A question I have seen in my microeconomics textbook is as follows:
Consider a monopoly supply to both a domestic and foreign market, where the market demands are:
Yd(pd) = 20 - 2pd, hence pd(yd) = 10 - Yd/2
Yf(pf) = 20 - pf, hence pf(Yf) = 20 - Yf
Total cost = .5Y^2 +20
Total output, Y = Yd + Yf
We are assuming the monopolist cannot price discriminate and therefore pf = pd = p
We are asked what price should the monopolist now set for its output? What quantity will it sell to each market?
To solve this question i first calculated the new total market demand, or aggregate demand by summing both the foreign and domestic markets.
D(p) = 20 - 3p + 20 - p = 40 -3p, hence p = 40/3 - Y/3
I then calculated total revenue and marginal revenue.
TR = (40/3)Y - (Y^2)/3 , hence MR = 40/3 - 2Y/3
I then calculated marginal cost.
MC = Y
I then solved for Y where MR = MC and substituted the value into the market price function.
Y = 40/3 - 2Y/3, hence Y = 8, p(8) = 32/3
My problem arises when i substitute this value for P into the domestic market's output function to calculate how many units will now be supplied to the domestic market.
Yd(8) = 20 - 2(32/3) = -4/3
My interpretation of this is that the monopoly is purchasing 4/3 units from the domestic market to sell into the international market, however this concept is not familiar to me. Having a negative answer for units does not sit well with me. Any guidance as to something i did wrong in calculating the question or an economic interpretation of the solution would be much appreciated! I am very confused.