Assignment 3 The price of a shirt is 80 yuan, the price of fast food is 20 yuan, and the consumer is at the equilibrium point of the utility maximization of the two products. Seek: Marginal rate of substitution of fast food to shirts 2.A consumer’s income is 540 yuan, who purchase goodsx1,x2. The prices of the two product are p1 = 20 yuan, p2 = 30 yuan, and the consumer’s utility function is U=3x1x22. Seeking: 1. How much do two consumers buy?

Assignment 3

1. The price of a shirt is 80 yuan, the price of fast food is 20 yuan, and the consumer is at the equilibrium point of the utility maximization of the two products.

Seek: Marginal rate of substitution of fast food to shirts

2.A consumer’s income is 540 yuan, who purchase goodsx₁,x₂. The prices of the two product are p₁ = 20 yuan, p₂ = 30 yuan, and the consumer’s utility function is U=3x₁x₂².

Seeking: 1. How much do two consumers buy?

2. What is the total utility?

3.Douglas Cornfifield’s preferences are represented by the utility function U (x₁,x₂) =. The prices of x₁ and x₂ are p₁ and p₂.

(a) The slope of Cornfifield’s indifference curve at the point (x₁,x₂) is

_______？

(b) If Cornfifield’s budget line is tangent to his indifference curve at (x₁,x₂), then p₁x₁ / p₂x₂=?. (Hint: Look at the equation that equates the slope of his indifference curve with the slope of his budget line.) When he is consuming the best bundle he can afford, what fraction of his income does Douglas spend on x₁? .

(c) Other members of Doug’s family have similar utility functions, but the exponents may be different, or their utilities may be multiplied by a positive constant. If a family member has a utility function U (x₁,x₂) =.where a, b, and c are positive numbers, what fraction of his or her income will that family member spend on x₁?

4.The consumer’s utility function is: , The prices of the two commodities are p₁ and p₂, and the consumer’s income is m. Find: consumer demand function for commodity 1 and commodity 2.

5.Consumer utility function: , where q is the consumption of goods and M is the income.

Seek: 1.The consumer’s demand function;

2.The consumer’s inverse demand function;

7.Someone’s utility function for x and y is. The price of the x is p₁, and the price of the y is p₂.

(1) When someone earns 100 yuan, where is his consumer equilibrium?

(2) What is the curve of someone’s price offer for the x commodity?

(3) What is someone’s demand curve for the x commodity?

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8. Neville’s passion is fifine wine. When the prices of all other goods are fifixed at current levels, Neville’s demand function for highquality claret is q = .02m-2p, where m is his income, p is the price of claret (in British pounds), and q is the number of bottles of claret that he demands. Neville’s income is 7,500 pounds, and the price of a bottle of suitable claret is 30 pounds.

1. If the price of claret rose to 40 pounds, how much income would Neville have to have in order to be exactly able to afffford the amount of claret and the amount of other goods that he bought before the price change? At this income, and a price of 40 pounds, how many bottles would Neville buy?

2. At his original income of 7,500 and a price of 40, how much claret would Neville demand?

3. When the price of claret rose from 30 to 40, the number of bottles that Neville demanded decreased by 20. The substitution effect (increased, reduced) reduced his demand by 2 bottles and the income effect (increased, reduced) reduced his demand by_____?

9. Please prove that why the quasi-linear utility function,，（）, can represent consumers’ preference for life necessities

10.Analyze the substitution effect and income effect of normal items, low-end items, and Giffen items with graphics.Please give examples in reality and further explain the characteristics of the demand curves of these three types of items.