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Consumer Demand Analysis and Estimation Applied Problems
Please complete the following two applied problems:
Problem 1:
Patricia is researching venues for a restaurant business. She is evaluating three major attributes
that she considers important in her choice: taste, location, and price. The value she places on
each attribute, however, differs according to what type of restaurant she is going to start. If she
opens a restaurant in a suburban area of Los Angeles, then taste is the most important attribute,
three times as important as location, and two times as important as price. If she opens a
restaurant in the Los Angeles metropolitan area, then location becomes three times as important
as taste and two times as important as price. She is considering two venues, respectively, a steak
restaurant and a pizza restaurant, both of which are priced the same. She has rated each attribute
on a scale of 1 to 100 for each of the two different types of restaurants.
Steak RestaurantPizza Restaurant
Taste
80
70
Location
55
80
Price
65
50
Show all of your calculations and processes. Describe your answer for each question in complete
sentences.
1. Which of the two options should Patricia pursue if she wants to open a restaurant in a
suburban area of Los Angeles? Calculate the total expected utility from each restaurant
option and compare. Graph is not required. Describe your answer, and show your
calculations.
Weight of taste attribute=3
Weight of price attribute=2
Weight of location attribute=1
Total expected utility for steak restaurant=80*3+55*1+65*2=425
Total expected utility for pizza restaurant=70*3+80*1+50*2=390
Patricia should open a steak restaurant in the suburban area of Los Angeles since the total
expected utility of opening a steak restaurant is higher than the total expected utility of
opening a pizza restaurant.
2. Which of the two options should she pick if she plans to open a restaurant in the Los
Angeles metropolitan area? Describe your answer, and show your calculations.
Weight of taste attribute=1
Weight of price attribute=2
Weight of location attribute=3
Total expected utility for steak restaurant=80*1+55*3+65*2=375
Total expected utility for pizza restaurant=70*1+8*3+50*2=410
Patricia should open a pizza restaurant in the metropolitan area of Los Angeles since the total
expected utility of opening a pizza restaurant is higher than the total expected utility of opening a
steak restaurant.
3. Which option should she pursue if the probability of finding a restaurant venue in a
suburban area can be reliably estimated as 0.7 and in a metropolitan area as 0.3? Describe
your reasoning and show your calculations.
For steak restaurant total utility taking into consideration the availability of a venue in
both locations
0.7*425+0.3*375=410
For pizza restaurant total utility taking into consideration the availability of a venue
0.7*390+0.3*410=396
Comparing the values above it will be prudent for Patricia to open the steak restaurant
since its value is higher than that of pizza restaurant.
4. Provide a description of a scenario in which this kind of decision between two choices,
based on weighing their underlying attributes, applies in the “real-world” business
setting. Furthermore, what are the benefits and drawbacks, if any, to this method of
decision making?
Problem 2:
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.
1. Calculate the price elasticity of demand for Newton’s Donuts and describe what it means.
Describe your answer and show your calculations.
Price elasticity of demand = (dQx/dPx )* (Px/Qx)
Qx=37.9
Price elasticity of demand = - 54 * 0.95/37.9
= - 1.35
It means that holding other thing constant , if price of X increases by 1% , then quantity
demanded of X will decrease by 1.35%.This means demand will decrease (increase)
1.35% when price increase (decrease) 1%
2. Derive an expression for the inverse demand curve for Newton’s Donuts. Describe your
answer and show your calculations.
Inverse Demand Curve function: Px = f(Qx)
Qx = -14 - 54Px + 45Py + 0.62 Ax
=> Px = 1/54( -Qx - 14 + 45 Py + 0.62 Ax)
Pluge in Py=0.64 and Ax=120 ( assume they are constant) : Px = 1/54 ( -Qx +89.2
3. 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)?
Because the elasticity is -1.35 => if they decrease price by 1%, the demand will increase
1.35% => They can decrease the price at an extent to increase profit; but they can only do
that until the elasticity get to 1
4. Should Newton’s Donuts spend more on advertising?
with $1000 increase in advertising cost, the demand will increase by 620 donuts.
The profit you receive from an increase of 620 donuts is 620 x ( 0.95 - 0.15) = 496 < 1000 cost
of adverstising
=> No increase in advertising
Answer: Qx = -14 – 54Px + 45Py + 0.62Ax At Ax=120, Px=0.95, and Py=0.64 , Qx = 37.9 a)
Price elasticity of demand = dQx/dPx * Px/Qx = - 54 * 0.95/37.9 = - 1.35 It means that holding
other thing constant , if price of X increases by 1% , then quantity demanded of X will decrease
by 1.35%. b) An inverse demand function is a function p(q) that maps from a quantity of output
to a price in the market . Hence , inverse demand function is given by : 54Px = -14 – Qx + 45Py
+ 0.62Ax Px = -0.26 - 0.018Qx + 0.83Py + 0.01Ax c) As , Marginal cost is constant , Profit will
be maximize when MR = MC and we are having MR>MC . So , quantity should be increased