Finance Answers

28. Explain Income Elasticity and Cross Elasticity.
R.J. Smith Corporation is a publisher of novels. The Corporation hires an economist to determine the demand for its product. After months of hard work, the analyst tells the company that the demand for the firm's novels (Qx) is given by the following equation:
Q¬x = 12,000 - 5,000Px + 5I + 500Pc
Where Px is the price charged for the R.J. Smith novels, I is income per capita and Pc is the price of books from competing publishers. Using this information the board of directors want you to
(a) Determine what effect a price increase would have on total revenues.
(b) Evaluate how sales of the novels would change during a period of rising incomes.
(c) Assess the probable impact if competing publishers raise their prices.
Assume initial values of Px, Pc and I are $5, $10,000 and $6 respectively.

29. Suppose the market demand for playing cards is given by the equation
Q = 6,000,000 – 1,000,000P where Q is the number of decks of cards demanded each year and P is the price in dollars. For a price increase from $2 to $3 per deck, what is the arc price elasticity?

30. Max, a graduating senior, has accumulated an impressive file of tests during his college career. But now he needs to sell his test collection to obtain money for his impending marriage. Three wealthy friends express interest in buying some of the tests. Max determines that their individual demand equations are as follows:
Q1 = 30.00 – 1.00P
Q2 = 22.50 – 0.75P
Q3 = 37.50 – 1.25P
Where the quantity subscripts denote each of the three friends and price is measured in dollars per test.
What is the market demand equation for Max’s tests, and how many more tests can he sell for each 1-dollar decrease in price? If he has a file of 60 tests, what price should he charge to sell his entire collection?

31. It is known that quantity demanded decreases by 2 units for each $1 increase in price. At a price of $5, quantity demanded is 10 units.
i) What will be the quantity demanded if price is zero?
ii) Write an equation for quantity demanded as a function of price.
iii) Write an equation that expresses price as function of quantity.
iv) Write an equation for total revenue.

32. A market consists of two individuals. Their demanded equations are Q1 = 16- 4P and Q2 = 20 –2P, respectively.
What is the market demand equation?
At a price of $2, what is the point price elasticity for each person and for the market?

33. The demand equation faced by DuMont Electronics for its personal computers is given by P == 10,000 – 4Q.
(a) Write the marginal revenue equation.
(b) At what price and quantity will marginal revenue be zero?
(c) At what price and quantity will total revenue be maximized?
(d) If price is increased from $6,000 to $7,000, what will be the effect on total revenue? What does this imply about price elasticity?

34. Sailright Inc. manufactures and sells sailboards. Management believes that the price elasticity of demand is – 3.0. Currently, boards are priced at $500 and the quantity demanded is 10,000 per year.
(a) If the price is increased to $600, how many sailboards will the company be able to sell each year?
(b) How much will total revenue change as a result of the price increase?

35. Demand for a managerial economics text is given by Q = 20,000 – 300P. The book is initially priced at $30:
i) Compute the point price elasticity of demand at P= $30.
ii) If the objective is to increase total revenue, should the price be increased or decreased? Explain.
iii) Compute the arc price elasticity for a price decrease from $30 to $20.
iv) Compute the arc price elasticity for a price decrease from $20 to $15.

36. A consultant estimates the price-quantity relationship for New World Pizza to be P = 50 –5Q.
i) At what output is demand unitary elastic?
ii) Over what range of output is demand is elastic?
iii) At the current price, 8 units are demanded each period. If the objective is to increase total revenue, should the price be increased or decreased? Explain.

37. The price elasticity for rice is estimated to be –0.4 and the income elasticity is 0.8. At a price of $0.40 per pound and a per capita income of $20,000, the demand for rice is 50 million tons per year.
i) Is rice an inferior good, a necessity, or a luxury? Explain.
ii) If per capita income increases to $20,500, approximately what will be the quantity demanded rice?