1. A Kid Scout wants to sell cookies to as many people as she can. The demand function is as follows:
Q = f (P, E, R, C, H, T)
Where P = price per box
The demand equation facing the Kid Scout is:
Q = 27 + 73P - 3E + 68R - 52C - 5H + 12T
a. For the last three years the price of a box of cookies has been $2.50, the economy has been steady at 5.25, most of her customers have purchased from her before (or are family members) so she believes that they would rate her an 80, competition has been stiff this year as the other council started selling 14 days earlier, and as usual the taste is good (she would give it a 92), there are three varieties of lower fat cookies available also. How many boxes should she expect to sell this year?
QEXP = -450 - 7.3(2.50) + 3 (5.25) + 6.8 (80) - 5.2 (14) - 5 (3) + 1.2(92)=114.1
Þ 115 boxesb. Assuming for the duration of this sale, all factors stay constant with the exception that when her grandmother found out she was selling, dear old granny asked her bridge club and friends at work to buy cookies from her little darling. What would be the revised demand function, and the inverse demand function (based on this relationship)?
QNEW = -429.90 + 6.8 RO
RO = -63.22 + 0.147 QNEW
c. The cost for the troop is $2.14 per box. If it could change its price, keeping all other factors equal to the original values, what would be the profit - maximizing output, price and profit?
Based on price, the demand function equals:
Q = 132.35 - 7.3 P or P = 18.13 - 0.137 Q
Thus MR = 18.13 - 0.274 Q
Setting MR=MC where MC=2.14: 18.13 - 0.274 Q = 2.14
Q = 58.36
Þ 59 boxes and P = $10.14p
= TR - TC = 613.60 - 126.26 = $487.34
d. The competitor council has been charging $3.00 a box for the same cookies. What would be the price elasticity if our troop changed its price also and what would the effect be on the quantity of boxes sold? Graph the demand curve (with respect to price) and show these elasticity's. Which price is more elastic?
Using Q = 132.35 - 7.3 P
at P1 = $2.50, Q1 = 115
at P2 = $3.00, Q2 = 111
Therefore, quantity will decrease with the increase in price
Ep1 = (-7.3) (2.50/115) = -0.159
Ep2 = (-7.3) (3.00/111) = -0.197
(The
demand curve is slightly more elastic at P2 than P1)
e. Using an Ep of 3.28 what would the optimum markup price be? What would it be at an Ep of -0.328?
P = ( Ep )/(1+EP) * MC = $1.64
The Ep of -0.328 is inelastic so that profit at the corresponding price cannot be maximized
f. This troop decides that the best way to earn money is to take donations for the cookies and let customers determine their own price (above their cost) per box. What kind of price discrimination is this? What would be the maximum profit possible for this girl?
This is an example of perfect price discrimination (if customers voluntarily pay the maximum on their demand curve. Will they?)
At a price equal to cost ($2.14), Q = 116.73
Þ 117 boxesp
= 0.5(117)(18.13-2.14) = $935.42
2. CAF Corporation manufactures covers in India at a marginal cost of $10 and ships them to the United States for $2.
The price equations are: PI = 11 - .0005QI PUS = 200 - .002QUS
a. What are the optimal sales quantities and prices for CAF in each market?
b. Due to a shipping shortage, shipping costs have increased $10 per cover. What effect does this have on the optimal price and quantity in the U.S. market.
Answers
a. MRI = MCI
-.001QI + 11 = 10
QI = 1000
PI = 10.50
MRUS = MCUS
-.004QUS + 200 = 12
QUS = 47000
PUS = 106
b.
MRUS = MCUS2
-.004QUS2 + 200 = 22
QUS2 = 44500
PUS2 = 111
c.
P = TR - TC
P = (TRI + TRUS)- (TCI + TCUS)
P 1 = (10500 + 1982000) - (10000 + 564000)
P 1 = 4418500
P 2 = (10500 + 4939500) - (10000 + 979000)
P 2 = 3961000
Total Profit decreases 19.8%
d.
Demand in the U.S. is much more inelastic than the demand in India.