Question

The demand for Greta’s Grinders can be characterized by the following point elasticities: price elasticity = -0.8, cross-price elasticity with Melvin’s Mashers = -2, and income elasticity = 1.2. Which of the following statements is false?

1. A price increase for Greta Grinders will decrease both the number of units demanded and the total revenue Gail gets.
2. The cross-price elasticity indicates that a 4% increase in the price of Melvin’s Mashers will cause an 8% increase in quantity demanded of Greta Grinders.
3. An 8% price reduction for Greta Grinders would be necessary to overcome the effects of a 4% decline in income.
4. All the above statements are false.  

Answer 1

(a) Price elasticity = (% change in quantity demand for Greta's Grinders / % change in price for Greta's Grinders)

Suppose there is 1% increase in price for Greta's Grinders.

-0.8 = (% change in quantity demand for Greta's Grinders / 1)

% change in quantity demand for Greta's Grinders = -0.8 * 1

% change in quantity demand for Greta's Grinders = -0.8

There would be a 0.8% decrease in quantity demand for Greta's Grinders.

Tota revenue = Quantity of Greta's Grinders * Price of Greta's Grinders.

% change in total revenue = % change in the quantity of Greta's Grinders + % change in Price of Greta's Grinders.

% change in total revenue = -0.8 + 1

% change in total revenue = 0.2

There will be a 0.2 % increase in total revenue if the price increases by 1%.

So increase in price will decrease the quantity demanded and increase the total revenue.

Therefore, Option (a) is false.

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(b) Cross price elasticity = (% change in demand for Greta's Grinders / % change in price of Melvin Mashers)

-2 = (% change in demand for Greta Grinders / 4)

% change in demand for Greta Grinders = -2 * 4

% change in demand for Greta Grinders = -8

There would be an 8% decrease in the demand for Greta Grinders in response to an increase in Melvin Mashers' price by 4%.

Therefore, option (b) is false.
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(c)

Price elasticity = (% change in quantity demand for Greta's Grinders / % change in price for Greta's Grinders)

Suppose there is 8% decrease in price for Greta's Grinders.

-0.8 = (% change in quantity demand for Greta's Grinders / -8)

% change in quantity demand for Greta's Grinders = -0.8 * (-8)

% change in quantity demand for Greta's Grinders = 6.4

There would be a 6.4% increase in quantity demand for Greta's Grinders in response to decrease in price by 8%.

Income elasticity = (% change in demand for Greta Grinders / % change in inocme)

1.2 = ( % change in demand for Greta Grinders / -4)

% chnage in demand for Greta Grinders = 1.2 (-4)

% change in demand for Greta Grinders = -4.8

There would be 4.8% decrease in demand for Greta's Grinders in response to decrease in income by 4%.

Therefore, option (C) is false.

All the above statements are false.

Answer: Option (D)