Suppose the quantity demanded in the market for scooters can be expressed as
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represents the quantity of scooters demanded,
represents the price of a scooter,
represents the price of a hospital visit,
represents the price of a bicycle, and
represents disposable income.
In the same market, the quantity supplied can be expressed as:
- Write out a simplified demand function (quantity demanded as a function of the goodâ€™s price alone) holding constant the other variables at the following values: , , and .
- Using the above equations, find the equilibrium price and quantity in the market. Draw a (fully labeled) supply and demand graph representing this market and its equilibrium.
- What is the price elasticity of demand at the equilibrium price and quantity? Be sure to note if demand is relatively elastic or inelastic at equilibrium.
- What is the cross-price elasticity between the price of a hospital visit () and the quantity of scooters demanded () at equilibrium? What does this indicate about the relationship between these two goods?
- Suppose disposable income increases such that . What effect does this change have on the equilibrium price and quantity? Show using a graph and mathematical explanation.
- Return to the original supply and demand conditions and equilibrium found in Questions 1 and 2. Suppose a price ceiling, defining a maximum price of $50, is imposed on this market. How does this affect the quantities of scooters demanded and supplied? Show using a graph and mathematical explanation, being sure to indicate any shortage or surplus.