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Problem Set Three

Part One: Multiple Choice Questions

(A Note:  The  number of correct answers to multiple choice questions can be one or more than one.)

Q1. As for exogenous variables and endogenous variables, which expression/expressions is/are correct ?  (     ) (5 points)

A. An exogenous variable is determined outside the model.

B. An exogenous variable is a variable has no effect on endogenous variables.

C. An endogenous variable is determined outside the model.

D. An endogenous variable is a variable has no effect on exogenous variables.

Q2. In our simple closed one-period model in class, which expression/expressions is/are correct ?  (     ) (5 points)

A. TFP, government tax, and capital input are exogenous variables.

B. TFP, real wage rate, and government purchase are exogenous variables.

C. TFP, labor supply, and labor demand are endogenous variables.

D. TFP, and capital input are exogenous variables.

Q3.   As for the government budget, in our simple closed one-period model in class,

which expression/expressions is/are wrong ?  (     ) (5 points)

A. If the government purchase is greater than consumer’s consumption, then it is bud-get deficit.

B. If the government purchase is greater than consumer’stax payment, then it is budget deficit.

C. If the government purchase is negative, then it is budget deficit.

D. If the tax collected by the government is zero, then it is budget deficit.

Q4. Suppose in the world, there were only two people (individual A and individual B)

and 100 apples. In below cases, which is/are Pareto Optimality ?  (     ) (5 points)

A. Both A and B get 50 apples.

B. A gets 100 apples, and B gets 0 apples.

C. A gets 0 apples, and B gets 100 apples.

D. A gets 70 apples, and B gets 30 apples.

Q5. In below cases, which can lead to social inefficiencies ?  (

A. Positive externality

B. Perfect competition market

C. A high level of lump-sum tax collected by the government

D. Negative externality

) (5 points)

Q6. In the competitive equilibrium in our basic simple model, which expression/expressions

is/are wrong ?  (     ) (5 points)

A. Government purchase can not be lower than consumer’s consumption.

B. The labor supply is equal to the labor demand.

C. Government budget can has a surplus.

D. The profit earned by the firm can be improved if the firm hires more workers.

Q7.  If MRSC,l   = , and MPN

competitive equilibrium ? (     ) (5 points)

A. h = 8, C = 5, and Nd  = 2

B. h = 10, C = 5, and w = 2

C. h = 8, C = 1, and w = 1

D. h = 10, C = 2, and Nd  = 2

Q8. In the competitive equilibrium, if real wage rate is 2, and the government suddenly put a the distorting tax rate, which is 0.2, then which expression/expressions is/are

correct ?  (     ) (5 points)

A. This equilibrium is still Pareto optimal.

B. The marginal product is greater than real wage rate.

C. The marginal rate of substitution is less than real wage rate.

D. The marginal product is greater than the marginal rate of substitution.

Q9. In the competitive equilibrium, an increase in government tax will lead to (     ) (5

points)

A. A decrease in both labor supply and labor demand.

B. A decrease in consumption but an increase in labor supply.

C. An increase in total output.

D. An increase in real wage rate.

Q10. In the competitive equilibrium, a reduction in total factor productivity will lead

to (     ) (5 points)

A. An increase in total output.

B. A decrease in real wage rate.

C. A decrease in consumer’s consumption.

D. An increase in capital.

Q11. As for the welfare theorems, which expression/expressions is/are Correct ?  (     )

(5 points)

A. A competitive equilibrium is better than a Pareto optimal allocation.

B. First fundamental theorem of welfare economics states that the consumer can find

optimal consumption bundle in the competitive equilibrium.

C. Second fundamental theorem of welfare economics discusses the relationship between

Pareto optimal and consumer’s utility.

D. Both first and second fundamental theorems of welfare economics discuss the rela-

tionship between competitive equilibrium and Pareto optimality.

Q12. Among below expressions, which is/are correct?  (     ) (5 points)

A. In the competitive equilibrium in our simple model in class, the real wage rate is

always equal to marginal product of labor.

B. In the competitive equilibrium in our simple model in class, if the government put a lump-sum tax to the consumer, the real wage rate will always be equal to marginal

rate of substitution.

C. In the competitive equilibrium in our simple model in class, if the government put a positive proportional wage income tax to the consumer, the real wage rate will never

be equal to marginal rate of substitution.

D. All points in the production possibilities frontier give same utility for the represen-

tative consumer.

Part Two

Q1. Given the utility function of the representative consumer:

U = C2 l2

C = w(h l) + π T

the production function of the representative firm:

Y = 3K1/3(Nd )2/3

In the competitive equilibrium, if K = 8, h = 10, and Nd*  = 8, what is the optimal consumption bundle, (C* , l* ), for the representative consumer?  (10 points) What is the

government tax T?  (10 points)

Q2. Given the utility function of the representative consumer:

U = C3 l3

C = w(1 t)(h l) + π

the production function of the representative firm:

Y = K1/2(Nd )1/2

If the proportional government tax t = 0.5, capital is K =  16, and total hours are

h = 16, is wage rate w = 1 a competitive equilibrium wage rate?

Please show your process.  Note:  in this case, total tax collected by the government is

t × w × (Ns ), so the government purchase G = t × w × (Ns ) (20 points)