How to find a Marshallian demand? Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Economics supply and demand questionGiven supply and demand curves, and a tax, how can I find the tax burdens and revenue?How to find the price elasticity of demand?Utility to demand functionHow to calculate y when given the demand function?Econ: Given demand $x_1$, $x_2$ under locally non-satiated preferences find the demand for $x_3$Use price elasticity of demand value and demand function to find price charged and quantity?Demand FunctionFinding the Minimum Price | Supply, Demand EquationSupply/Demand Shift (Find New Equilibrium)
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How to find a Marshallian demand?
Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Economics supply and demand questionGiven supply and demand curves, and a tax, how can I find the tax burdens and revenue?How to find the price elasticity of demand?Utility to demand functionHow to calculate y when given the demand function?Econ: Given demand $x_1$, $x_2$ under locally non-satiated preferences find the demand for $x_3$Use price elasticity of demand value and demand function to find price charged and quantity?Demand FunctionFinding the Minimum Price | Supply, Demand EquationSupply/Demand Shift (Find New Equilibrium)
$begingroup$
I have many doubts with this exercise of microeconomics. I do not know if anyone could help me please. Thanks in advance.
Let $x$ be the food consumption of a household, and be $y$ the consumption of clothes. The preferences of a household can be represented as $U(x,y)=3ln x + 5ln y$.
Additionally, this household faces the unit prices: $p_x=$ , 10 ,$ and $,p_y=$ , 4.$
Determine the Marshallian demands of each good considering a budget of $$ , 100.$
And it also determines the level of the level of utility reached.
economics
asked Apr 1 at 7:21
mathsalomonmathsalomon
715415
$endgroup$
add a comment |
$begingroup$
I have many doubts with this exercise of microeconomics. I do not know if anyone could help me please. Thanks in advance.
Let $x$ be the food consumption of a household, and be $y$ the consumption of clothes. The preferences of a household can be represented as $U(x,y)=3ln x + 5ln y$.
Additionally, this household faces the unit prices: $p_x=$ , 10 ,$ and $,p_y=$ , 4.$
Determine the Marshallian demands of each good considering a budget of $$ , 100.$
And it also determines the level of the level of utility reached.
economics
asked Apr 1 at 7:21
mathsalomonmathsalomon
715415
$endgroup$
add a comment |
$begingroup$
I have many doubts with this exercise of microeconomics. I do not know if anyone could help me please. Thanks in advance.
Let $x$ be the food consumption of a household, and be $y$ the consumption of clothes. The preferences of a household can be represented as $U(x,y)=3ln x + 5ln y$.
Additionally, this household faces the unit prices: $p_x=$ , 10 ,$ and $,p_y=$ , 4.$
Determine the Marshallian demands of each good considering a budget of $$ , 100.$
And it also determines the level of the level of utility reached.
economics
asked Apr 1 at 7:21
mathsalomonmathsalomon
715415
$endgroup$
I have many doubts with this exercise of microeconomics. I do not know if anyone could help me please. Thanks in advance.
Let $x$ be the food consumption of a household, and be $y$ the consumption of clothes. The preferences of a household can be represented as $U(x,y)=3ln x + 5ln y$.
Additionally, this household faces the unit prices: $p_x=$ , 10 ,$ and $,p_y=$ , 4.$
Determine the Marshallian demands of each good considering a budget of $$ , 100.$
And it also determines the level of the level of utility reached.
economics
economics
asked Apr 1 at 7:21
mathsalomonmathsalomon
715415
asked Apr 1 at 7:21
mathsalomonmathsalomon
715415
edited Apr 1 at 7:31
mathsalomon
asked Apr 1 at 7:21
mathsalomonmathsalomon
715415
asked Apr 1 at 7:21
mathsalomonmathsalomon
715415
asked Apr 1 at 7:21
mathsalomonmathsalomon
715415
715415
add a comment |
add a comment |
1 Answer
1
active
oldest
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$begingroup$
Here are the steps to determine the Marshallian demands:
$textbf1.$ Maximizing the Lagrange function:
$$maxmathcal L=3ln x + 5ln y+lambdacdot (100-10x-4y)$$
$textbf2$. Calculating the partial derivatives w.r.t $x,y$ and $lambda$.
