<p>Following are the set of equations describing the demand and supply of two goods X and Y:</p>

<p>Demand functions: 
<span class="math-container">$$X_d = a_1 - b_1P_x + c_1P_y$$</span></p>

<p><span class="math-container">$$Y_d = a_2 - b_2P_y +c_2P_x$$</span></p>

<p><span class="math-container">$a_1,~ a_2,~ b_1,~ b_2,~ c_1,~ c_2$</span> are positive.</p>

<p>Supply functions:</p>

<p><span class="math-container">$$X_s = -f_1 + g_1P_x$$</span></p>

<p><span class="math-container">$$Y_s = -f_2 + g_2Py$$</span></p>

<p><span class="math-container">$f_1,~ f_2,~ g_1,~ g_2$</span> are positive</p>

<p>Government imposed <span class="math-container">$t\%$</span> tax on <span class="math-container">$X$</span> and allows <span class="math-container">$s\%$</span> subsidy on <span class="math-container">$Y$</span> such that government budget remains balanced. Find out the required tax rate.
(Clearly show How the set of equations change and the equilibrium prices ?)</p>

<p>I replaced <span class="math-container">$P_x$</span> by <span class="math-container">$P_x(1+t)$</span> in the two demand equations as according to my understanding consumers now face a higher effective price for <span class="math-container">$X$</span>. But I'm not sure how to incorporate the subsidy and what would be the economic logic behind such a change.</p>

CC BY-SA 4.0
2019-07-14T02:39:39.110Z
Why can't you use s the same way you use t? If Px(1+t) why not Py(1-s)?
123
CC BY-SA 4.0
2019-07-14T04:20:42.773Z
The reasoning behind replacing Px by Px(1+t) in the demand functions only was that consumers now have to pay a new price but the producers still recieve the same so supply functions were unchanged. Now in case of subsidy, producers will charge a lower price, Py(1-s), so I can replace it in supply equations. The problem is that consumers also face the lower price of Y so should I change the price of Y in demand functions as well?
Shoaib Ashraf
<microeconomics><mathematical-economics><general-equilibrium><competitive-equilibrium>
Equilibrium price determination in a 2 commodity framework
Shoaib Ashraf
# Equilibrium price determination in a 2 commodity framework

(Asked by: username_0 on 2019-07-13)

Following are the set of equations describing the demand and supply of two goods X and Y:

Demand functions:
$$X\_d = a\_1 - b\_1P\_x + c\_1P\_y$$

$$Y\_d = a\_2 - b\_2P\_y +c\_2P\_x$$

$a\_1,~ a\_2,~ b\_1,~ b\_2,~ c\_1,~ c\_2$ are positive.

Supply functions:

$$X\_s = -f\_1 + g\_1P\_x$$

$$Y\_s = -f\_2 + g\_2Py$$

$f\_1,~ f\_2,~ g\_1,~ g\_2$ are positive

Government imposed $t\%$ tax on $X$ and allows $s\%$ subsidy on $Y$ such that government budget remains balanced. Find out the required tax rate.
(Clearly show How the set of equations change and the equilibrium prices ?)

I replaced $P\_x$ by $P\_x(1+t)$ in the two demand equations as according to my understanding consumers now face a higher effective price for $X$. But I'm not sure how to incorporate the subsidy and what would be the economic logic behind such a change.

**Tags:** microeconomics, mathematical-economics, general-equilibrium, competitive-equilibrium

> **Comments:**
> **username_1**: Why can't you use s the same way you use t? If Px(1+t) why not Py(1-s)?  
> **username_0**: The reasoning behind replacing Px by Px(1+t) in the demand functions only was that consumers now have to pay a new price but the producers still recieve the same so supply functions were unchanged. Now in case of subsidy, producers will charge a lower price, Py(1-s), so I can replace it in supply equations. The problem is that consumers also face the lower price of Y so should I change the price of Y in demand functions as well?  

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## 0 answers

