Question

Answer the following questions and show all working. Use the midpoint formula to calculate elasticities.

1.    If the price elasticity of demand is 4.0 (in absolute terms), then a 10% off sale would lead to what change in quantity demanded? Let’s say customer purchases were 200,000 before the sale, what would be the total number of customer purchases after the sale? (4) show working

2.    The price of stadium seats at a baseball game increases from $20 to $30 and ticket sales fall from 45,000 per game to 35,000 per game. If other things remained constant, what is the price elasticity of demand? State whether it is elastic or inelastic and explain how this can be determined from the total revenue rule? (5) show working

3.    Calculate the elasticity of supply when an increase in demand causes the equilibrium price and quantity to change from $2.00 and 500 to $2.80 and 1,000, respectively and state whether it is elastic or inelastic? (4) show working

              4. Suppose that when good X price increases from $3.00 to $4.00 the quantity of good Y also increases from 150 to 250. What is the cross price elasticity of good X and Y and are they complements or substitutes. (4) show working

                                             

5.    If the demand for widgets increases from 8 to 12 as a result of an increase in average incomes from $28,500 per year to $31,500 per year, what is the income elasticity of demand for widgets and is widget a normal or inferior good? (4) show working

                                             

6.    If the elasticity of supply of a good was 2, how much would the price have to increase to lead to an increase in output of 6 percent? (2) show working

7.    Fantastic Cuts Hair Salon knows that a 15% increase in the price of their haircuts will result in a 5% decrease in the number of haircuts sold. What is the elasticity of demand facing Fantastic Cuts? If Fantastic Cuts Hair Salon is concerned about increasing their total revenues, should proceed with this increase in price? Explain. (5) show working

Answer 1

Question 1

Price elasticity of demand = 4

It has been stated that there is 10% off sale.

10% off sale implies a price decrease. When price decreases, quantity demanded increases.

So,

Percentage change in price = 10%

As we know that,

Price elasticity of demand = % change in quantity demanded/% change in price

So,

% change in quantity demanded = Price elasticity of demand * % change in price

% change in quantity demanded = 4 * 10 = 40%

So,

The quantity demanded will increase by 40%.

Initial quantity demanded = 200,000

% increase in quantity demanded = 40%

Increase = 200,000 * 0.40 = 80,000

New quantity demanded = Initial quantity demanded + Increase = 200,000 + 80,000 = 280,000

So,

The total number of customer purchases after the sale is 280,000.