<p>Marginal cost is only guaranteed to be equal to marginal revenue in optima where <span class="math-container">$Y &gt; 0$</span> (and when the profit function is concave, but in your case it is). If 
<span class="math-container">$$
MC(0) &gt; MR(0)
$$</span>
the producing the first unit results in a loss, and a profit maximizing monopolist would not produce at all (if the profit function is concave).</p>

<p>An example: I am willing to buy golf ball sized diamonds from you. I am willing to pay 5 dollars for the first, 4 dollars for the second, 3 dollars for the third and so on, ending in 0 dollars for the sixth and any further units. How many golf ball sized diamonds will you sell me?</p>

CC BY-SA 4.0
2019-05-31T04:41:27.127Z
2019-05-31T04:41:27.127Z
Giskard
<p>A question I have seen in my microeconomics textbook is as follows:</p>

<p>Consider a monopoly supply to both a domestic and foreign market, where the market demands are:</p>

<p>Yd(pd) = 20 - 2pd, hence pd(yd) = 10 - Yd/2</p>

<p>Yf(pf) = 20 - pf, hence pf(Yf) = 20 - Yf</p>

<p>Total cost = .5Y^2 +20</p>

<p>Total output, Y = Yd + Yf</p>

<p>We are assuming the monopolist cannot price discriminate and therefore pf = pd = p</p>

<p>We are asked what price should the monopolist now set for its output? What quantity will it sell to each market?</p>

<p>To solve this question i first calculated the new total market demand, or aggregate demand by summing both the foreign and domestic markets. </p>

<p>D(p) = 20 - 3p + 20 - p = 40 -3p, hence p = 40/3 - Y/3</p>

<p>I then calculated total revenue and marginal revenue.</p>

<p>TR = (40/3)Y - (Y^2)/3 , hence MR = 40/3 - 2Y/3</p>

<p>I then calculated marginal cost. </p>

<p>MC = Y </p>

<p>I then solved for Y where MR = MC and substituted the value into the market price function. </p>

<p>Y = 40/3 - 2Y/3, hence Y = 8, p(8) = 32/3</p>

<p>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. </p>

<p>Yd(8) = 20 - 2(32/3) = -4/3</p>

<p>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. </p>

<microeconomics><price-discrimination>
Can a monopoly supply negative units to one of its two markets?
Matt_G
# Can a monopoly supply negative units to one of its two markets?

(Asked by: username_0 on 2019-05-31)

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.

**Tags:** microeconomics, price-discrimination

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## 1 answers

### Answer by username_1 on 2019-05-31. Score: 1

Marginal cost is only guaranteed to be equal to marginal revenue in optima where $Y > 0$ (and when the profit function is concave, but in your case it is). If
$$
MC(0) > MR(0)
$$
the producing the first unit results in a loss, and a profit maximizing monopolist would not produce at all (if the profit function is concave).

An example: I am willing to buy golf ball sized diamonds from you. I am willing to pay 5 dollars for the first, 4 dollars for the second, 3 dollars for the third and so on, ending in 0 dollars for the sixth and any further units. How many golf ball sized diamonds will you sell me?


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