PROBLEMS 1. The following function describes the demand condition for a company that makes caps featuring names of college and professional teams in a variety of sports. Q = 2,000 - 100P where Q is cap sales and Pis price. a. How many caps could be sold at $12 each? b. What should the price be in order for the company to sell 1,000 caps? c. At what price would cap sales equal zero? CHAPTER 3 Supply and Demand 59 2. Consider the following supply and demand curves for a certain product. Qs = 25.000P Qn = 50.000 - 10,000P a. Plot the demand and supply curves. b. What are the equilibrium price and equilibrium quantity for the industry? Determine the answer both algebraically and graphically. (Round to the nearest cent.) 3. The following relations describe the supply and demand for posters. QD = 65.000 - 10,000P Qs = -35,000 + 15,000P where Q is the quantity and Pis the price of a poster, in dollars. a. Complete the following table. Price Surplus or Shortage $6.00 5.00 4.00 3.00 2.00 1.00 b. What is the equilibrium price? 4. The following relations describe monthly demand and supply for a computer support ser- vice catering to small businesses. Qo = 3,000 - 10P Qs = -1,000 + 10P where Q is the number of businesses that need services and Pis the monthly fee, in dollars. a. At what average monthly fee would demand equal zero? b. At what average monthly fee would supply equal zero? c. Plot the supply and demand curves, d. What is the equilibrium price/output level? e. Suppose demand increases and leads to a new demand curve: QD = 3,500 - 10P What is the effect on supply? What are the new equilibrium Pand Q? f. Suppose new suppliers enter the market due to the increase in demand so the new supply curve is Q=-500 + 10 P. What are the new equilibrium price and equilibrium quantity? g. Show these changes on the graph. 5. The ABC marketing consulting firm found that a particular brand of tablet PCs has the following demand curve for a certain region: Q= 10,000 - 200P + 0.03Pop + 0.61 + 0.24 where Q is the quantity per month, Pis price ($). Pop is population, / is disposable income per household (S), and A is advertising expenditure ($). a. Determine the demand curve for the company in a market in which P= 300. Pop = 1,000,000. 1 = 30,000, and A = 15,000. b. Calculate the quantity demanded at prices of $200, $175, $150, and $125. c. Calculate the price necessary to sell 45,000 units.19. A Canadian apparel company, Roots, agreed to provide the U.S. Olympic team at the 2002 Winter Olympics with various types of clothing, including berets, for free, and further, to turn over a portion of its profits on sales of this clothing to the U.S. Olympic Committee. The beret became an instant success, and Roots sold a large number of them. What type of elasticity does this arrangement represent? 96 CHAPTER 4 Demand Elasticity PROBLEMS 1. The Acme Paper Company lowers its price of envelopes (1,000 count) from $6 to $5.40. If its sales increase by 20 percent following the price decrease, what is the elasticity coefficient? 2. The demand function for a cola-type soft drink in general is Q = 20 - 2P, where Qstands for quantity and Pstands for price. a. Calculate point elasticities at prices of 5 and 9. Is the demand curve elastic or inelastic at these points? b. Calculate arc elasticity at the interval between P = 5 and P = 6. c. At which price would a change in price and quantity result in approximately no change in total revenue? Why? 3. ABC Sports, a store that sells various types of sports clothing and other sports items, is plan- ning to introduce a new design of Arizona Diamondbacks' baseball caps. A consultant has estimated the demand curve to be Q = 2,000 - 100P where Q is cap sales and Pis price. a. How many caps could ABC sell at $6 each? b. How much would the price have to be to sell 1,800 caps? c. Suppose ABC were to use the caps as a promotion. How many caps could ABC give away free? d. At what price would no caps be sold? e. Calculate the point price elasticity of demand at a price of $6. 4. The equation for a demand curve has been estimated to be Q = 100 - 10P + 0.5Y, where Q is quantity, Pis price, and Y'is income. Assume P = 7 and Y = 50. a. Interpret the equation. b. At a price of 7, what is price elasticity? c. At an income level of 50, what is income elasticity? Now assume income is 70. What is the price elasticity at P = 82 III O