$textbf3$. Setting the partial derivatives equal to $0$.
$$fracpartial mathcal Lpartial x=frac3x-10lambda=0Rightarrow frac3x=10lambda$$
$$fracpartial mathcal Lpartial y=frac5y-4lambda=0Rightarrow frac5y=4lambda$$
$$fracpartial mathcal Lpartial lambda=100-10x-4y=0$$
$textbf4$. Divide the first equation by the second equation. $lambda$ can be cancelled.
$textbf5$. Solve the result of step 4 for $x$ and insert the corresponding expression into the third equation of step 3. Then solve the equation for $y$ to obtain the Marshallian demand of good $y$.
$textbf6$. Solve the result of step 4 for $y$ and insert the corresponding expression into the third equation of step 3. Then solve the equation for $x$ to obtain the Marshallian demand of good $x$.
$textbf7$. Finally use the results of step 6 and step 7 and the utility function to calculate the level of utility.
answered Apr 1 at 12:33
callculuscallculus
18.8k31428
$endgroup$
$begingroup$
Thank you. And the utility function mentioned in step 7 is $U(x,y)=3ln x+5ln y$, right?
$endgroup$
– mathsalomon
Apr 1 at 17:48
1
$begingroup$
Yes, it is the utility function $U(x,y)=...$.
$endgroup$
– callculus
Apr 1 at 17:53
$begingroup$
"If the consumption of good $y$ a tax of $r =3$ is applied for each unit consumed. What are the optimal demands and the level of utility achieved with the application of the tax?". I would like to know at least how step 3 changes.
$endgroup$
– mathsalomon
Apr 2 at 7:16
1
$begingroup$
@mathsalomon The price which has to be payed for good y increases from $4$ to $7$. So the new budget constraint is $100-10x-7y=0$.
$endgroup$
– callculus
Apr 2 at 10:30
add a comment |
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1 Answer
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1 Answer
1
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oldest
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$begingroup$
Here are the steps to determine the Marshallian demands:
$textbf1.$ Maximizing the Lagrange function:
$$maxmathcal L=3ln x + 5ln y+lambdacdot (100-10x-4y)$$
$textbf2$. Calculating the partial derivatives w.r.t $x,y$ and $lambda$.
$textbf3$. Setting the partial derivatives equal to $0$.
$$fracpartial mathcal Lpartial x=frac3x-10lambda=0Rightarrow frac3x=10lambda$$
$$fracpartial mathcal Lpartial y=frac5y-4lambda=0Rightarrow frac5y=4lambda$$
$$fracpartial mathcal Lpartial lambda=100-10x-4y=0$$
$textbf4$. Divide the first equation by the second equation. $lambda$ can be cancelled.
$textbf5$. Solve the result of step 4 for $x$ and insert the corresponding expression into the third equation of step 3. Then solve the equation for $y$ to obtain the Marshallian demand of good $y$.
$textbf6$. Solve the result of step 4 for $y$ and insert the corresponding expression into the third equation of step 3. Then solve the equation for $x$ to obtain the Marshallian demand of good $x$.
$textbf7$. Finally use the results of step 6 and step 7 and the utility function to calculate the level of utility.
answered Apr 1 at 12:33
callculuscallculus
18.8k31428
$endgroup$
$begingroup$
Thank you. And the utility function mentioned in step 7 is $U(x,y)=3ln x+5ln y$, right?
$endgroup$
– mathsalomon
Apr 1 at 17:48
1
$begingroup$
Yes, it is the utility function $U(x,y)=...$.
$endgroup$
– callculus
Apr 1 at 17:53
$begingroup$
"If the consumption of good $y$ a tax of $r =3$ is applied for each unit consumed. What are the optimal demands and the level of utility achieved with the application of the tax?". I would like to know at least how step 3 changes.
$endgroup$
– mathsalomon
Apr 2 at 7:16
1
$begingroup$
@mathsalomon The price which has to be payed for good y increases from $4$ to $7$. So the new budget constraint is $100-10x-7y=0$.
