Explain:

The problem of scarcity in economics:

A exists only in economies which rely on the market mechanism.

B could be eliminated if we force prices to fall.

C means that there are shortages of some goods.

D exists because there are insufficient resources to satisfy human wants.

Aneconomy can produce either Good X or Good Y. The opportunity cost of producing an extra

unit of Good X is:

A the value of the capital and labour used to produce Good X.

B the number of units of Good Y that must be given up in order to produce an extra unit of

Good X.

C the cost of producing Good X less the cost of producing Good Y.

D the amount of Good X that would have been produced in the following year.

Define the two branches of economics: macroeconomics and microeconomics.

Describe and discuss the scope of economics in terms of the problems of the allocation of scarce

resources.

Explain the differences between a command economy and a free market economy.

The random variable Z is the present-value random variable for a whole life insurance of unit amount payable at the moment of death and issued to {x}. If E = 0.05 and p.10) = 0.0]: a. Display the formula for the p.d.f. of Z. b. Graph the p.d.f. of Z. c. Calculate 14,, = E[Z] and Var(Z). The random variable Z is the present-value random variable for an 31-year endowment insurance as dened in Section 4.2.2. Exhibit the it of Z in terms of the d.f. of T. The random variable Z is dened as in Exercise 4.12. If 5 = 0.05,. l-lxlil = 0.01, and n = 20: a. Display the d.f. of Z. b. Graph the d.f. of Z. c. Calculate A: = E[Z] using the distribution of Z. [Hint Consider using the complement of the d.f.] m 4.3 11:1!Jr = 100 - x for 0 s x 5 100 and 1' = 0.05, evaluate a. Aw. b. (114)\". Show that Ara = A151 + 0'\" mp, AHWW for m c: n and interpret the result in words. If A: = 0.25, Aha, = 0.40, and Asia = 0.55, calculate a. Amicl b. Aim. a. Describe the benets of the insurance with actuarial present value given by the symbol HALE. b. Express the actuarial present value of (a) in terms of the symbols given in Tables 4.2.1 and 4.3.1. In Example 4.3.2, let the expected size of the fund it years after the agreement, and immediately after the payment of death claims, be denoted by ER, where E0 = (100](1,000 A30) = 10,248.35. a. Start with (4.3.10) and develop the forward recursion formula E, = 1.05E,_, 100,000k_1|q30. b. Use the recursion formula developed in (a) to conrm that E5 = 12,762.58. an. 4.4 Consider the timescale measured in intervals of length 1/ m where the unit is a year. Let a whole life insurance for a unit amount be payable at the end of the m-thly interval in which death occurs. Let k be the number of complete insurance years lived prior to death and let ,5 be the number of complete m-ths of a year lived in the year of death