Question

You manage a farm that is looking to sell oranges in both California and Oregon. The demand for oranges in California is given by PCA = 25 - 0.5QCA and the demand for oranges in Oregon is POR = 19 - 0.3QOR. 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 $ in California and a price of $ in Oregon.

Answer 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