Assignment:
1. You are the Lay's Potato Chip distributor for Denver. You hire a consultant to estimate the demand for your product. Here is the estimated demand curve that he provided:
QL = 100 + 0.2PL + 1.5Pp + 0.4Pd + 2I
Where QL stands for bags of Lay's (in thousands), PL is the price of a bag of Lay's (in cents), Pp is the price of Pringle's Potato Chips (in cents), Pd is the price of Doritos Tortilla Chips (in cents), and I is average income in Denver (in thousands of dollars).
a. Upon examining this estimated demand curve, you promptly fire the consultant and file suit to get your money back. Why was this the correct action?
Your new consultant provided the following demand curve (the variables are defined as above)
QL = 250P L -2.5 P p 2 P d I -0.5
Use this much better estimate of the demand function to answer the following questions.
b. Are Lay's Potato Chips a normal or inferior good?
c. Are Doritos a substitute or complement for Lay's?
d. What is the cross price elasticity between Lay's and Pringle's EL,Pp ?
e. You decide to run a sale and lower the price of Lay's by 5%. By what percent and in what direction does quantity demanded change?
f. The marginal cost of producing a bag of Lay=s is 60 cents. How much should you charge per bag?
2. The demand for Goodyear Radial Tires was estimated to be
Q = 12P - 1.5Pg2Pb I - 4,
where P is the price of Goodyear Radials; Pg is the price of gasoline (a complementary good); Pb is the price of Bridgestone Radial Tires (a substitute good); and I is income (all prices and income are measured in dollars) There are some problems with this estimated demand function. Please list two.
3. The demand for your product has been estimated to be
Q = 10 - 4P - 1.5Pr1 + 0.6Pr2 + 22I - 2.6A
where Q stands for quantity (in thousands of units), P is the price of your product, Pr1 is the price of related good 1, Pr2 is the price of related good 2 (all prices are in dollars), I is the average income in the area (in thousands of dollars), and A is the amount you spend on advertising (in thousands of dollars). The averages for the series are 50,000 units (i.e., Q = 50) average price of $10 (i.e., P = 10), and the average income in the area was $30,000 (i.e., I = 30). Use this information to answer the following questions.
a. Calculate the elasticity of demand, EQ,p.
b. Is this demand elastic, inelastic, or unitary elastic?
c. To increase total revenue, what should you do to the price?
d. You run a sale, lowering your price by 10%. By what percent will quantity demanded change, and will it increase or decrease?
The product with demand given above is spring training baseball tickets. One of the related goods is parking at the baseball stadium. The other related good is hockey tickets.
e. Parking is which related good?
f. Spring training tickets are normal goods. Using the data from above, are tickets luxuries or necessities. You must show your work (no credit for guessing).
g. Are you happy with your advertising agency? Please explain why or why not.
4. You are the Lykes hot dogs distributor for Timber County. You hire a consultant to estimate the demand for your product. Here is the estimate that he provided:
Q = 250P L -0.5 Pgb 0.2 P b -0.5I 0.5
Where Q stands for packages of Lykes hot dogs (in thousands), PL is the price of a package of hot dogs (in cents), Pgb is the price of a pound of ground beef (in cents), Pb is the price of a package of hot dog buns (in cents), and I is average income in Timber County (in thousands of dollars).
Assume that this estimate is as close to correct as possible. Use it to answer the following questions.
a. Is the demand for Lykes hot dogs elastic, inelastic or unitary elastic?
b. Is ground beef a substitute or complement for hot dogs?
c. What is the cross price elasticity between Lykes and hot dog buns?
d. Due to an increase in the price of pork, you need to raise the price of Lykes hot dogs by 15%. By what percent and in what direction does quantity demanded change?
f. If the price of ground beef increases by 10%, what happens to the demand for Lykes?
g. Again, assuming that this demand is correct, should your manager be happy with your performance as a brand manager? Why (or why not)?
5. You are the regional sales representative of a product. The regional generalized demand function for the product was estimated to be
Q = 6 - 2.5P + 3Pr - 0.6M + 0.15T
Where Q stands for quantity demanded (in thousands), P is the price of your product, Pr is the price of a related product (both prices are measured in $), M is the average income (in thousands of $) of the people in your region, and T is the average temperature in your region. Currently, Pr = 7, M = 20 (i.e., income is 20,000), and T = 60. The supply curve is Q = 2P - 12. Use this information to answer the following questions.
a. Is this good a normal or inferior good? Explain how you determined your answer.
b. Is the related good a substitute or compliment? Explain how you determined your answer.
c. Assuming the other parameters are fixed at their current value, find the demand curve.
d. What is the equilibrium price and quantity?
e. Suppose now that the related good=s price increases to Pr = 8.5. Find the new equilibrium price and quantity.
6. This problem uses the included spreadsheet. For parts a and b, assume that laborers are paid $100 per day, trenchers can be rented for $75 per day, the cost of pipe, glue and sprinkler heads run 90¢ per square foot. The firm can charge $1 per square foot irrigated.
a. In the short run, the number of laborers is fixed at 5. How many trenchers should the firm rent?
b. Instead, in the short run the number of trenchers is fixed at 3. How many laborers should the firm hire?
For parts c and d, assume the input prices are the same, but now the firm can only charge 92¢ per square foot irrigated.
c. Calculate the optimal number of trenchers to rent when the number of laborers is fixed at 6.
d. Calculate the optimal amount of labor to hire when the number of trenchers is fixed at 2.
7. You employ fishermen to work on your fishing boat. Historically, the relationship between number of fish caught and number of fishermen has followed the following production schedule.
# of fishermen fish caught
0 0
1 40
2 95
3 130
4 160
5 175
6 185
7 190
Fish sell for a net price of $10 each.
a. What is the marginal product of the third fisherman?
b. With which fisherman does the law of diminishing returns set in?
c. What is the marginal revenue product of the 3rd fisherman?
d. Fishermen are paid $140 per trip. How many should the firm hire?