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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?

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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.

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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 ...

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