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 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.)

I tried $40 and it was incorrect

Answer 1

When you cannot price discriminate then the price charged in both markets would be equal.

Add both the demand functions

PCA + POR = 25 - 0.5QCR + 19 - 0.3QOR

=> 2P = 44 - 0.8Q

=> P = 22 - 0.4Q

TR = 22Q - 0.4Q^2

MR = 22 - 0.8Q

Equate it to MC

22 - 0.8Q = 1

=> 0.8Q = 22 - 1

=> 0.8Q = 21

=> Q = 26.25

P = 22 - 0.4 × 26.25 = $ 11.50

Profit = TR - TC

=> Profit = 11.50×26.25 - (10+26.25) = $ 265.625

Part 2 answer you have not answered so, I have to calculate the Part 2 answer too.

Calculate the TR of California market

TRc = 25Qc - 0.5Qc^2

Differentiate above equation wrt Qc

MRc = 25 - Qc

Equate it to MC

25 - Qc = 1

=> Qc = 24

Pc = 25 - 0.5 × 24 = $ 13

TRc = $ 13 × 24 = $ 312

Similarly in case of Oregon market TR will be

TRo = 19Qo - 0.3Qo^2

MRo = 19 - 0.6Qo

Equate it to MC,

19 - 0.6Qo = 1

=> 0.6Qo = 18

=> Qo = 30

Po = 19 - 0.3 × 30 = $ 10

TRo = $ 10 × 30 = $ 300

Profit = TRc + TRo - TC

=> Profit = 312 + 300 - 10 - 24 - 30 = $ 548

Difference in profit = 548 - 265.625 = 282.375

Compare it with you values calculated in part 2. The profit that you have calculated in part 2 has to be subtracted from the profit calculated in this part.that is $ 265.625.