The document discusses the demand function for Apple Watches and calculates key metrics to determine pricing. It finds: 1) Monthly demand is estimated at 177,200 units 2) Price elasticity is -4.73, indicating demand is elastic to price changes 3) The profit-maximizing price is $300.42 per unit with production of 293,800 units, while the revenue-maximizing price is lower at $211.42 per unit with production of 507,400 units. Profits are maximized at a lower output and higher price compared to revenue maximization.

1. Assignment 2:
Solution 1:
The estimated demand function is:
Q = -2,000 + 1,000P
Based on this demand function, if the price of the Apple Watch is increased to $399, the
quantity demanded would fall to 1.5 million units. However, at a price of $349, the quantity
demanded would be 2 million units. Thus, the launch team should have argued for a price of
$399 in order to maximize revenue.
Step-by-step explanation
Total revenue can be calculated using the following formula:
Total revenue = Quantity demanded x Price
At a price of $349, total revenue would be $698 million. However, at a price of $399, total
revenue would be $750.5 million. Thus, the launch team would have been able to increase
revenue by $52.5 million by charging a higher price.
The cost of producing each Apple Watch is $288. Thus, at a price of $349, the company
would have a profit margin of $61 per watch. However, at a price of $399, the company
would have a profit margin of $111 per watch. Thus, the launch team should have argued
for a higher price in order to maximize profits.
Solution 2:
Step-by-step explanation
the demand function for apple watch is given by:
QAW = -150,000 - 2400 PAW + 1520PGearS + 1200 PPebble - 1200 PiPhone6 + 44 A
given:
PAW =$349
PGearS =$380
PPebble =$220
PiPhone6 =$299
A=$15,500
substitute to get the quantity demanded
QAW = -150,000 - 2400 PAW + 1520PGearS + 1200 PPebble - 1200 PiPhone6 + 44 A
QAW = -150,000 - 2400(349)+ 1520(380) + 1200(220) - 1200(299) + 44 (15,500)
QAW= 177,200
Solution 3:
Đề gốc: Please read the case below and answer the following questions....
Please read the case below and answer the following questions. Please show your
calculations or attach a spreadsheet showing how you calculated each of the
responses:

2. As the Apple Watch team planned for their US launch for the first quarter of 2015, an
estimated monthly demand function for the US market was derived as shown in
Figure 1:
QAW =-150,000 -2400PAW +1520PGearS +1200PPebble -1200PiPhone6 +44A
Where QAW is the quantity demanded of the Apple Watch per month, PAWis the
price of the Apple Watch (dollars per unit), PGearS is the price of the Samsung Gear
S watch (dollars per unit), PPebble is the price of the Pebble Steel (dollars per unit),
PiPhone6 is the price of the mid-range iPhone 6 smartphone (dollars per unit), A is
the quarterly targeted advertising budget for the Apple Watch (in thousands of
Dollars per quarter). The estimated values are: PAW = $349, PGearS = $380,
PPebble = $220, PiPhone6 = $299, A = $15,500 . Calculate the following.
1. Calculate the Monthly estimated Quantity demanded for Apple Watch QAW
2. Use the relevant information from the estimated monthly demand function to
calculate the elasticity values for each of the explanatory variables and
interpret what the numbers mean.
3. Construct the Demand equation, Inverse Demand Equation
4. If the Marginal cost is assumed to be constant at $178, calculate and compare
the Profit Maximizing Price and Quantity with the Revenue Maximizing Price
and Quantity. Comment on your findings.
1.
QAW=177.200 units
2.
a)
Elasticity for PAW=-4.73
Apple watch has an elastic demand; its price elasticity of demand is greater than 1. A 1%
increase in price of apple watch will reduce its quantity demanded by 4.73%. A 1%
decrease in price of apple watch will increase its quantity demanded by 4.73%
b)
Elasticity for PGearS=3.26
Samsung gear S watch is a substitute product to Apple watch; the cross price elasticity
between Samsung gear S watch and apple watch is positive. A 1% increase in price of
Samsung gear S watch will increase demand of Apple watch by 3.26%. A 1% decrease in
price of Samsung gear S watch will decrease demand of Apple watch by 3.26%
c)
Elasticity for PPebble=1.49
Pebble steel is a substitute product to Apple watch; the cross price elasticity between
pebble steel and apple watch is positive. A 1% increase in price of Pebble steel will
increase demand of Apple watch by 1.26%. A 1% decrease in price of Pebble steel will
decrease demand of Apple watch by 1.26%

