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Please solve microeconomics problems that i submitted attached file.
1. A consumer’s income is w. He wants to buy two products:1 and 2. His utility function is
U=(x1+2)*(x2+2). x1 and x2 mean products’ quantity. Product 1 and 2’s market price is p1 and p2.
(1) Please deduce the marginal utility substitution rate of x1 to x2 and prove its decrease. That is the quantity of the consumer’s buying product 1 increasingly, he arbitrarily gives up to buy product 2 (on the same indifference curve). What is the equilibrium price and quantity of buying products 1 and 2?
(2) Please derive the Marshallian demand function and indirect utility function for two products.
(3) Is product2 a Inferior good or inferior good?
(4) For a given utility level μ, please derive the expenditure function. Use the expenditure function to find the Hicksian demand function for these two products.
One firm owns two factories, and factories’ cost functions are:
Consider the following incomplete information game:
City A’s policy is lineup for applicants to get a vehicle plate after they buy a new energy vehicle. From database, we know city A has 54,000 new energy vehicles plate per year. So city A’s applicants needs to wait eight years to get a vehicle plate. In another city B, this city’s policy is bidding, and the lowest price is at least 88,000. Use microeconomic theory to establish relevant model analysis:
c1(y1)=2y1^2 and c2(y2)=(y2+2)^2
(1) What conditions will the firm only use one factory for production? What conditions does the firm need two factories to produce together?
(2) Derive the firm’s cost function.
Game 1 Game 2
(1) Nature decides two participators to join Game 1 or game 2. Each game will be chosen equally.
(2) Participators knew Nature how to choose horizontal number, but participators did not know nature how to choose vertical number.
Please find the Bayes-Nash equilibrium of the above game.
(1) What are the advantages and disadvantages of lineup and bidding policies for solving urban traffic problems?
(2) Which would be more effective in reducing urban traffic problems: Fuel Tax or Charging in Congestion Roads ?
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1. A consumer’s income is w. He wants to buy two products:1 and 2. His utility function is
U=(x1+2)*(x2+2). x1 and x2 mean products’ quantity. Product 1 and 2’s market price is p1 and p2.
(1) Please deduce the marginal utility substitution rate of x1 to x2 and prove its decrease. That is
the quantity of the consumer’s buying product 1 increasingly, he arbitrarily gives up to buy
product 2 (on the same indifference curve). What is the equilibrium price and quantity of buying
products 1 and 2?
(2) Please derive the Marshallian demand function and indirect utility function for two products.
(3) Is product2 a Inferior good or inferior good?
(4) For a given utility level μ, please derive the expenditure function. Use the expenditure
function to find the Hicksian demand function for these two products.
2. One firm owns two factories, and factories’ cost functions are:
c1(y1)=2y1^2 and c2(y2)=(y2+2)^2
(1) What conditions will the firm only use one factory for production? What conditions does the
firm need two factories to produce together?
(2) Derive the firm’s cost function.
3. Consider the following incomplete information game:
Game 1
Game 2
(1) Nature decides two participators to join Game 1 or game 2. Each game will be chosen equally.
(2) Participators knew Nature how to choose horizontal number, but participators did not know
nature how to choose vertical number.
Please find the Bayes-Nash equilibrium of the above game.
4. City A’s policy is lineup for applicants to get a vehicle plate after they buy a new energy vehicle.
From database, we know city A has 54,000 new energy vehicles plate per year. So city A’s
applicants needs to wait eight years to get a vehicle plate. In another city B, this city’s policy is
bidding, and the lowest price is at least 88,000. Use microeconomic theory to establish relevant
model analysis:
(1) What are the advantages and disadvantages of lineup and bidding policies for solving urban
traffic problems?
(2) Which would be more effective in reducing urban traffic problems: Fuel Tax or Charging in
Congestion Roads ?
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