The demand function for Einstein Bagels has been estimated as follows: Qx = -15.

Question

The demand function for Einstein Bagels has been estimated as follows:

Qx = -15.87 %u2013 40.73Px + 84.17Py + 0.55Ax

where Qx represents thousands of bagels; Px is the price per bagel; Py is the average price per bagel of other brands of bagels; and Ax represents thousands of dollars spent advertising Einstein Bagels.

      The demand function for Einstein Bagels has been estimated as follows:

Qx = -15.87 %u2013 40.73Px + 84.17Py + 0.55Ax

where Qx represents thousands of bagels; Px is the price per bagel; Py is the average price per bagel of other brands of bagels; and Ax represents thousands of dollars spent advertising Einstein Bagels. The current values of the independent variables are Ax=216, Px=0.85, and Py=0.79.

a.       Calculate the price elasticity of demand for Einstein%u2019s Bagels and explain what it means.

b.      Derive an expression for the (inverse) demand curve for Einsteins%u2019s Bagels.

c.       If the cost of producing Einstein%u2019s Bagels is constant at $0.10 per bagel, should they reduce price and thereafter, sell more bagels (assume profit maximization is the company%u2019s goal)?

d.      Should Einstein Bagels spend more on advertising?

Explanation / Answer

Qx = -15.87 - 40.73Px + 84.17Py + 0.55Ax

Py = 0.85

Ax = 216 so

Qx = -15.87 - 40.73*Px + 84.17*0.79 + 0.55*216

Qx = 169.4243 - 40.73*Px

at Px = 0.85

Qx = 134.8038

a.       Calculate the price elasticity of demand for Einstein's Bagels and explain what it means.

Ans : dQ/dP = - 40.73 ;

Price Elasticity = (dQ/dP) *(P/Q) = -40.73*0.85/166.5438 = -0.2568

elasicity > -1 ..so it is relatively inelastic ;

This means change in price is not going to affect demand much.

b.      Derive an expression for the (inverse) demand curve for Einsteins's Bagels.

Qx = -15.87 - 40.73Px + 84.17Py + 0.55Ax

40.73*Px = -15.87 - Qx + 84.17Py + 0.55Ax

Px = -0.3896 - 0.0245*Qx + 2.066*Py + 0.0135*Ax

at Ax = 216 and Py = 0.79

Px = 4.16 - 0.0245*Qx

c.       If the cost of producing Einstein's Bagels is constant at $0.10 per bagel, should they reduce price and thereafter, sell more bagels (assume profit maximization is the company's goal)?

MC =0.1

Total Revenue = Px*Qx = 4.16*Qx - 0.0245*Qx^2 ;

MR = 4.16 - 0.049*Qx

MR = MC ---for profit max.

4.16 - 0.049*Qx = 0.1

Qx = 82.857

so it should increase prices because they have to reduce no. of bagel's sold for profit max.

d.      Should Einstein Bagels spend more on advertising?

Yes . Because Quantity Demanded is Directly proportional to Ax

In Qx = -15.87 - 40.73Px + 84.17Py + 0.55Ax

if Ax increases Qx also increases

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