The type of economic theory we cover in this course originates from the neoclassical school of thought. The origins of this school stem from the work of Alfred Marshall (1842- 1924). Marshall's work set in motion the marginalist revolution in economic thought, and hence the neoclassical school is occasionally referred to as the marginalist school. Explain in your own words the concept of marginal (in the mathematical sense) and how it relates to the economic concepts we've been studying. Why is the concept of marginal so important in the theory of the consumer? (Hint: ∂U ∂X , ∂U ∂Y ).

(High school busing problem) The Arden County, Maryland, superintendent of education is responsible for assigning students to the three high schools in his county. He recognizes the need to bus a certain number of students, for several sectors of the county are beyond walking distance to a school. The superintendent               partitions the county into three geographic sectors as he attempts to establish a plan that will minimize the total         number of student miles traveled by bus. He also recognizes that if a student happens to live in a certain sector             and is assigned to the high school in that sector, there is no need to bus that student because he or she can walk               to school. The three schools are located in sectors B, C, and D.

              The following table reflects the number of high-school-age students living in each sector and the distance in               miles from each sector to each school:

              Each high school has a capacity of 500 students. Please define variables and set up the objective function and constraints of this problem using Linear Programming (LP) so that the total number of student miles traveled by bus is minimized. (5 points)

A clinical trial tests a method designed to increase the probability of conceiving a girl. In the​ study, 357 babies were​ born, and 201 of them were girls. Use the sample data with a 0.01 significance level to test the claim that with this​ method, the probability of a baby being a girl is greater than 0.5. Use this information to answer the following questions.

a. List the null and alternative hypothesis.

b. P-value =

c. What is the conclusion?

d. Does the method appear to be effective?

Assume that we want to construct a confidence interval. Do one of the​ following, as​ appropriate: (a) find the critical value t alpha/ 2​, ​(b) find the critical value z Subscript alpha/02​, or​ (c) state that neither the normal distribution nor the t distribution applies. Here are summary statistics for randomly selected weights of newborn​ girls: n=291​, x over b+31.3 ​hg, s=7.6 hg. The confidence level is 90​%.

Gelmite & Sons Hardware is considering introducing a cash discount policy to its customers so as to

improve current sales. There are three possible scenarios that include monthly estimates. Gelmite

& Sons uses a 60% mark up on cost on all their products as a general rule. Fixed costs are R8 000

per month.

Scenario A: Representing the Current Scenario

Company sold 600 units of the spark nail which they ordered at a wholesaler in Shoppers Town for

a cost price of R100 each.

Scenario B: Representing initial sales target

Company will sell 800 units of the spark nail which they ordered at a wholesaler in Shoppers Town

for a cost price of R100 each.

These sales units are achieved after the introduction of a 20% markdown on the original selling

price.

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Scenario C: Representing a scenario where sales targets are surpassed

Company will sell 1 000 units of the spark nail which they ordered at a wholesaler in Shoppers Town

for a cost price of R100 each. In order to achieve the increased sales, additional marketing costs of

R3 000 will be incurred.

These sales units are achieved after the introduction of a 20% markdown from original selling price.

Required:

Which of the three scenarios would you recommend to management? Provide a reason for your

answer with reference to net profit before tax.

Scenario 1:

The elected officials in a west coast university town are concerned about the "exploitative" rents being charged to college students. The town council is contemplating the imposition of a $350 per month rent ceiling on apartments in the city. An economist at the university estimates the demand and supply curves as:

            QD = 5600 - 8P    QS = 500 + 4P,               

where P = monthly rent, and Q = number of apartments available for rent. For purposes of this analysis, apartments can be treated as identical.

Consider Scenario 1 in the Supplement. Which of the following would vote for this price ceiling to be imposed? (Mark all that apply)

Consider Scenario 1 in th Supplement. Which of the following things are likely to happen as a direct result of implementing the price ceiling? (mark all that apply)

Demand and supply are Key elements of the U.S. economic system. So, too, is competition. This exercise will challenge you to better understand the ethical dimensions of a system that relies on demand, supply, and competition.

The Situation

You are a businessperson in a small town, where you run one of two local pharmacies. The population and economics base are fairly stable. Each pharmacy controls about 50 percent of the market. Each is reasonably profitable, generating solid if unspectacular revenues.

The Dilemma

You have just been approached by the owner of the other pharmacy. He has indicated an interest either in buying your pharmacy or in selling his to you. He argues that neither of you can substantially increase your profits and complains that if one pharmacy raises its prices, customers will simply go to the other one. He tells you outright that if you sell to him, he plans to raise prices by 10 percent. He believes that the local market will have to accept the increase for two reasons: (1) The town is too small to attract national competitors, such as Walgreens, and (2) locals customers can’t go elsewhere to shop because the nearest town with a pharmacy is 40 miles away.

Questions for Discussion -

1. What are the roles of supply, demand, and competition in this scenario?

2. What are the underlying ethical issues?

3. What would you do if you were actually faced with this situation?

A real estate expert wanted to find the relationship between the sale price of houses and various characteristics of the houses. He collected data on five variables, recorded in the table, for 12 houses that were sold recently. The five variables arePrice: Sale price of a house in thousands of dollars. Lot Size: Size of the lot in acres. Living Area: Living area in square feet. Age: Age of a house in years. Type of house: town house (T) or Villa (V) Price Lot Size Living Area Age Type of house

Price 255 178 263 127 305 164 245 146 287 189 211 123

Lot Size1.4 0.9 1.8 0.7 2.6 1.2 2.1 1.1 2.8 1.6 1.7 0.5

Living area 2500 2250 2900 1800 3200 2400 2700 2050 2850 2600 2300 1700

Age 8 12 5 24 10 18 9 28 13 9 8 11

Type of the house T T T T T T T V V V V V

Find the regression equation for the town house e) Find the regression equation for the Villa f) What is the price of a town house with a lot size of 1.3, living area of 1800, and is 7 years old?