Bus 640 - Consumer Demand Analysis and Estimation Applied Problems

...

- Calculate the price elasticity of demand for Newton’s Donuts and describe what it means. Describe your answer and show your calculations.

Solution

Price elasticity of Demand for Newton’s Donuts is the percentage change in the demand of Newton’s donuts for per unit change in its price

Qx = -14 – 54Px + 45Py + 0.62Ax

DQx / dPx = - 54

So, price elasticity of Demand of Newton’s Donuts is -54. It means that for every unit percentage increase in price of bagel, the demand decreases by 54 times

- Derive an expression for the inverse demand curve for Newton’s Donuts. Describe your answer and show your calculations.

Solution

Demand of Donut’s is

Qx = -14 – 54Px + 45Py + 0.62Ax

- 54Px = -14 –Qx + 45 Py + 0.62 Ax

- Px = 1/54( -14 – Qx + 45Py + 0.62Ax)

So, the price of Newton’s Donut depends upon the demand of Donuts, the price of competitor bagels and the advertising spent

If we assume Py and Ax to be constant

Px = 1/54( -14 – Qx + 45*0.64 + 0.62*120) = 1/54 (89.2 – Qx)

- 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)?

Solution

At current price of $0.95,

Qx = -14 – 54Px + 45Py + 0.62Ax = -14 – 54*0.95 + 45*0.64 + 0.62*120 = 37.9 thousand

Profit = 37900*0.95 – 37900*0.15 = $30320

If the cost of Purchase is $0.15

Profit = Revenue – Cost = (Px*Qx) – 0.15*Qx = 1/54 (89.2 – Qx)*Qx – 0.15Qx

So,

For profit maximization

D(profit)/dQx = 1/54 (89.2 – 2Qx) – 0.15 = 0

- Qx = 40.55 thousand bagel = 40550 bagels

Price, Px = 1/54 (89.2 – Qx) = 1/54*(89.2 – 40.55) = $0.90

Profit = 4050*1.63 – 40550*0.15 = $30412.5

So, we see that if price is reduced by 5 cents to $0.9 per bagel, the profit increases by 30412.5 – 30320 = $92.5

- Should Newton’s Donuts spend more on advertising?

Solution

Qx = -14 – 54Px + 45Py + 0.62Ax

DQx / dAx = 0.62

So, for every percentage increase in advertising the demand increases by 0.62%

So, they should spend more on advertising

Reference:

Douglas, E. (2012). Managerial Economics (1st ed.). San Diego, CA: Bridgepoint Education.