Please briefly explain the utility function and the pro superposition conformation 10

Suppose a certain consumption is copied.

The utility function of the consumer is u=q, where q is the consumption of the consumer and m is the income, and the demand function of the consumer is found. First of all, recall the general utility function: the general utility function is u=f(x1,x2), which is about two goods, and the solution method is based on consumer equilibrium:

mu1/p1=mu2/p2。

In this problem, the utility function has only one commodity and income m, but you can follow the example of income m, you can think of income m as another commodity, i.e., commodity 2, according to the marginal utility of mu1 p1=m, where the marginal utility of money income m is not ?

So: mu1 p1 = (1).

And u=q, find the first-order partial derivative of m for u, i.e. =3 (2) and then find the first-order partial derivative of q for u, i.e., mu1= (3) substitute (2)(3) into equation (1), sort out:

q=1/(36p^2)

From the utility function, it can be seen that xy is a complementary product, so the consumer's utility function is a right-angled line parallel to the horizontal and vertical axes.

So the substitution effect is zero.

The income effect is the total effect (i.e., the total amount of change).

Use the principle of marginal utility to calculate ha.

Here's an example.

Suppose that the utility function of a consumer is u=q, where q is the consumer's consumption and m is the income, find the consumer's demand function.

Think of it this way:

First of all, recall the general utility function: the general utility function is u=f(x1,x2), which is about two goods, and the solution is based on the consumer equilibrium: mu1 p1=mu2 p2.

In this problem, the utility function has only one commodity and income m, but you can follow the example of income m, you can think of income m as another commodity, i.e., commodity 2, according to the marginal utility of mu1 p1=m, where the marginal utility of money income m is not ?

So: mu1 p1=

1) And u=q, find the first-order partial derivative of m for u, i.e., =3(2) and then find the first-order partial derivative of q for u, i.e., mu1=

3) Substituting (2) and (3) into equation (1) to get q=36p 2 and doing so.

You imitate it.

Perform monotonic transformation first, basically to make it easier when calculating, because it is more troublesome for me to type on a computer, hehe Please remember that monotonic transformation does not change monotonicity. This essentially means that there is no unique form of functional expression for a particular preference relationship.

logu=muxi=

mux2=mrsx1,x2=muxi mux2=x2 x1=p1 p2x2=(p1 p2)*x1 Equation 1.

m=p1x1+p2x2 Eq. 2.

This results in x1=m 2p1

x2=m/2p2

Actually, there are formulas for calculating the Marshall demand function of Cobb-Douglas.

u=xayb m=p1x+p2y

x=am/（a+b)p1

y=bm/（a+b)p2

Of course, you can find it by pulling a Lang Ri method, and the result is the same.

Hope it works

Hello, first of all, this is the amount of the Cobb-Douglas type utility function in which the problem should be like this x represents 1, y....2...

I'll give you a formula to derive u=(x)y)=1

To satisfy consumers, it is necessary to use the maximum has.

1)mux/muy=px/py

2)px·x+py·y=m

mux=au/ax=αx^(α1)y

muy=au ay=(x)y( 1)]

x=αm/px

y=βm/py

Here =3 8 =5 8

Hope it helps.

A function that represents the quantitative relationship between the utility that consumers gain in consumption and the mix of goods consumed. It is used to measure the degree to which a consumer derives satisfaction from consuming a given mix of goods.

2x+3y=180

Find the maximum value of u=xy.

180=2x+3y≥2√2x√3y

xy≤1350

If and only if 2x=3y=90, i.e., x=45

y=30 when the equal sign holds.

A 25% drop in PX becomes so.

xy≤1800

If and only if x=60

y=30 when the equal sign holds.

1.You first use the utility function to find partial derivatives of q and m, respectively, and set them to the marginal utility mu and the marginal utility of money income, respectively.

As long as you find the partial derivatives of the above two respectively, and then use the consumer equilibrium formula mu p = of the cardinal utility theory, you can immediately find the demand function, the dependent variable is the output q, and the independent variable is **p, calculate it yourself.

Knowing the demand function, we can immediately know the inverse demand function, that is, in turn, the dependent variable is **p, and the independent variable is the yield q.

2.Knowing the inverse demand function, asking the consumer to have a surplus, you have to find the integrals. If you still don't understand, look at the definitions and formulas in the book.

Note that the inverse demand function must be used here, because the horizontal axis of the graph is the output, and the vertical axis is **, so the inverse demand function must be used instead of the demand function, and the dependent variable of the inverse demand function is **, the same as the graph).

According to the conditions given in 2:

You can get the answer by letting the inverse demand function take the integral, and then subtract (1 12 times 4) to get the answer, and the integral value ranges from 0 to 4 (p=4 above), and finally the consumer surplus is equal to 1 3.

I'll write down the answers to each question, and you'll do the math yourself.

1.Demand function q=1 36p2

The inverse demand function p=1 6q

2.Consumer surplus = 1 3