3. d)
Elasticity for PiPhone6=-2.02
IPhone 6 is a complement product to Apple watch; the cross price elasticity between
Iphone 6 and apple watch is negative. A 1% increase in price of IPhone 6 will increase
reduce of Apple watch by 2.02%. A 1% decrease in price of IPhone 6 will increase demand
of Apple watch by 2.02%.
e)
Advertisement elasticity=3.85
A 1% increase in advertising budget will increase demand of apple watch by 3.85%. A 1%
decrease in advertising budget will decrease demand of apple watch by 3.85%.Apple watch
has an elastic advertising elasticity of demand; its advertising elasticity is greater than 1.
3.
Demand function;QAW=1,014,800-2400PAW
Inverse Demand function;PAW =422.8333-QAW/2400
4.
Profit maximising price and quantity is $300.42 and 293,800 units respectively
Revenue maximising price and quantity is $211.42 and 507,400 units respectively
Profit is maximised at a much lower output and higher price than revenue.
Step-by-step explanation
1.
QAW =-150,000-2400PAW+1520PGearS+1200PPebble-1200PiPhone6+44A
We substitute the values of PAW, PGearS, PPebble, PiPhone6 and A in the equation to
determine the quantity demanded
QAW=-150,000-2400*349+1520*380+1200*220-1200*299+44*15500
QAW=-150,000-837600+577600+264000-358800+682000
QAW=177.200 units
2.
a)
Elasticity for PAW=∂QAW/∂PAW*PAW/QAW
Elasticity for PAW=-2400*349/177200
Elasticity for PAW=-4.73
Apple watch has an elastic demand; its price elasticity of demand is greater than 1. A 1%
increase in price of apple watch will reduce its quantity demanded by 4.73%. A 1%
decrease in price of apple watch will increase its quantity demanded by 4.73%
b)
Elasticity for PGearS=∂QAW/∂PGearS*PGearS/QAW
Elasticity for PGearS =1520*380/177200
Elasticity for PGearS=3.26
Samsung gear S watch is a substitute product to Apple watch; the cross price elasticity
between Samsung gear S watch and apple watch is positive. A 1% increase in price of
Samsung gear S watch will increase demand of Apple watch by 3.26%. A 1% decrease in
price of Samsung gear S watch will decrease demand of Apple watch by 3.26%
c)

4. Elasticity for PPebble=∂QAW/∂PPebble*PPebble/QAW
Elasticity for PPebble =1200*220/177200
Elasticity for PPebble=1.49
Pebble steel is a substitute product to Apple watch; the cross price elasticity between
pebble steel and apple watch is positive. A 1% increase in price of Pebble steel will
increase demand of Apple watch by 1.26%. A 1% decrease in price of Pebble steel will
decrease demand of Apple watch by 1.26%
d)
Elasticity for PiPhone6=∂QAW/∂PiPhone6*PiPhone6/QAW
Elasticity for PiPhone6=-1200*299/177200
Elasticity for PiPhone6=-2.02
IPhone 6 is a complement product to Apple watch; the cross price elasticity between
Iphone 6 and apple watch is negative. A 1% increase in price of IPhone 6 will increase
reduce of Apple watch by 2.02%. A 1% decrease in price of IPhone 6 will increase demand
of Apple watch by 2.02%.
e)
Advertisement elasticity=∂QAW/∂A*A/QAW
Advertisement elasticity=44*15500/177200
Advertisement elasticity=3.85
A 1% increase in advertising budget will increase demand of apple watch by 3.85%. A
1% decrease in advertising budget will decrease demand of apple watch by
3.85%.Apple watch has an elastic advertising elasticity of demand; its advertising
elasticity is greater than 1.
3.
QAW =-150,000-2400PAW+1520PGearS+1200PPebble-1200PiPhone6+44A
We substitute the values of PGearS, PPebble, PiPhone6 and A in the equation to determine
the quantity demanded
QAW=-150,000-2400PAW+1520*380+1200*220-1200*299+44*15500
QAW=-150,000-2400PAW+577600+264000-358800+682000
QAW=1,014,800-2400PAW
In order to determine the inverse demand function, we make PAW the subject
QAW=1,014,800-2400PAW
2400PAW=1014800-QAW
PAW =(1014800-QAW)/2400
PAW =422.8333-QAW/2400
4.
Profit maximisation
Profit is maximised at the level of output where MR=MC
P=422.8333-Q/2400
TR=P*Q
TR=(422.8333-Q/2400)*Q
TR=422.8333Q-Q2
/2400
MR=∂TR/∂Q
MR=422.8333-Q/1200
MC=178
Therefore;
422.8333-Q/1200=178

5. Q/1200=422.8333-178
Q/1200=244.8333
Q=244.8333*1200
Q=293,800
P=422.8333-293800/2400
Price=300.42
Profit maximisation
Revenue is maximised at the level of output where MR=0
P=422.8333-Q/2400
MR=422.8333-Q/1200
Therefore;
422.8333-Q/1200=0
Q/1200=422.8333
Q=422.8333*1200
Q=507,400
P=422.8333-507400/2400
Price=$211.42
Profit is maximised at a much lower output and higher price than revenue. Revenue is
maximised at higher output levels because the more watches are sold, the higher the
revenue. However the increase in output also increases production costs as much as it
increases revenue. Profits increase with output initially then start to decline. Therefore
profits are not maximised at the highest output level