# Calculate the questions

**nstructions: **Use the information below to answer the following questions. You will submit your assignment (on paper) at the beginning of class on Thursday 9/6. No late submissions will be accepted.

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

${}_{}$

Q

d

=

1000

−

80

p

−

2

p

h

+

10

p

b

+

12

Y

,

where:

${}_{}$

Q

d

represents the quantity of scooters demanded,

$p$

represents the price of a scooter,

${}_{}$

p

h

represents the price of a hospital visit,

${}_{}$

p

b

represents the price of a bicycle, and

$Y$

represents disposable income.

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

${}_{}$

Q

s

=

5000

+

20

p

.

- 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:

${}_{}$

p

h

=

500

,

${}_{}$

p

b

=

300

, and

$Y$

=

1000

.

- 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 (

${}_{}$

p

h

) and the quantity of scooters demanded (

${}_{}$

Q

d

) at equilibrium? What does this indicate about the relationship between these two goods?

- Suppose disposable income increases such that

$Y$

=

1500

. 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.