<p>Isn't the excess burden of the tax just the change in the size of the deadweight loss triangle?</p>
<p>If <span class="math-container">$q^m$</span> and <span class="math-container">$q^t$</span> are the initial and after-tax monopoly quantities then, the increase in deadweight loss from a tax is (in the case of linear demand and marginal cost):</p>
<p><span class="math-container">$$\frac{1}{2}\Big([P(q^m)-MC(q^m)]+[P(q^t)-MC(q^t)]\Big)(q^m-q^t)$$</span></p>
<p>In your case we get</p>
<p><span class="math-container">$$\frac{1}{2}\Big((17.70-11.40)+(19.20-9.40)\Big)(42-32)=80.50.$$</span></p>

CC BY-SA 4.0
2024-12-12T10:31:17.300Z
2024-12-12T10:31:17.300Z
smcc
<p>A monopolist has a short run cost function given by:</p>
<p><span class="math-container">$\mathrm{TC}=0.1 q^2+3 q+40 \quad q \geq 2$</span></p>
<p>where q is output per day and TC is the total cost per day in dollars. The firm has fixed costs of <span class="math-container">$\\\$ 30$</span> (already included in the TC equation above). The TC equation generates minimum average costs of <span class="math-container">$\\\$ 7$</span> (per unit) at <span class="math-container">$\mathrm{q}=20$</span>.</p>
<ol start="25">
<li><p>Suppose that the firm faces an industry demand curve given by the equation
<span class="math-container">$$
P=24-0.15 Q
$$</span>
We know that the number of units produced by the firm per day in the short run is 42 units. I know how to solve out this question by using MR = MC.</p>
</li>
<li><p>Continuing question 25 , the price charged by the firm in the short run is $17.70. I know how to solve this by simply plugging 42 to the demand equation.</p>
</li>
<li><p>Imagine now that a tax of <span class="math-container">$\\\$ 5$</span> per unit is placed on the output in this industry. How much of this tax will be borne by the monopolist (i.e., what will be the seller's share)?</p>
</li>
</ol>
<p>My solution is Original MC = 0.2q + 3
New MC = 0.2q + 3 + 5 = 0.2q + 8</p>
<p>MR remains the same: MR = 24 - 0.3Q</p>
<p>Set new MR = MC</p>
<p>Solve for new Q and find new price using demand equation. The answer is the monopolist bears 3.50 of the 5 tax.</p>
<p><strong>Question: I don't know how to answer question 28: The tax discussed in Question 27 will cause excess burden. How much is the excess burden of the tax on the monopolist?</strong></p>

CC BY-SA 4.0
2024-12-09T20:05:11.857Z
Could you please clarify the fixed costs?  From your equation for TC we can infer they are 40 per day, but then you state they are 30 (presumably also per day).
Adam Bailey
CC BY-SA 4.0
2024-12-09T23:40:31.320Z
@AdamBailey You can ignore the fixed cost. I admit it's weird here. Sometimes when we compute the short-run operation/shutdown rule, we use TC-FC. But here the question doesn't need this condition.
Chao
<microeconomics>
How to compute the excess burden of the tax on the monopolist?
Chao
# How to compute the excess burden of the tax on the monopolist?

(Asked by: username_0 on 2024-12-09)

A monopolist has a short run cost function given by:

$\mathrm{TC}=0.1 q^2+3 q+40 \quad q \geq 2$

where q is output per day and TC is the total cost per day in dollars. The firm has fixed costs of $\\\$ 30$ (already included in the TC equation above). The TC equation generates minimum average costs of $\\\$ 7$ (per unit) at $\mathrm{q}=20$.

25. Suppose that the firm faces an industry demand curve given by the equation
    $$
    P=24-0.15 Q
    $$
    We know that the number of units produced by the firm per day in the short run is 42 units. I know how to solve out this question by using MR = MC.
26. Continuing question 25 , the price charged by the firm in the short run is $17.70. I know how to solve this by simply plugging 42 to the demand equation.
27. Imagine now that a tax of $\\\$ 5$ per unit is placed on the output in this industry. How much of this tax will be borne by the monopolist (i.e., what will be the seller's share)?

My solution is Original MC = 0.2q + 3
New MC = 0.2q + 3 + 5 = 0.2q + 8

MR remains the same: MR = 24 - 0.3Q

Set new MR = MC

Solve for new Q and find new price using demand equation. The answer is the monopolist bears 3.50 of the 5 tax.

**Question: I don't know how to answer question 28: The tax discussed in Question 27 will cause excess burden. How much is the excess burden of the tax on the monopolist?**

**Tags:** microeconomics
> **Comments:**
> **username_1**: Could you please clarify the fixed costs?  From your equation for TC we can infer they are 40 per day, but then you state they are 30 (presumably also per day).  
> **username_0**: @AdamBailey You can ignore the fixed cost. I admit it's weird here. Sometimes when we compute the short-run operation/shutdown rule, we use TC-FC. But here the question doesn't need this condition.  

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## 1 answers

### Answer by username_2 on 2024-12-12. Score: 1 | Accepted answer

Isn't the excess burden of the tax just the change in the size of the deadweight loss triangle?

If $q^m$ and $q^t$ are the initial and after-tax monopoly quantities then, the increase in deadweight loss from a tax is (in the case of linear demand and marginal cost):

$$\frac{1}{2}\Big([P(q^m)-MC(q^m)]+[P(q^t)-MC(q^t)]\Big)(q^m-q^t)$$

In your case we get

$$\frac{1}{2}\Big((17.70-11.40)+(19.20-9.40)\Big)(42-32)=80.50.$$


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