Consumer Demand Analysis and Estimation Applied Problems

Roshima is considering two options of studying for her MBA degree: the MBA program at Arizona State University (ASU) and the MBA program at University of Phoenix (UOP). To make a decision about which of the two options is better for her, she needs to compare the total expected utility from both universities. The total expected utility is calculated as a sum of three major attributes: ranking, price and location. She rated each attribute on a scale of 1:100, as in the table:

AttributeASUUOP
Ranking 80 70
Location 50 70
Price 45 45

Table 1. Attribute rates.

The value she places on each attribute differs, depending if she remains full-time employed or quits her job. If Roshima continues to work full time, then the location would be the less important attribute. Its coefficient of importance will be equal to 1. The ranking is three times as important as location. Its coefficient is 3. The price is two times less important than the ranking. Therefore, its coefficient is equal 1.5.

If Roshima quits her job and attends school full time, then location will become the most important factor. Its coefficient is 3. Ranking becomes the less important attribute with coefficient of importance equal 1. And the price is twice less important than ranking. Its coefficient will be 1.5.

Let us rewrite the table of the attribute rates with the coefficients of importance of the attributes in different cases:

AttributeASUUOPKempKquit
Ranking 80 70 3 1
Location 50 70 1 3
Price 45 45 1.5 1.5

Table 2. Attribute rates and importance coefficients.

Recalculate the value of utility levels, considering the importance of factors:

If Roshima continues to work full time, then the values of utility level, considering their importance, are the following:

  • ASU
  • 80 * 3 = 240
  • 50 * 1 = 50
  • 45 * 1.5 = 67.5
  • UOP
  • 70 * 3 = 210
  • 70 * 1 = 70
  • 45 * 1.5 = 67.5

If Roshima quits her job and attends school full time, then the values of utility level, considering their importance, are the following:

  • ASU
  • 80 * 1 = 80
  • 50 * 3 = 150
  • 45 * 1.5 = 67.5
  • UOP
  • 70 * 1 = 70
  • 70 * 3 = 210
  • 45 * 1.5 = 67.5

The total expected utility are calculated as a sum of utilities of all attributes. Thus, for the full-time work the ASU total expected utility is calculated as: TEU(ASU,work) = 240 + 50 + 67.5 = 357.5, and the UOP’s total expected utility is calculated as: TEU(UOP,work) = 210 + 70 + 67.5 = 347.5.

For the full-time study: TEU(ASU,study) = 80 + 150 + 67.5 = 297.5 and TEU(UOP,study) = 70 + 210 + 67.5 = 347.5. Rewrite the table of attribute rates, considering the importance of factors and add the total expected utilities:

AttributeFull-time workFull-time study
ASUUOPASUUOP
Ranking 80 70 3 1
Location 50 70 1 3
Price 45 45 1.5 1.5

Table 3. Attribute rates with different importance and total expected utilities.

By comparing the total expected utilities of the two options, we can see that if Roshima wants to keep her full time job, then she should pursue the MBA program at Arizona State University. Its total expected utility 357.5 is higher than the total expected utility of the MBA program at University of Phoenix, which is 347.5.

If Roshima plans to quit her job and dedicate to her studies, then she should pick the University of Phoenix, because its total expected utility 347.5 is higher than total expected utility of the second option, which is 297.5.

If the probability of being laid off and unable to find a new job is estimated as 0.6, then the total expected utilities of the options are calculate as:

TEU(ASU,0.6) = 357.5%u22190.4 + 297.5%u22190.6 = 321.5

TEU(UOP,0.6) = 347.5%u22190.4 + 347.5%u22190.6 = 347.5

Total expected utility of UOP, which is 347.5, is higher than the total expected utility of ASU. Thus, in this case Roshima should pursue the MBA program at University of Phoenix.

The demand function for Einstein Bagels has been estimated as follows: Qx = -15.87 - 40.73Px + 84.17Py + 0.55Ax, where Qx is the thousands of bagels; Px represents the price per bagel; Py is the average price per bagel of other brands of bagels; 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.

The price elasticity of demand is the measure of responsiveness of demand value to changes in price. It is calculated as derivative of the expression:

Edp = Q’(Px) = -40,73%u2219(Px/Qx)

Knowing the current values of independent variables, calculate Qx from expression:

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

Qx = -15.87 - 40.73%u22190.85 + 84.17%u221979 + 0.55%u2219216 = 134.8038

Using the value Qx, calculate the price elasticity of demand as following:

Edp = Q’(Px) = -40,73%u2219(0.85/134.8038) = -0.2568.

It means that changes in price will cause lower changes in the amount of demand. Thus, lowering the price for 1% will cause increasing of demand value only by 0.2568%.

An expression for the inverse demand curve for Einstein’s Bagels is the following:

Px = (-15.87 + 84.17Py + 0.55Ax - Q)/40.73

Px = -0.3896 + 2.0665Py + 0.0135Ax - (Q/40.73)

They should not reduce the price to sell more bagels if the cost of producing Einstein’s Bagels is constant at $0.10 per bagel. If profit maximization is the company’s goal, then the condition of profit maximization is MR = MC, where MR represents marginal revenue and MC is marginal cost. If the cost of producing is constant, then it is equal to the marginal revenue.

Thus, MC = $0.10.

Calculate the marginal revenue as derivative of the total revenue (TR):

TR = Px%u2219Qx = -0.3896%u2219Qx + 2.0665%u2219Py%u2219Qx + 0.0135%u2219Ax%u2219Qx - (Qx2/40.73)

MR = (TR’) = -0.3896 + 2.0665%u2219Py + 0.0135%u2219Ax - (Qx/20.365) = 0.10

Knowing the current values of independent variables, calculate Qx and Px from expression above:

Qx = 82.6602

Px = -0.3896 + (2.0665%u22190.79) + 0.0135%u2219216 - (82.6602/40.73) = 2.12

Thus, for the profit maximization they should increase the price to $2.12 per bagel. Einstein Bagels should not spend more on advertising due to low advertising elasticity of demand:

Ead = 0.55%u2219(216/134.8038) = 0.8813

It means that advertising spending will grow faster than the value of demand.

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