Dr. WesterholdName:______
Econ 330
HW # 3: Mathematical Determination of Equilibrium, Shortages, and Surpluses (Due Monday,October 11th). Homework is graded on completeness and accuracy. Remember, assignments are collected at the beginning of class. Late assignments receive a penalty of 15% per week day. Assignments not stapled receive a 15% penalty
You must show your work for full credit (especially in situations where a graphing calculator can provide answers eliminating your need to work through the algebra).
------
1. Assume that in the market for travel coffee mugs, the reservation price is $15.00 and at a price of $8.50 the quantity demanded is estimated at 1000 units. Assume that these estimates are based on the underlying assumptions that income is $25,000 and the price of a regular coffee mug is $4.00.
A. Use this information to sketch a demand curve and label all variables being held constant.
B. Derive the inverse demand equation and the demand equation for travel coffee mugs:
C. Assuming a firm has an excess inventory of 542 units estimate the highest price a firm could charge and eliminate the inventory.
D. Estimate sales when the firm charges $6.99 for a travel mug.
E. Suppose with a recent factory closing that we expect the median income to decrease to $22,000. If we continued to charge a price of $8.50, explain the theoretical impact on the market for travel coffee mugs assuming they are anormal good (no calculation). Show the effect on your graph in part A. Briefly explain your answer.
2. As an economic analyst you estimated the following inverse supply and demand relationships for Maytag Refrigerators
Supply: P= 1200 + 5.2Qs
Demand:P= 5000 – 3.5Qd
- Determine the demand and supply equations for this market:
B. Mathematically determine the equilibrium price (PE) and equilibrium quantity (QE). Please round each estimate to two decimal places.
C. Calculate the intercept values for demand and supply.
D. Graph the demand and supply equations including values for the x-intercepts and y-intercepts. Plot the equilibrium price and quantity on your graph.
E. If the current market price is $1500, what would be the value of the resulting surplus or shortage? Show this on your graph in part D.
F. If the current market price is $4500, what would be the value of the resulting surplus or shortage? Show this on your graph in part D.
3. Assume you have the following information on production and sales for Calvin Klein jeans.
Price / Quantity Demanded / Quantity Supplied$75 / 1545 / 1000
$85 / 1330 / 1500
$95 / 1115 / 2000
$105 / 900 / 2500
A) Derive the demand equation using the data provided above. Show your work(Determine the equation algebraically. Do not simply expand the table to find the reservation price).
B) Derive the supply equation using the data provided above. (Same as above, determine the equation algebraically and not by simply expanding the values in the chart).
C) Algebraically determine values for all intercepts (x and y for both demand and supply).
D)Algebraically solve the system for the equilibrium price and quantity.
E)Graph the intercepts for demand and supply and the equilibrium price and quantity.
4. Consider the demand and supply for rye bread:
Qs= -350 + 220Prye
Qd=2000 + 0.05I - 250Prye + 275Pwheat
Where Pryeis the price of a loaf of rye bread
Iis the average monthly income in dollars for our target market
Pwheatis the price of a loaf of wheat bread
A)Determine the demand equation for the market for Rye Bread if I=$28,000, Pwheat=$2.75
B)Calculate the x and y intercepts for both the demand and supply curves and plot them on a graph below.Show the factors held constant or underlying assumptions.
C) What is the equilibrium price and quantity when I=$28,000 and the price of wheat is $2.75. Show this on your graph in part B.
D) Suppose the price of wheat bread decreases to $2.50. Determine the new demand equation, and plot the new demand curve on your original graph in Part B showing the values of the x and y intercepts.
E) Determine the new equilibrium price and quantity for rye bread.Show this on your graph in part B.
F) Compare your two equilibria in the market for Rye Bread. What is the economic explanation for the change in equilibrium (i.e., is this a shift of a curve or a movement along a curve and what caused this to occur?)
5. Suppose every Buick owner’s demand forgasoline is 20 -5p for p less than or equal to 4 and 0for p > 4. Every Dodge owner’s demand is 15 -3p forp less than or equal to 5 and 0 for p > 5. Suppose thatGas Pump, South Dakota, has 100 Buick owners and200 Dodge owners. Determine the market demand equation for gasoline. If the price of gasoline is $3.50,what is the total amount of gasoline demanded in GasPump?
6. The demand function for sandwiches is200 -4PS- 2PLand the demand function for lemonade is
200-3PL- PS, where PSand PLarerespectively the price of sandwiches and lemonade. The world supply (Qs) of Sandwiches is 140 and the world supply of lemonade is 180. Determine the equilibrium prices and quantities for both sandwiches and lemonade.
End of Assignment.
1