Answers to Homework #3
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Part I: Excise Tax
1. Consider the ice cream market in Madison. In July, the ice cream market demand and supply curves are given by the following equations where Q is the quantity to ice cream units and P is the price in dollars per unit of ice cream:
Demand: Q = 14000 – 10P
Supply: Q = 2000 + 20P
a) Find the equilibrium price and quantity of ice cream in July.
In equilibrium, we know that the quantity demanded = quantity supplied. Thus, by solving the two equations, we have the equilibrium price = $400 per unit of ice cream and the equilibrium quantity = 10,000 units of ice cream.
b) Calculate the price elasticity of demand and supply at the equilibrium price in July. Use the point elasticity formula to compute these two values of these elasticities.
The point elasticity of demand formula is
Elasticity of Demand = (-1/slope)(P/Qd)
and the point elasticity of supply formula is
Elasticity of Supply = (1/slope)(P/Qs)
At the equilibrium quantity and price we know (Q, P) = (10000, 400). We also have the demand and supply equations, but they are not in slope-intercept form. So, rewriting the two equations in slope-intercept form we have:
Demand Equation: P = 1400 – (1/10)Qd
Supply Equation: P = (1/20)Qd – 100
Now, we are ready to use the point elasticity formulas:
Point Elasticity of Demand = [-1/(-1/10)][400/10000] = .4 (hence, demand is inelastic at the point of equilibrium in this market)
Point Elasticity of Supply = [1/(1/20)][400/10000] = .8
In October, ice cream demand in Madison decreases. So, the new demand curve is given by
Demand: Q = 7000 – 30P
Assume the supply curve doesn’t change.
c) Find the equilibrium price and equilibrium quantity in October, and calculate the price elasticity of demand and supply at this new equilibrium price. Use the point elasticity formula in calculating these values.
By solving the two equations, we obtain the equilibrium price of $100 per unit of ice cream and quantity of 4,000 units.
To find the price elasticity of demand using the point elasticity formula:
Price elasticity of demand = [(-1)/(-1/30)][100/4000] = (30)(1/40) = .75
To find the price...