This question examines the market for coffee. You will use a demand schedule to

Question

This question examines the market for coffee. You will use a demand schedule to calculate the price elasticity of demand at different points along a linear demand curve and determine whether demand is elastic or inelastic at different points.

Below, you are provided with the demand schedule for coffee. Each price-quantity pair represents a point along the demand curve for coffee.

Price

(per pound of coffee)

Quantity of Coffee Demanded (pounds)

$1

300

2

240

3

180

4

120

5

60

Task 1: Calculate the price elasticity of demand between $1 and $2 using the midpoint formula.

Task 2: Is the demand for coffee elastic or inelastic between $1 and $2?

Task 3: Calculate the price elasticity of demand between $4 and $5 using the midpoint formula.

Task 4: Is the demand for coffee elastic or inelastic between $4 and $5?

Price

(per pound of coffee)

Quantity of Coffee Demanded (pounds)

$1

300

2

240

3

180

4

120

5

60

Explanation / Answer

Answer : Let for below calculations , P1 = Old price level and P2 = New price level ; Q1 = old quantity demand level and Q2 = New quantity demand level.

1) When price = P1 = $1 ; quantity demand = Q1 = 300

When price = P2 = $2 ; quantity demand = Q2 = 240

Average of price level = (P2 + P1) / 2 = (2 + 1) / 2 = 3 / 2

Average of quantity level = (Q2 + Q1) / 2 = (240 + 300) / 2 = 540 / 2

% change in price by using mid point formula = (P2 - P1) / Average price level = (2 - 1) / (3 / 2) = 1 / (3/2) = 2 / 3

% change in quantity demanded by using mid point formula = (Q2 - Q1) / Average quantity level

= (240 - 300) / (540 / 2) = - 60 / (540/2) = - (60*2) / 540 = - 120 / 540 = - 2/9

Now, price elasticity of demand = % change in quantity demanded / % change in price = (- 2/9) / (2/3) = - 1/3

Therefore, here the price elasticity of demand is - 1/3.

2) From task 1 it is clear that the pice elasticity of demand between $1 and $2 is negative because of existing negative sign. In case of negative price elasticity of demand the demand is elastic. Therefore, the coffee demand is elastic between $1 and $2.

3) When price = P1 = $4 ; Qunatity = Q1 = 120

when price = P2 = $5 ; Quantity = Q2 = 60

Average of price level = (P2 + P1) / 2 = (5 + 4) / 2 = 9/2

Average of quantity level = (Q2 + Q1) / 2 = (60+120) / 2 = 180/2

% change in price by using mid point formula = (P2 - P1) / Average price level = (5-4) / (9/2) = 1 / (9/2) = 2/9

% change in quantity demanded by using mid point formula = (Q2 - Q1) / Average quantity level

= (60-120) / (180/2) = (- 60) / (180/2) = - (60*2) / 180 = - 120 / 180 = - 2/3

Now, price elasticity of demand = % change in quantity demanded / % change in price = (- 2/3) / (2/9) = - 3

Therefore, here the price elasticity of demand = -3 .

4) From the calculation of task 3, it is clear that the price elasticity of demand between $4 and $5 is negative. As in case of negative price elasticity of demand, the demand is elastic. Therefore, coffee demand is elastic between $4 and $5 .

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