Question

. The firm's total cost function is TC(q)=1/4q2 Demand in US is Q=100-2Pa Demand in Canada...

. The firm's total cost function is TC(q)=1/4q2 Demand in US is Q=100-2Pa Demand in Canada is 100-4Pc. What is the price for each country?

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Homework Answers

Answer #1

Given,

Differentiating the above equation wrt Q we get

MC = 0.5Q

Demand in US is given by

Now determine the total revenue = PQ

Differentiate TR wrt Q we get

In order to maximize profit firm must equate MR to MC

50 - Q = 0.5Q

1.5Q = 50

Q = 33.33 units

Pa = 50 -0.5Q=50 - 0.5*33.33 = $ 33.33 per unit

Similarly we can solve for Canadian market

Given, Q = 100 - 4Pc

Pc = 25 - 0.25Q

TRc = 25Q - 0.25Q2

MRc = 25 - 0.5Q

Now equate MRc to MC

25 - 0.5Q = 0.5Q

Q = 25 units

Pc = 25 -0.25Q = 25 - 0.25*25 = $ 18.75 per unit.

Price in US = $ 33.33 per unit

Price in Canada = $ 18.75 per unit.

Please contact if having any query thank you. Will be obliged if you contact through comment. Once again thank you.

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