Ask for a computational problem in microeconomics A consumer consumes 540 yuan of goods X and Y every year, and the prices of the two goods are 30 and 20 yuan respectively The utility function of is u = XXY, and the quantity of the two commodities purchased each year is calculated

Ask for a computational problem in microeconomics A consumer consumes 540 yuan of goods X and Y every year, and the prices of the two goods are 30 and 20 yuan respectively The utility function of is u = XXY, and the quantity of the two commodities purchased each year is calculated

This is the maximum value problem of binary function under constraints
30X+20Y=540
U=X^2Y
U=X^2Y-V(30X+20Y-540)
dU/dX=2XY-30V=0
dU/dY=X^2-20V=0
dU/dV=30X+20Y-540=0
X=120,Y=90

Several computational problems in microeconomics~ The short-term total cost function of an enterprise is STC = 500 + 120q-2q square + 1 / 6 Q cubic~ (1) What is the output when SMC reaches the minimum value of yes? (2) When AVC reaches the minimum value, what is the output? 2 Mr. A's utility function is u = f (x, y). The price of X is PX = 2 yuan and the price of Y is py = 3 yuan. He is going to spend 120 yuan on these two kinds of goods (1) How much do you buy for each of the two commodities in order to live the most? (2) How many utility units does he get? (3) When the utility is maximum, what is the marginal substitution rate? (4) If the price of x increases by 40% and the price of Y remains unchanged, how much must the cost increase in order to maintain the original effective use level?

1、STC=500+120Q-2Q2+1/6*Q3
SMC=dSTC/dQ=120-4Q+0.5Q2
When SMC is the smallest, DSMC / DQ = 0, i.e. - 4 + q = 0, q = 4
According to the STC expression, the fixed cost is 500,
So SVC = 120q-2q2 + 1 / 6 * Q3, AVC = SVC / Q = 120-2q + 1 / 6 * Q2
When AVC is minimum, davc / DQ = 0, i.e. - 2 + 1 / 3 * q = 0, q = 6
2. Does the utility function not give a specific expression? No way
Idea: (1) when the maximum utility is obtained, MUX / PX = muy / py, QX and QY are further calculated
(2) The result of the above question can be substituted
（3）MRSxy=MUx/MUy=Px/Py=2/3
(4) The specific formula of utility function is unknown and cannot be calculated

If the utility function of the consumer is u = XY, the income is 120 yuan, the price of X commodity PX = 2, and the price of Y commodity py = 3 What is the marginal utility and total utility of money? 2 when the utility is the greatest, how many units of X and Y goods should be purchased? 3. When the price of X commodity increases by 44%, and the price of Y commodity remains unchanged, how much should the income increase?

It's so hard

It is known that the utility function of a consumer is u = 3xy, the prices of two commodities are PX = 1, p y = 2, and the consumer's income is 12. Find the maximum utility? It is known that the utility function of a consumer is u = 3xy, the prices of two commodities are PX = 1, p y = 2, and the consumer's income is 12. The maximum utility obtained by consumers when seeking equilibrium

Let the consumption quantity of two commodities be x and y
Then PX * x + py * y = 12 x + 2Y = 12
U=3XY=3(12-2Y)*Y=6(-Y^2+6Y)=-6(Y-3)^2+54
Therefore, u goes to the maximum value when y = 3, and x = 6
maxU=54

The income of commodity 1 and commodity 2 is 540 yuan, and the price of the two commodities P1 = 20 yuan and P2 = 30 yuan. The utility function of the consumer is u = 3x1 (x2) 2 (x2 square The income of commodity 1 and commodity 2 is 540 yuan, and the price of the two commodities P1 = 20 yuan and P2 = 30 yuan. The utility function of the consumer is u = 3x1 (x2) 2 (x2 Square). Calculate the number of the two commodities purchased by the consumer and the total utility obtained each year

Because u = 3xix22
So mux1 = 3x22, MUX2 = 6x1x 2
According to the principle of maximizing consumer utility: mux1 / P1 = MUX2 / P2
So 4x1 = 3x2
P1 * X1 + P2 * x2 = 540, P1 = 20, P2 = 30
By substituting X1 = 9 and X2 = 12, the total utility Mu = 3888 is obtained by substituting X1 and X2 into the utility function

Brief answer: the content of the law of diminishing marginal utility

Law of diminishing marginal production: that is, under the condition of constant technical level, increase the input of a certain factor of production. When the input of the factor of production increases to a certain extent, the increase in output brought by adding a unit factor is decreasing. Applicable conditions: in the case of no significant change in production technology, in the short term