Principles of Microeconomic Theory 1: Problem Set 2
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Principles of Microeconomic Theory 1: problem set 2.
Part A：Answer the following multiple choice questions.
Question 1. suppose that the demand function for a good is given by:
Q = 100 - 0.8p + 0.6psub + 0. 1Y
where p is the good,s own price, psub is the price of a substitute, and Y is the consumer,s income. suppose that p = 8, psub = 10 and Y = 2000. which one of the following statements is correct?
(a) The price elasticity of demand is 0.21 and the cross price elasticity is 0.02.
(b) The price elasticity of demand is 21 and the cross price elasticity is 2.
(c) The cross price elasticity is 0.2 and income elasticity is 6.7.
(d) The price elasticity of demand is -0.02 and the income elasticity is 0.67.
(e) The price elasticity of demand is -0.21 and the income elasticity is 6.7.
Question 2. (E认clidean pre∫erences). The distance between two bundles a = (a1 , a2 ) and b = (b1 , b2 ) in commodity space is given by1 :
‘(a1 - b1 )2 + (a2 - b2 )2 .
suppose that a consumer has a bliss point, e. Bundle e is the most preferred bundle. she is indiferent between bundles that are the same distance frome, and closer toe is always preferred. which one of the following statements is correct?
(a) The consumer,s preferences are rational, but violate the axiom of monotonicity.
(b) The consumer,s preferences are rational and also satisfy the axiom of monotonicity.
(c) The consumer,s preferences are not rational.
(d) The consumer,s preferences are not transitive.
(e) None of the above.
Question 3. suppose that there are three individuals (1, 2, and 3) who must choose between options a, b,c. These individuals have the following preferences:
a >1 b >1 c,
c >2 a >2 b,
b >3 c >3 a.
To construct a social pre∫erence >* the individuals consider using a democratic, majority voting procedure. That is, a >* b if at least two individuals prefer a to b, and soon. which one of the following statements is false?
(a) The social preference is not rational.
(b) The social preference is not transitive.
(c) The social preference is rational.
(d) There is no option that is the most socially preferred.
(e) There is no option that is the least socially preferred.
Part B：provide written answers for the following questions.
Question 4. suppose that consumer demand is given by Q = AP-2 and theirm,s supply function is given by Q = BP2.5 , where A, B > 0. A policy maker, Mr. Meanswell, is proposing that a unit tax t is imposed on the good. He claims that, by collecting the tax from irms, consumers will not be harmed.
Assuming that the tax is small, calculate the incidence of the tax on consumers in this market. Explain why Mr. Meanswell is incorrect.
Question 5. Explain fully the axioms of rational preferences and the axiom of monotonic- ity. Explain why indiference curves must bethin, downward sloping, and cannot intersect.
2023-08-25