Answer all the questions below well.

The quantity theory of money assumes that the:

A velocity of circulation and nominal output are reasonably stable.

B ratio of the velocity of circulation to the price level is reasonably stable.

C ratio of the money supply to the velocity of circulation is reasonably stable.

D velocity of circulation and real output are reasonably stable.

Keynes rejected the classical view that people should be encouraged to save to get out of

recession because increased savings will:

A be channelled into investment.

B reduce interest rates and hence the currency.

C reduce consumption and hence investment.

D improve confidence and increase investment.

When national income is less than full-employment national income, by how much must aggregate

demand be increased to achieve full employment?

A the amount by which the equilibrium level of national income falls short of the full employment level

B the amount by which injections exceed withdrawals at the full-employment level of

output

C the amount by which national income exceeds aggregate demand at the full-employment

level of national income

D the size of the balance of payments deficit at the full-employment level of national

income

16.7 Which of the following is inconsistent with the co-existence of unemployment and inflation?

A structural unemployment

B a downward-sloping Phillips curve

C a smaller multiplier effect than in an economy with no inflation

D a horizontal AS curve

The accelerator principle states that:

A investment is increased when interest rates fall.

B an increase in investment will lead to a more than proportionate increase in output.

C the level of investment expenditure is determined by the rate of change of national

income.

D investment is increased when interest rates rise.

Discuss the role that consumption plays in the business cycle.

Describe the accelerator theory and explain how it can be used to explain business cycles.

Determine the benet reserve for t = 2, 3, 4, and 5 for the insurance in Ex ample 6.1.1. Determine the exponential reserve for t = 2. 3,. 4. and 5 for the insurance in Example 6.1.1. Determine the exponential reserve for t = 1, 2, 3. 4, and 5 for the insurance in Exercise 6.2. Consider the insurance in Example ?.1.1 and the insurer of Exercise 6.3 with utility function act) = x {1.01 x2. 0 x: x s': 50. Determine the reserve. W, for k = 1, 2,. 3. and 4 such that the insurer, with wealth 10 at each duration, will be indifferent between continuing the risk while receiving premiums of 0.3036 (from Exercise 6.3} and paying the amount RV to a reinsurer to assume the risk. Consider a unit insurance issued to (0} on a fully continuous basis using the following assumptions: i. De Moivre's law with to = 5 ii. i = 0.06 iii. Principle III of Example 6.1.1 with o: = [1.1. a. Display equations which can be solved for the exponential premium and the exponential reserve at t = 1. For an n-year unit endowment insurance issued on a fully continuous basis to (x), define ,L, the prospective loss after duration t. Confirm that Var(,LIT > t) = - (8a x7)2 The prospective loss, after duration t, for a single benefit premium n-year continuous temporary life annuity of 1 per annum issued to (x) is given by L = JaT-A t s T f] and Var(,LT > t) in symbols of actuarial present values. Write prospective formulas for a. 38V(A 35:30) b. the benefit reserve at the end of 5 years for a unit benefit 10-year term insurance issued to (45) on a single premium basis. a. For the fully continuous whole life insurance with the benefit pre- mium determined by the equivalence principle, determine the outcome un = T(x) - t such that the loss is zero. [Caution: For large values of t, a solution may not exist.] b. Determine the value of up for t = 20 in Example 7.2.3 and compare it to Figure 7.2.1 for reasonableness. The assumptions of Example 7.2.3 are repeated. Find the value of t such that the minimum loss is zero. Check your result by examining Figure 7.2.2. a. Repeat the development leading to (7.2.9) to obtain the d.f. for the loss variable associated with an n-year fully continuous endowment insurance. b. Draw the sketch that corresponds to Figure 7.2.1 for this endowment insurance. Repeat Exercise 7.11 for an n-year fully continuous term insurance. Confirm that (7.2.10) satisfies the conditions for a p.d.f. ion 7.3 Write four formulas for ?:V(A.). Write seven formulas for 10 V(A 40:20). Give the retrospective formula for 20V(30 35)<>