You are encouraged to form study groups to work on these problems. However each student must hand in a separate assignment: the group can work together to discuss the papers and comment on drafts, but each study group member must write it up herself/himself. Please submit homework assignments on Blackboard.
1. What are the names of people in your study group?
2. Consider demand elasticities:
a. What goods do you personally demand (be creative!), which have a low price elasticity?
b. Which have a high price elasticity?
c. If we narrow the range to just phone apps (if you don't have a smartphone, then imagine), which ones would be highest/lowest elasticity?
d. What about environmental goods? Give an example of high and low elasticity.
3. Uber's surcharges have gotten recent publicity, for example on New Year's - what do these imply (if anything) about demand and supply elasticities?
4. Consider the supply and demand for gasoline. Sketch the changes (if any) for each contingency.
a. What would be the effect of a slowdown in Chinese economic growth? Would price increase or decrease? Would quantity increase or decrease?
b. What would be the effect, on supply and demand for gasoline, of the end of Iran sanctions? Would gas prices increase or decrease? Would quantity of gas sold increase or decrease?
c. What would be the effect of new battery technology lowering the cost of hybrid or electric vehicles? Would gas prices increase or decrease? Would quantity of gas sold increase or decrease?
d. Suppose the Saudis kept enough reserve production capacity to be able to increase or decrease production by 3%, with the aim of steadying prices?
e. What would be the effect, in the gasoline market, of completing the Keystone pipeline? Would price increase or decrease? Would quantity increase or decrease?
f. How does fracking and enhanced recovery of 'tight oil' react to gasoline prices? What is that effect in the gasoline market?
g. (extra) How does the gasoline price affect employment in the Detroit area?
5. Consider a market that can be represented by a linear demand curve, QD = 100 - PD, (where QD is the quantity demanded and PD is the price that demanders pay) and a linear supply curve that QS = 4PS (where QS is the quantity supplied and PS is the price that suppliers get).
a. Graph the two functions with P on the vertical axis.
b. At a price of 10, how many units are demanded? How many are supplied? What would be Consumer and Producer Surplus at this price? (Remember that short side rules - can't buy something not produced nor sell something not bought!) (Recall that the area of a triangle is half the base times the height.)
c. At a price of 30, how many units are demanded and supplied? What would be Consumer and Producer Surplus at this price?
d. Set PD = PS and QD = QS and solve the system of equations to find the equilibrium (find the intersection of the lines). Show on the graph.
e. What are CS & PS now? Show on the graph. Compare Total Surplus for the 3 cases.
f. Suppose the government sets a tax of $2 per unit. This means that PD = PS + 2. What is now the quantity demanded & supplied? (You can rewrite the equations, that currently show Q as a function of P, to instead get P as a function of Q. Then substitute in the algebraic expressions for PD and PS to solve.) What are CS & PS now? What is government revenue (which adds to total surplus)? What is DWL (deadweight loss)?
g. Suppose that production of this good has a marginal external cost of $3 per item. What is the DWL of the free market equilibrium? What is the DWL of the tax case?
6. A locality can use its coast for tourism (people are attracted to pristine coastline) or business/industry (which destroys the tourist appeal). It wants to choose what percent of coast should be preserved for tourism and how much should be kept for industry. Assume that the two industries can be modeled as follows. The coast (C) can be used for tourism, T, or business, B, where each is a percentage so CT + CB = 100 . The jobs from businesses (in hundreds) can be modeled as B = √3CB and the number of tourists (in thousands) is T = √2CT.
From combining the first two equations we can write B = √3(100 - CT); from the third equation we can write CT = T2/2 .
a. If 100% of the coast is used for tourism, what is the maximum number of tourists? If 100% were used for business, what is the maximum number of jobs? If there were a 50/50 split, how many tourists and how many jobs?
b. Write the equation giving B as a function of T. Graph it. (You can use Excel to plot points if it's easier.)
c. What is the opportunity cost, of business given up, if the island moves from zero to one tourist unit? (You can use calculus or find the change between values.)
d. What is the opportunity cost, of business jobs given up, for each unit of tourism, if the island moves to 100% tourism? Plot the opportunity cost.
e. Do the same exercise (find opportunity cost and plot), but find opportunity cost in terms of tourists, for integer units of business jobs.
f. What is the best combination? What additional information is needed, to answer this?