Economics GAME THEORY FINAL EXAM

1. Demand and Supply in the Housing Market (20%)

Suppose the demand function for squared meters of housing in Oslo is a standard downward sloping curve, while the supply function is a standard upward sloping curve.

(a) Draw the equilibrium in the Oslo housing market in a diagram. Explain what you show on your diagram.

(b) Suppose housing is a normal good and that income of the consumers increases sub- stantially. What happens to demand, supply, the equilibrium price and quantity? Show this on a new diagram and explain what happened.

(c) Show and explain how your answer to question “b” changes if supply was perfectly inelastic.

(d) Show and explain how your answer to question “b” changes if supply was perfectly elastic.

(e) We can formally represent the demand curve for housing in Oslo as follows D = −0.2Po + 0.1Ps + 0.5I, where D is quantity demanded, Po is the price per squared meter of housing in Oslo (downtown), Ps is the price per squared meter in Oslo’s suburbs, and I is average income of the consumers. Explain what happens to demand for housing in Oslo when Ps increases an...

2. Behavior of consumers in the market for water (15 %)

(a) The residents of Norway consume water (W ) and spend the rest of their income on other goods (O). The price of water is PW , while the price of other goods is PO. The income of a typical Norwegian is I. Write down the budget constraint for this typical 1 Norwegian and explain what each of the components mean and why this represents a budget constraint.

(b) Draw a diagram with an initial budget line, putting water on the horizontal axis. Use a standard indifference curve with a smoothly declining marginal rate of substitution to illustrate an initial optimal consumption choice for a typical Norwegian. Label this initial consumption point as “a,” and explain why it represents the optimal consumption choice.

(c) In the year 2040, Belgium is plagued by severe droughts and Norway starts exporting water to Belgium. Illustrate in your diagram the impact of the resulting increase in the price of water for your Norwegian consumer, noting that water is a normal good. Label your new consumption point as “b.” Explain how and why the Norwegian consumer changes their c...

3. Production of taxi rides (15%)

GlobalTaxi runs taxi services around the globe. GlobalTaxi uses two inputs in production: capital K and labor L. Capital has a rental cost of r, while labor is paid a wage w.

(a) Derive the expression for GlobalTaxi’s isocost function with labor on the right-hand side, and explain what it means.

(b) Explain what happens to the slope of the isocost function when the wage w increases. How will an increase in w typically affect the choice of inputs for a company that has a smoothly declining marginal rate of technical substitution? Why?

(c) Let’s fast forward to the year 2030, where GlobalTaxi is now producing taxi rides with the following production function for offering a certain number of taxi rides T : T = H + D, where H is a taxi ride delivered by a Human driver, and D is a taxi ride delivered by a Driverless car (or robot driver). Hold the number of taxi rides T constant. 2 • Derive an expression for the number of driverless taxi rides D needed to reach the number T of taxi rides, given a certain number H of human taxi rides. • What do we call the expression you derived? &...