Question 1.
a. Suppose that demand for sweaters among Drexel undergraduate students is given by QDU = 98.7 - 2.2P, where QD is the number of sweaters and P is measured in dollars. Draw the demand curve for sweaters among Drexel undergraduate students, putting the price (P) on the y-axis and the quantity (QDU) on the x-axis (note: it may be easier to rearrange the demand and supply functions to put them in terms of P first).
b. Suppose that demand for sweaters among UPenn undergraduate students is also given by QPU = 98.7 - 2.2P. Write down the aggregate demand function for Drexel and UPenn undergraduate students.
c. Draw the aggregate demand curve for sweaters among Drexel and UPenn undergraduate students, putting the price (P) on the y-axis and the quantity (QU) on the x-axis.
d. Suppose that demand for sweaters among Drexel graduate students is given by QDG = 41.7 - 2.8P, and that demand for sweaters among UPenn graduate students is given by QPG = 41.7 - 2.8P. Write down the aggregate demand function for Drexel and UPenn graduate students.
e. Write down the aggregate demand function for sweaters among Drexel and UPenn students, including undergraduate and graduate students.
f. Draw the aggregate demand curve for sweaters among Drexel and UPenn students, putting the price (P) on the y-axis and the quantity (Q) on the x-axis.
g. Suppose that there are only two suppliers of ugly holiday sweaters in University: firm A, which has a supply function of QA = P - 5, and firm B, which has a supply function of QB = 2P. Write down the aggregate supply function for ugly sweaters in University City.
h. Draw the aggregate supply curve for sweaters in University City, putting the price (P) on the y-axis and the quantity (Q) on the x-axis.
i. Assuming there are no other buyers or sellers of ugly sweaters in University City, find the equilibrium price and quantity of ugly holiday sweaters in this market.
Question 2:
Suppose that demand for Philadelphia Flyers t-shirts in the city of Philadelphia is given by Q = 110 - 5P, where Q is measured in thousands of t-shirts and P is in dollars. Supply is given by Q = 5P.
a. Find the equilibrium quantity and price of t-shirts in this market.
b. Draw the demand and supply curves on a figure, putting the price (P) on the y-axis and the quantity (Q) on the x-axis. Shade in and label the areas representing the consumer surplus and the producer surplus.
c. Calculate the total consumer surplus in this market (remembering that Q is measured in thousands of t-shirts and P is measured in dollars).
d. What is the price elasticity of demand at the equilibrium quantity and price in the market? Is demand for t-shirts at the equilibrium elastic, inelastic, or unitary elastic? Describe the in words the meaning of the elasticity you calculate.
e. Suppose that the Philadelphia city government decides that t-shirts are too expensive and decides to cap Flyer t-shirt prices at $8 per shirt. Is this price cap binding? If so, how much excess demand or supply is there in the market at a price of $8?
f. Calculate the new consumer surplus in the market with the price cap (again remembering that Q is measured in thousands of t-shirts and P is measured in dollars). Is it higher or lower with the cap than without?
g. Suppose that the cap were instead set at $2 per shirt. What would the excess demand or supply be in this case? Would the consumer surplus with a $2 price cap be higher or lower than without any cap?
h. Suppose that instead of the price cap, the Philadelphia city government subsidizes the production of Flyers t-shirts, leading to a new supply curve of Q = 40 + 5P. Calculate the new equilibrium quantity and price of t-shirts in this market.
i. Draw a new graph showing the demand curve, the old supply curve, and the new supply curve.
j. Calculate the new consumer surplus in the market with the subsidy (again remembering that Q is measured in thousands of t-shirts and P is measured in dollars). Is it higher with the subsidy than without?
k. What is the price elasticity of demand at the new equilibrium quantity and price in the market? Is demand for t-shirts at the equilibrium elastic, inelastic, or unitary elastic? Describe the in words the meaning of the elasticity you calculate.
Question 3: Suppose that you derive utility from consuming two goods, bagels (B) and avocados (A).
a. Suppose that the price of each bagel is $1, the price of each avocado is $4, and your weekly income is $24. Write down your budget constraint.
b. Now assume your utility function takes the following form:
U(B, A) = B0.5 + A
You want to maximize utility subject to your budget constraint. Determine the amount of bagels and avocados you will consume each week. What is the utility level associated with this consumption choice?
c. Suppose that your income increases to $36. Determine the number of bagels and avocados you will consume given this higher level of income. What is the utility level associated with this new consumption choice, and how does it compare to that which you found in part b?
d. Without doing any further math, draw the budget constraints and indifference curves associated with your solutions in parts b and c (the figure does not need to be perfectly to scale, but be sure to label all axes and lines).
e. Now suppose that the government wants to discourage consumption of bagels. It places a tax on bagels such that the price consumers now face is $2 per bagel instead of $1 per bagel. Assuming the price of avocados remains at $4 and your income is $36, determine the new optimal consumption of bagels and avocados. What is the utility level associated with this new consumption choice? How does it compare to that which you found in part c?
f. Without doing any further math, draw the budget constraints and indifference curves associated with your solutions in parts c and e.
Question 4. Dana's utility over coffee (C) and tea (T) at Joe in University City is given by
U(C, T) = 100(C0.5T0.5)
a. Suppose Dana has income of $Y to spend on coffee and tea at Joe each week. Derive Dana's demand functions for coffee and for tea.
b. Suppose Y = $20 and tea costs $2 per cup. Using the demand function you derived for coffee in part a, draw Dana's demand curve for coffee (where the price per ounce is on the y-axis and the quantity in cups in on the x-axis).
c. Still assuming Y = $20 and tea costs $2 per cup, if the price of coffee were $1 per cup, how much coffee and tea would Dana consume? What would Dana's utility level be with this consumption choice?
d. Suppose that poor coffee yields in South America drive the price of coffee up to $2 per cup. Derive the income and substitution effects of this price change both for coffee and for tea for Dana. Do the two effects work in the same direction or not for each of the two goods?