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# Price and advertising elasticity of demand for donuts

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The demand function for Newton's Donuts has been estimated as follows:

Qx = -14 - 54Px + 45Py + 0.62Ax

where Qx represents thousands of donuts; Px is the price per donut; Py is the average price per donut of other brands of donuts; and Ax represents thousands of dollars spent on advertising Newton's Donuts. The current values of the independent variables are Ax=120, Px=0.95, and Py=0.64.

Show all of your calculations and processes. Describe your answer for each question in complete sentences, whenever it is necessary.

a.Calculate the price elasticity of demand for Newton's Donuts and describe what it means. Describe your answer and show your calculations.
b.Derive an expression for the inverse demand curve for Newton's Donuts. Describe your answer and show your calculations.
c.If the cost of producing Newton's Donuts is constant at \$0.15 per donut, should they reduce the price and thereafter, sell more donuts (assuming profit maximization is the company's goal)?
d.Should Newton's Donuts spend more on advertising?

#### Solution Preview

Qx = -14 - 54Px + 45Py + 0.62Ax

a) Price elasticity of demand using the point formula = {dQ/dPx}.{Px/Q}
dQ/dPx = -54
Px = 0.95 (given)
Qx = -14 - 54(0.95) + 45(0.64) + 0.62(120) = -14 - 51.3 + 28.8 + 74.4 = 37.9
therefore, the price elasticity of demand = (-54)(0.95/37.9) = - 1.35
It means if price change by one percent, the quantity demanded will change in the ...

#### Solution Summary

The price elasticity of demand for Newton's Donuts is very elastic. Similarly for the advertising elasticity of demand. Newton's Donuts should lower down its price to increase total revenue. And at the same time they should increase advertising expenditures since it is elastic.

\$2.19

## Supply and Demand: Markets, Prices and Price Setting

1. Explain what happens to price and quantity of coffee when the following events occur:
a. An advertising campaign highlights scientific studies that find drinking coffee can help reduce weight gain.
b. Coffee plants from major producing countries are affected by drought. (fun fact: a coffee bean is a misnomer for the seed of a coffee plant)
c. The price of tea decreases.
d. In order to protect growers that have better working conditions for workers (referred to as Fair Trade), a price floor on coffee is implemented.

For each event, you must specify how it effects either demand, quantity demanded, supply, or quantity demanded. It is also important to demonstrate how the change will affect the market demand or supply curve. Also, be sure to state any assumption you are making regarding the relationship of the event and coffee.

e.g. Price of donuts decrease.

Assume that cookies are a complement to coffee. If donuts are cheaper, then the consumer will increase quantity demanded of donuts. If consumers buy more donuts, then there will be a need for more coffee to go with the donuts so the demand for coffee will increase. This event causes a shift of the demand curve to the right. The shift will cause price and quantity of coffee to increase.

2. What are the major determinants of elasticity in your own words?

3. What type of elasticity (elastic, inelastic, zero, etc.) do you think coffee has based on the major determinants of elasticity. Explain your reasoning.

4. Based on your answer above, what happens to total revenue when the price of coffee is increased. Why?

Recall from the powerpoint presentation:

Inelastic goods (goods in which consumers are less responsive to changes in price): e < 1

Elastic goods (goods in which consumers are more responsive to changes in price): e >1

In this course, we use the absolute value of elasticity. It is always a calculated value of -1 due to the law of demand.

Rittenberg L. and T. Tregarthen (2009). Chapter 3: Demand and Supply Principles of Microeconomic Analysis. FlatworldKnowledge.com.

Rittenberg L. and T. Tregarthen (2009). Chapter 5: Elasticity and A Measure of Response Sections 1 and 2 Principles of Microeconomic Analysis. FlatworldKnowledge.com.

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