Market for radio advertising.

1. Suppose you are looking at the market for radio advertising. Three variables are given to you: price of
   advertising, quantity of advertising, and the extent of financial meltdown precipitated by the sub-prime
   market fiasco. Which variable(s) would you consider exogenous and which would be endogenous.
   Explain your answer. (Begin by defining these terms according to your lecture notes.)
2. Suppose you want to analyze the level of foreign aid that Canada gives to developing countries each year.
   You are told that Canada’s aid depends on the population of these countries, their level of poverty, and
   how good governance is in these countries (measured by absence of corruption, etc.) Indicating your
   notation, write this information:
   (3) i) As a general function.
   (3) ii) As a linear function.
   (6) iii) Comment on the likely sign of the coefficients in your linear function. (Note: your mark will
   depend heavily on the quality of your explanation. So be sure to be clear; explain your line
   of reasoning.)
   (6) 3. In a closed economy with no government the savings and investment functions are given by
   S = Y2
   – 40 Y + 10
   I = 60
   where Y is national income. What is the plausible equilibrium level of national income in this economy?
   Explain how you obtained your answer.
   (10) 4. A child with an ear infection is given a 200-mg ampicillin tablet once every four hours. About 12% of
   the drug in the body at the start of a four-hour period is still there at the end of that period. Calculate
   the quantity of ampicillin in the body right after taking the third tablet is given. If we keep on giving
   tablets to the child forever, what level of the drug in the body do we converge to? Explain.
3. Consider the following demand and supply functions for milk:
   Q
   d = 300 - 100P
   Q
   s = 50P
   where P is price (in dollars) and Q
   d
   and Q
   s
   are the quantity demanded and quantity supplied of milk
   (in thousands of 4-litre bags), respectively.
   (5) i) Find the equilibrium price and quantity of milk.
   (7) ii) Suppose the government offers a subsidy to milk producers equal to 30¢ for each 4-litre bag
   of milk sold. Find the new equilibrium price and quantity under this policy. Describe the
   incidence of the subsidy by giving the exact dollar amounts. (Note: You must provide an
   algebraic answer for this part. A diagrammatic answer will receive only partial credit.)
   (7) iii) Return to the original question (i.e., ignore what takes place in part ii)). Now suppose the
   government offers a subsidy to consumers equal to 10¢ for each 4-litre bag of milk bought.
   Describe the incidence of the subsidy now. (Again, provide an algebraic answer.)
   (10) 6. According to an article in the Maclean’s magazine, “Cable, satellite and wireless companies may be
   charging illegal late fees. Companies may calculate a compounded late-fee rate of two percent a month.
   However, because they charge even if a customer is late by one week, that can mean an effective
   annualized interest rate above the maximum allowed by the Criminal Code: 60 percent.” (Maclean’s
   November 28, 2005, p.16.) Calculate the annualized interest rate these companies are charging if the
   penalty is two percent a month. What if the penalty was two percent a week?
   (10) 7. New members of a golf club are admitted at the start of each year and pay an initiation fee of $2,000
   immediately. Thereafter, members pay an annual membership fee of $400, which falls due at the
   beginning of each year. How much does the club make from a new member over the first 10 years,
   assuming an interest rate of 5.5% compounded annually. (Note: In answering this question you must
   use the formula for finding sums. If you keep on adding the numbers manually, you will receive only
   partial credit, even if your final answer is correct.)
4. Around January 1, 1993, Barbara Streisand (a singer/actress for those of you too young to know!)
   signed a recording contract with Sony Corporation for $2 million each year for 10 years. Suppose the
   first payment of $2 million was made on the day of signing the deal and all other payments to her were
   made on the first day of each subsequent year. Suppose all payments were directed into her bank
   account earning 4% a year, compounded semi-annually.
   (7) i) Assuming she never made any withdrawals from the account, how much money was in
   her account on the day the last payment was made? (Be sure to use the formula for
   finding sum of a series. If you do not, you will receive only ½ of the credit for this part.)
   (7) ii) What was the present discounted value of the recording contract to her the day it was
   signed? (Be sure to use the formula for finding sum of a series. If you do not, you will
   receive only ½ of the credit for this part.)
   (5) 9. Suppose the price of an item (say, a television set) is $P at two Ontario retail stores. One retailer tells you
   he will knock 13% off the price as a discount. Another says she will give you a HST break instead (i.e.,
   you do not pay the tax). Which retailer should you buy the item from? [Note: Do not substitute a
   numerical value for P. The answer is to be formulated, in general terms, in term of P – not in terms of a
   number.]
   (7) 10. An individual agrees to pay $6,000 per year for three years to payoff a car loan. His payments are always
   made at the end of each year. If the interest rate in year 1 is 3%, in year 2 is 3.5% and in year 3 is 4%,
   and if compounding is done twice a year, how much did the car originally cost? (That is, work out the
   price he must have agreed to pay for the car.

Sample Solution