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Equilibrium price

1. Suppose the government wishes to spur the production of soybeans for their potential usage in making biodiesel in order to reduce our dependence on foreign oil. Further suppose that the market demand and supply for soybean oil are given by QD = 100 - P and QS = 50 + .3P, where Q = barrels of soybean oil, and P = price per barrel.
a. What is the equilibrium price in this market with no government intervention? Show your work.

b. What is the equilibrium quantity in this market? Show your work.

c. If the government now sets a price ceiling of $30 on soybean oil, what is the impact on price and quantity? Explain.

d. If the government agrees to buy any surplus created by the price ceiling it has set, what is the cost to the government? Explain.
2. You own a small company and are trying to decide which of three possible business strategies to take to maximize the value of the firm over the next three years. The following table shows year-end profits for each strategy. Interest rates are expected to be stable at 7 percent over the next three years.
Option Profits in Year 1 Profits in Year 2 Profits in Year 3
A $65,000 $80,000 $90,000
B $55,000 $90,000 $100,000
C $34,000 $100,000 $115,000
a. What are the present values of the 3 options? Show your calculations.
b. What option do you choose? Why?
3. Suppose you work at WalMart, where you earn $45,000 per year. Your rich Aunt Betty recently died and left you an inheritance, so you are thinking of starting your own business. The business you wish to pursue will retrofit gasoline automobiles with electric motors that allow them to operate as gasoline/electric hybrid vehicles. You predict that you can retrofit approximately 1,000 units during the first year at a selling price of $2,000 per automobile. Your overhead (fixed) costs are estimated at $1,000,000, and your operating costs (material, labor, etc.) are expected to be $1,200 per automobile. Note: Show your work and explain your logic for each of the following questions.
a. What are your first year accounting costs?
b. What are your first year economic costs?
c. What are your accounting profits (or losses)?
d. What are your economic profits (or losses)?

4. Suppose your work for a company that makes chocolate-flavored dental floss. You know from experience that the most significant factors influencing sales of your product are the amount your company spends on advertising and the average disposable income of consumers in the marketplace.
Having just finished a statistics course, you decide to use your company's historical data on sales and advertising expenditures, combined with government income data, to create a regression equation that relates sales of your floss to advertising and income. When you do so, the results are:
S = 320,500 +1.07A + 1.05I where
S= sales (in dollars) of dental floss
A = advertising expenditures
I = average consumer income
Anxious to impress, you give the equation to your boss and add that the t statistics for the A and I variables are 3 and 4.6, respectively. Finally, you add as icing to the cake the following: when the absolute value of the t-statistic is greater than 2, one can be 95 percent confident that the true value of the underlying parameter in the regression is not zero.
Your boss responds by stating that he failed fifth grade arithmetic and didn't understand any of your explanation, but
a. Wants to know in plain English what the so-called regression equation and your other statistical gibberish means, and
b. Wants to know how many sales the company could expect if it didn't advertise and the average income of the target audience was $40,000 per year.
How do you respond?
5. A MBA student conducts a study during an internship for Boulevard Brewing and estimates the following:
a. Own price elasticity of demand for Boulevard Pale Ale = -.19.
b. Cross-price elasticity of Pale Ale with Layes Potato Chips = -2.5.
c. Income elasticity of demand for Boulevard Pale Ale = 0.2.
Based on the above:
a. What exactly would happen to the quantity of Pale Ale sold if Boulevard raises its price by 10%? Show your calculations.
b. What happens to the sales of Pale Ale if the price of Layes potato chips increases by 5%? Show your calculations.
c. Are Pale Ale and Layes potato chips substitutes or complements (not compliments)? Explain how you arrived at your answer and what it means.
d. Is Pale Ale a normal or inferior good? Explain how you arrived at your answer and what it means.
6. The demand for taxi service in Boston is elastic and sensitive to market prices. Given that, describe the effect of each of the following on the quantity demanded or the demand for taxi service in Boston. Indicate whether the effect of each is an upward or downward movement along a given demand curve or instead involves an outward or inward shift in the demand curve for taxi service. Explain your answers.
a. A decrease in the average price for taxi service in Cleveland.
b. A rise in the average price of commuter train fares from the Airport to downtown Boston.
c. An increase in the average price for taxi service in Boston.
d. A large group of poor single Boston Mothers who ride the bus to work because taxis are expensive and who cannot afford a car, but would rather taxi to work if they could, get raises at work.

Solution Preview

Dear Student,
1. a.The equilibrium price is the price at which quantity demanded and quantity supplied remains same. So 100-p= 50+0.3P at equilibrium price. By simple euation, we can deduce that p= 38.46 from the above equation.
b.The equilibrium quantity is = 50+0.3*38.46 =61.54 (62)
c. The equilibrium price is 38.46. If the government fixes the price at 30, then the supply will be qs= 50+0.3p= 50+0.3*30= 59. The demand on the other hand will be qd= 100-p = 100-30= 70. So the demand is more than the supply. This will result in shortage of goods and price will increase until it reaches the equilibrium.
d.The equilibrium is at 38.46, if the goverment fixes the price lower than this, there will be no excess supply. But if the government fixes a higher price than the equilibrium price say 40, then the supply will be 50+0.3*40= 62. The demand will be 100-40= 60. The 2 extra units will cost ...

Solution Summary

Equilibrium price is discussed.