$endgroup$
– callculus
Apr 2 at 10:30
add a comment |
$begingroup$
Here are the steps to determine the Marshallian demands:
$textbf1.$ Maximizing the Lagrange function:
$$maxmathcal L=3ln x + 5ln y+lambdacdot (100-10x-4y)$$
$textbf2$. Calculating the partial derivatives w.r.t $x,y$ and $lambda$.
$textbf3$. Setting the partial derivatives equal to $0$.
$$fracpartial mathcal Lpartial x=frac3x-10lambda=0Rightarrow frac3x=10lambda$$
$$fracpartial mathcal Lpartial y=frac5y-4lambda=0Rightarrow frac5y=4lambda$$
$$fracpartial mathcal Lpartial lambda=100-10x-4y=0$$
$textbf4$. Divide the first equation by the second equation. $lambda$ can be cancelled.
$textbf5$. Solve the result of step 4 for $x$ and insert the corresponding expression into the third equation of step 3. Then solve the equation for $y$ to obtain the Marshallian demand of good $y$.
$textbf6$. Solve the result of step 4 for $y$ and insert the corresponding expression into the third equation of step 3. Then solve the equation for $x$ to obtain the Marshallian demand of good $x$.
$textbf7$. Finally use the results of step 6 and step 7 and the utility function to calculate the level of utility.
answered Apr 1 at 12:33
callculuscallculus
18.8k31428
$endgroup$
$begingroup$
Thank you. And the utility function mentioned in step 7 is $U(x,y)=3ln x+5ln y$, right?
$endgroup$
– mathsalomon
Apr 1 at 17:48
1
$begingroup$
Yes, it is the utility function $U(x,y)=...$.
$endgroup$
– callculus
Apr 1 at 17:53
$begingroup$
"If the consumption of good $y$ a tax of $r =3$ is applied for each unit consumed. What are the optimal demands and the level of utility achieved with the application of the tax?". I would like to know at least how step 3 changes.
$endgroup$
– mathsalomon
Apr 2 at 7:16
1
$begingroup$
@mathsalomon The price which has to be payed for good y increases from $4$ to $7$. So the new budget constraint is $100-10x-7y=0$.
$endgroup$
– callculus
Apr 2 at 10:30
add a comment |
$begingroup$
Here are the steps to determine the Marshallian demands:
$textbf1.$ Maximizing the Lagrange function:
$$maxmathcal L=3ln x + 5ln y+lambdacdot (100-10x-4y)$$
$textbf2$. Calculating the partial derivatives w.r.t $x,y$ and $lambda$.
$textbf3$. Setting the partial derivatives equal to $0$.
$$fracpartial mathcal Lpartial x=frac3x-10lambda=0Rightarrow frac3x=10lambda$$
$$fracpartial mathcal Lpartial y=frac5y-4lambda=0Rightarrow frac5y=4lambda$$
$$fracpartial mathcal Lpartial lambda=100-10x-4y=0$$
$textbf4$. Divide the first equation by the second equation. $lambda$ can be cancelled.
$textbf5$. Solve the result of step 4 for $x$ and insert the corresponding expression into the third equation of step 3. Then solve the equation for $y$ to obtain the Marshallian demand of good $y$.
$textbf6$. Solve the result of step 4 for $y$ and insert the corresponding expression into the third equation of step 3. Then solve the equation for $x$ to obtain the Marshallian demand of good $x$.
$textbf7$. Finally use the results of step 6 and step 7 and the utility function to calculate the level of utility.
answered Apr 1 at 12:33
callculuscallculus
18.8k31428
$endgroup$
Here are the steps to determine the Marshallian demands:
$textbf1.$ Maximizing the Lagrange function:
$$maxmathcal L=3ln x + 5ln y+lambdacdot (100-10x-4y)$$
$textbf2$. Calculating the partial derivatives w.r.t $x,y$ and $lambda$.
$textbf3$. Setting the partial derivatives equal to $0$.
$$fracpartial mathcal Lpartial x=frac3x-10lambda=0Rightarrow frac3x=10lambda$$
$$fracpartial mathcal Lpartial y=frac5y-4lambda=0Rightarrow frac5y=4lambda$$
$$fracpartial mathcal Lpartial lambda=100-10x-4y=0$$
$textbf4$. Divide the first equation by the second equation. $lambda$ can be cancelled.
