micro

1. A consumer has the utility function U ( X , Y ) = MIN(3X, 6Y) and $109 to spend. The price of X = $5, and the price of Y = $1. Calculate the equivalent variation when the price of X changes to $8. Round your answer to two decimal places. Your answer should be a positive number.

2.A consumer has the utility function U(X,Y)=X1/2Y1/2 and $100 to spend. The price of X = $5, and the price of Y = $1. Calculate the compensating variation when the price of X changes to $7. Round your answer to two decimal places. Your answer should be a positive number.

3.Suppose a consumer's utility function is given by U(X,Y) = X1/4Y3/4. The price of X is PX = 3, and the price of Y is PY = 1. If the consumer has $32 to spend, how much of Good X will the consumer buy in her optimal bundle? Round your answer to 2 decimal places

4.Suppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 7units of X and a TOTAL of 7 units of Y. The consumers' utility functions are given by:

UA(X,Y) = 3X + Y

UB(X,Y) = X2* Y

For Each of the following allocations, answer True if it is Pareto Efficient, and False if it is not Pareto Efficient.

5. Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 2 units of good X and 2 units of good Y. Consumer B is given an initial endowment of 2 units of good X and 2 units of good Y. Consumer A's utility function is given by:

UA(X,Y) = X*Y4,

and consumer B's utility function is given by

UB(X,Y) = X*Y.

Therefore, consumer A's marginal utilities for each good are given by:

MUX =Y4

MUY = 4XY3

Also, consumer B's marginal utilities for each good are given by:

MUX = Y

MUY = X

Suppose the price of good Y is equal to one. What price of good X will lead to a competitive equilibrium? Please round your answer to 4 decimal places.

Suppose the demand for x1 is x1 = p1ap2bmc, where p1 and p2 are prices of x1 and x2, respectively and m is income. What are the values of the own-price, cross-price and income elasticities of demand in this equation? Write the estimable form of this demand equation. What restrictions must govern the magnitudes of the coefficients to ensure the demand function you estimate is homogeneous of degree zero?

For thirty years, the U.S. government subsidized ethanol directly and indirectly with the goal of replacing 15% of U.S. gasoline use with this biofuel. The explicit ethanol subsidy was eliminated in 2012. (However, as of 2015, the government continued to subsidize corn, the main input, and required that gas stations sell a gasoline-ethanol mix, which greatly increases the demand for ethanol). In 2011, the last year of the ethanol subsidy, the subsidy cost the government $6 billion. A 2010 Rice University study reports that the government spent $4 billion in 2008 to replace about 2% of the U.S gasoline supply with ethanol, at a cost of about $1.95 per gallon on top of the gasoline retail price. The combined ethanol and corn subsidies amounted to about $2.59 per gallon of ethanol. According to a study (McPhail and Babcock, 2012), the supply elasticity of ethanol is about 0.13, and the demand elasticity is about -2.1. a. What was the incidence rate of the ethanol subsidy on purchasers of ethanol? b. Some free marketers argue that subsidies are inefficient. What was the deadweight loss, if any, associated with the ethanol subsidy? c. If the subsidy on ethanol were increased, how will it affect the incidence rate on purchasers relative to sellers of ethanol? How will it affect the deadweight loss? (Note: A subsidy is a negative tax through which the government gives people money instead of taking it from them).