answer these questions 67

Suppose the quantity demanded in the market for scooters can be expressed as

LaTeX: Q_d=1000-80p-2p_h+10p_b+12Y

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LaTeX: Q_drepresents the quantity of scooters demanded,

LaTeX: p represents the price of a scooter,

LaTeX: p_hrepresents the price of a hospital visit,

LaTeX: p_brepresents the price of a bicycle, and

LaTeX: Y represents disposable income.

In the same market, the quantity supplied can be expressed as:

LaTeX: Q_s=5000+20p

  1. Write out a simplified demand function (quantity demanded as a function of the good’s price alone) holding constant the other variables at the following values: LaTeX: p_h=500, LaTeX: p_b=300, and LaTeX: Y=1000.
  2. 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.
  3. 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.
  4. What is the cross-price elasticity between the price of a hospital visit (LaTeX: p_h) and the quantity of scooters demanded (LaTeX: Q_d) at equilibrium? What does this indicate about the relationship between these two goods?
  5. Suppose disposable income increases such that LaTeX: Y=1500. What effect does this change have on the equilibrium price and quantity? Show using a graph and mathematical explanation.
  6. 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.
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