$textbf5$. Solve the result of step 4 for $x$ and insert the corresponding expression into the third equation of step 3. Then solve the equation for $y$ to obtain the Marshallian demand of good $y$.
$textbf6$. Solve the result of step 4 for $y$ and insert the corresponding expression into the third equation of step 3. Then solve the equation for $x$ to obtain the Marshallian demand of good $x$.
$textbf7$. Finally use the results of step 6 and step 7 and the utility function to calculate the level of utility.
answered Apr 1 at 12:33
callculuscallculus
18.8k31428
answered Apr 1 at 12:33
callculuscallculus
18.8k31428
answered Apr 1 at 12:33
callculuscallculus
18.8k31428
answered Apr 1 at 12:33
callculuscallculus
18.8k31428
18.8k31428
$begingroup$
Thank you. And the utility function mentioned in step 7 is $U(x,y)=3ln x+5ln y$, right?
$endgroup$
– mathsalomon
Apr 1 at 17:48
1
$begingroup$
Yes, it is the utility function $U(x,y)=...$.
$endgroup$
– callculus
Apr 1 at 17:53
$begingroup$
"If the consumption of good $y$ a tax of $r =3$ is applied for each unit consumed. What are the optimal demands and the level of utility achieved with the application of the tax?". I would like to know at least how step 3 changes.
$endgroup$
– mathsalomon
Apr 2 at 7:16
1
$begingroup$
@mathsalomon The price which has to be payed for good y increases from $4$ to $7$. So the new budget constraint is $100-10x-7y=0$.
$endgroup$
– callculus
Apr 2 at 10:30
add a comment |
$begingroup$
Thank you. And the utility function mentioned in step 7 is $U(x,y)=3ln x+5ln y$, right?
$endgroup$
– mathsalomon
Apr 1 at 17:48
1
$begingroup$
Yes, it is the utility function $U(x,y)=...$.
$endgroup$
– callculus
Apr 1 at 17:53
$begingroup$
"If the consumption of good $y$ a tax of $r =3$ is applied for each unit consumed. What are the optimal demands and the level of utility achieved with the application of the tax?". I would like to know at least how step 3 changes.
$endgroup$
– mathsalomon
Apr 2 at 7:16
1
$begingroup$
@mathsalomon The price which has to be payed for good y increases from $4$ to $7$. So the new budget constraint is $100-10x-7y=0$.
$endgroup$
– callculus
Apr 2 at 10:30
$begingroup$
Thank you. And the utility function mentioned in step 7 is $U(x,y)=3ln x+5ln y$, right?
$endgroup$
– mathsalomon
Apr 1 at 17:48
$begingroup$
Thank you. And the utility function mentioned in step 7 is $U(x,y)=3ln x+5ln y$, right?
$endgroup$
– mathsalomon
Apr 1 at 17:48
1
1
$begingroup$
Yes, it is the utility function $U(x,y)=...$.
$endgroup$
– callculus
Apr 1 at 17:53
$begingroup$
Yes, it is the utility function $U(x,y)=...$.
$endgroup$
– callculus
Apr 1 at 17:53
$begingroup$
"If the consumption of good $y$ a tax of $r =3$ is applied for each unit consumed. What are the optimal demands and the level of utility achieved with the application of the tax?". I would like to know at least how step 3 changes.
$endgroup$
– mathsalomon
Apr 2 at 7:16
$begingroup$
"If the consumption of good $y$ a tax of $r =3$ is applied for each unit consumed. What are the optimal demands and the level of utility achieved with the application of the tax?". I would like to know at least how step 3 changes.
$endgroup$
– mathsalomon
Apr 2 at 7:16
1
1
$begingroup$
@mathsalomon The price which has to be payed for good y increases from $4$ to $7$. So the new budget constraint is $100-10x-7y=0$.
$endgroup$
– callculus
Apr 2 at 10:30
$begingroup$
@mathsalomon The price which has to be payed for good y increases from $4$ to $7$. So the new budget constraint is $100-10x-7y=0$.
$endgroup$
– callculus
Apr 2 at 10:30
add a comment |
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