ECON 361 – Mini Case on Pricing  - Some Answers (but not all)

You own an ice cream factory and retail store.  You are trying out some new pricing strategies.

1.       You have been thinking about trying second degree price discrimination when selling your cones in your retail outlet.  The marginal cost (MC) of each cone is $1.50.  You have demand information that tells you that your customers are willing and able to pay $4.00 for the first cone but only $3.00 for the second cone.

Explain how much you would “net” (P = MR – MC) if:

a.      You charge $3.00 for both the 1st and 2nd cones.

     $6.00 - 3.00 = $3.00

b.      You charge $4.00 for both the 1st and 2nd cones.

     $4.00 - 1.50 = $2.50

c.       You price discriminate and charge $4.00 for the first and $3.00 for the second

$7.00 - $3.00 = $4.00

d.      Should you price discriminate?  Explain. 

 Yes, you make an addition $1.00 over charging the same price (next best option).

e.   What about a way to use third degree price discrimination at your ice cream store?  Justify your scheme – don’t just make up something that does not have a good justification.

2.       Your factory produces different flavors of ice cream that consumers consider to be substitutes for each other.  In particular, your demand analysis indicates that your Rocky Road (RR) and Stoney Lane (SL) flavors are close substitutes.  You are trying to determine your marginal revenue for each (while considering the substitute).  You have the following information:

You can sell 1,000 gallons of RR for $5.00 each.

You can sell 1,000 gallons of SL for $5.00 each.

When you sell 1,000 gallons of RR, sales of SL decrease by 300 gallons.

When you sell 1,000 gallons of SL, sales of RR decrease by 400 gallons.

What is the MR of RR when you sell 1,000 gallons? 

 This is asking about change in total revenue when your change in QRR is 1000 gallons (MR).  Increase sales by 1000 x $5 - 300 x $5 = 5000 - 1500 = $3500.

What is the MR of SL when you sell 1,000 gallons? 

 This is asking about change in total revenue when your change in QSL is 1000 gallons (MR).  Increase sales by1000 x $5 - 400 x $5 = 5000 - 2000 = $3000

You then use this information to equate your MR with your MC for each product to determine your output level for each.  Had you not taken into consideration your substitutes, would your output level estimates been over or under stated – explain? 

 Overstated.  Your marginal revenue would have been higher than it should be and you would have overproduced the good.

3.     Your plant automatically produces fruit pulp when it makes fruit flavored ice cream.  The pulp (and the ice cream) can both be sold in the market.  You have the following information (per case of ice cream/pulp for one hour).

MC of producing the pulp and ice cream jointly is:  MC = 40 + 6Q

Demand and MR equations are:

Ice Cream:  Qd = 60 – 2P and MR = 30 – 1Q

Pulp:  Qd = 50 – 1P and MR = 50 – 2Q

Determine your best output and price levels.

Output: 

40 + 6Q = 80 - 3Q

40 = 9Q

Q = 4.44

Price of Ice Cream:

30 - 4.44(.5)  = P

P = $27.78

Price of Pulp: 

50 - 4.44 = P

P = $45.56

Are you sure this output level and these prices won’t lead to a negative MR for one of your products?  You better check:

MR ice cream =

 $25.56

MR pulp =

 $41.12

Now draw two graphs – one for ice cream and one for pulp.  Put your D and MR curves on the graphs.  Show numbers in the right places for your output level, MR and P for each good (numbers that you determined above). 

4.  You have not decided to add a sugar processing factory to your business.  You also decide to make both the ice cream factory and the sugar factory profit centers.  Since your ice cream factory uses sugar as an input you are trying to decide your transfer price.  What would it be if:

a.  there is an external market for your sugar?

 The market price - best indicator of consumer value.

b. there is no external market for your sugar.  You have determined that the MC of your ice cream at an output level of 100 units is $18 and the MC of the sugar at 100 units is $10.  Given that the output level of 100 is “profit maximizing – or better, satisficing” – graphically represent your pricing decision (you don’t have actual numbers for your two prices so just use Pic and Ps on your graph).  Put all other numbers on your graph.