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

We have the following information

Demand equation California: P_CA = 25 – 0.5Q_CA

Demand equation Oregon: P_OR = 19 – 0.3Q_OR

Total Cost (TC) = 10 + Q; where Q = Q_CA + Q_OR

Marginal cost (MC) = ΔTC/ΔQ = 1

In this situation the equilibrium will be the point where the marginal revenue from the two states (MR_CA and MR_OR) is equal to the marginal cost

MR_CA = MR_OR = MC

Total Revenue from California = Price × Quantity

TR_CA = P_CA × Q_CA

TR_CA = (25 – 0.5Q_CA)Q_CA

TR_CA = 25Q_CA – 0.5Q²_CA

MR_CA = ΔTR_CA/ΔQ_CA = 25 – Q_CA

Total Revenue from Oregon: TR_OR = P_OR × Q_OR

TR_OR = (19 – 0.3Q_OR)Q_OR

TR_OR = 19Q_OR – 0.3Q²_OR

MR_OR = ΔTR_OR/ΔQ_OR = 19 – 0.6Q_OR

MR_CA = MC

25 – Q_CA = 1

Equilibrium quantity in the case California: Q_CA = 24

MR_OR = MC

19 – 0.6Q_OR = 1

Equilibrium quantity in the case of Oregon: Q₂ = 30

P_CA = 25 – 0.5Q_CA

P_CA = 25 – 12

Equilibrium price in the case of California: P_CA = 13

P_OR = 19 – 0.3Q_OR

P_OR = 19 – 9

Equilibrium price in the case of Oregon: P_OR = 10