms in the industry)?
The market demand and supply functions for an electronic typewriter are
QD = 20,000 – 10P
QS = 10,000 + 20P
Western Electronics Inc. is one of many firms in this perfectly competitive industry. Its marginal and average cost functions are
MC = 10 + 2Q
AC = (1,000/Q) + 10 + Q
a/ What is the profit-maximizing output rate for Western?
b/ How much economic profit will be earned at that rate of output?
- Suggest a way how to use the parallelogram method to add more than two vectors.
- Is it possible to add two vectors having different magnitudes and yield zero resultant? Support your answer. How about instead of only two vectors, we have three vectors to be added? Support your answer.
- A given vector has at least one of its components not equal to zero. Is it possible for this vector to have zero resultant? Support your answer.
Midland Power and Light is the only seller of electricity in the area. The demand function facing the firm is Q = 250 – 0.5P
Where Q is quantity demanded and P is price. The firm total cost function is
TC = 100 – 10Q + 0.5Q, and the marginal cost is MC = -10 + Q
a/ Determine the profit-maximizing price and output rate for Midland.
b/ Determine the cost per unit, profit per unit, and total profit.
Find each of the following percentile points under the normal curve.
1. P99
2. P90
3. P68
4. P40
5. P32
The first principle of economics discussed in Chapter 1 of Mankiws book is that people face trade-offs. Use a production possibilities frontier to illustrate societys trade-off between two goodsa clean environment and the quantity of industrial output. What do you suppose determines the shape and position of the frontier? Show what happens to the frontier if engineers develop a new way of producing electricity that emits fewer pollutants.
Imagine a society that produces military goods and consumer goods, which well call guns and butter. a. Draw a production possibilities frontier for guns and butter. Using the concept of opportunity cost, explain why it most likely has a bowed-out shape. b. Show a point that is impossible for the economy to achieve. Show a point that is feasible but inefficient. c. Imagine that the society has two political parties, called the Hawks (who want a strong military) and the Doves (who want a smaller military). Show a point on your production possibilities frontier that the Hawks might choose and a point that the Doves might choose. d. Imagine that an aggressive neighboring country reduces the size of its military. As a result, both the Hawks and the Doves reduce their desired production of guns by the same amount. Which party would get the bigger peace dividend, measured by the increase in butter production? Explain
