Question

QUESTION 3

1. 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)? (Write answer without the negative sign nor the dollar sign.)
   
   (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 in Oregon.
   
   
   The answer is NOT 40.
   
   BOLD the Correct Answer

Answer 1

We have the following information

Demand in California: P^CA = 25 – 0.5Q^CA

Demand in Oregon: P^OR = 19 – 0.3Q^OR

Total cost (TC) = 10 + Q; where Q = Q^CA + Q^OR

Marginal cost (MC) = 1

Now it is given that we cannot differentiate between customers in California and Oregon, and are forced to charge the price that is optimal in California in both Oregon and California. So, for equilibrium we will equate the marginal revenue (MR^CA) of California with the MC.

Total Revenue of California: TR^CA = P^CA × Q^CA

TR^CA = (25 – 0.5Q^CA)Q^CA

TR^CA = 25Q^CA – 0.5(Q^CA)²

MR^CA = ΔTR^CA/ΔQ^CA = 25 – Q^CA

Equating MR^CA and MC

25 – Q^CA = 1

Q^CA = 24

P^CA = 25 – 0.5Q^CA

P^CA = 25 – 12

P^CA = 13

So, in Oregon also the price will be 13. P^OR = 13

P^OR = 19 – 0.3Q^OR

13 = 19 – 0.3Q^OR

0.3Q^OR = 6

Q^OR = 20

Profit = TR^CA + TR^OR – TC

TR^CA = P^CA × Q^CA = 13 × 24 = 312

TR^OR = P^OR × Q^OR = 13 × 20 = 260

TC = 10 + Q = 10 + (24 + 20) = 10 + 44 = 54

Profit = 312 + 260 – 54

Profit = 572 – 54

Profit = 518

Now it is given that when different prices are charged in California and Oregon then P^CA = 13 and P^OR = 10.

P^CA = 25 – 0.5Q^CA

13 = 25 – 0.5Q^CA

0.5Q^CA = 12

Q^CA = 24

P^OR = 19 – 0.3Q^OR

10 = 19 – 0.3Q^OR

0.3Q^OR = 9

Q^OR = 30

Profit = TRCA + TROR – TC

TR^CA = P^CA × Q^CA = 13 × 24 = 312

TR^OR = P^OR × Q^OR = 10 × 30 = 300

TC = 10 + Q = 10 + (24 + 30) = 10 + 54 = 64

Profit = 312 + 300 – 64

Profit = 612 – 64

Profit = 548

So, when we charge the equilibrium price of California in Oregon than the total profit declines by 30 (548 – 518).