Question

 

Price of $13 in California

You manage a farm that is looking to sell oranges in both California and Oregon. The demand for oranges in California is given by P^CA = 25 - 0.5Q_^CA and the demand for oranges in Oregon is P^OR = 19 - 0.3Q^OR. The total cost of selling oranges is TC = 10 + Q and the marginal cost is constant at MC = $1. If you cannot differentiate between customers in California and Oregon, and you are forced to charge the price that is optimal in California in both Oregon and California, how much profit will you lose compared to the profit you made in (2)?  

Question 2

You manage a farm that is looking to sell oranges in both California and Oregon. The demand for oranges in California is given by P^CA = 25 - 0.5Q_^CA and the demand for oranges in Oregon is P^OR = 19 - 0.3Q^OR. The total cost of selling oranges is TC = 10 + Q and the marginal cost is constant at MC = $1. If you can differentiate between customers in California and Oregon, you should charge a price of $13 in California and a price of $10.00 in Oregon.

Answer 1

Solution:

1) If we can differentiate between customers in California and Oregon, then

California

P_CA =25-0.5Q_CA

TR_CA = P_CA *Q_CA = 25 Q_CA – 0.5 Q_CA²

MR_CA = dTR_CA/dQ_CA

MR_CA = 25 - Q_CA

Profit Maximizing quantity is defined at MR=MC

25 - Q_CA = 1

Q_CA = 24

P_CA =25-0.5 *24 = 13

TR_CA = 24*13 = 312

Oregon

P_OR = 19 - 0.3Q_OR

TR_OR = P_OR *Q_OR = 19 Q_OR - 0.3Q_OR²

MR_OR = dTR_OR/dQ_OR

MR_OR = 19 – 0.6Q_OR

Profit Maximizing quantity is defined at MR=MC

19 – 0.6Q_OR = 1

30 = Q_OR

P_OR = 19 - 0.3*30 = 10

TR_OR = 30*10 = 300

2)

Given demand function for oranges in California-

Demand function for oranges in Oregon-

Price in California= 312, therefore the quantity can be determined using the demand function-

Price in Oregon= 300, the quantity is derived as follows-

Thus total quantity of oranges demanded= 674+1063.33=1737.33

Total Cost= 10+Q= 10+1737.33=1747.33

1. In case of no differentiation the market structure is assumed to be competitive which implies that the equlibrium condition is P=MC, i.e

So,

SImilarly, quantity of oranges in Oregon will be -

Now, Total quantity= 48+60=108

In such a case there is a loss.

Compared to the case of differentiation a cumulative loss of is made. The negative sign here is required to calculate the quantam of loss incurred.