Answer the questions below well:

Draw a diagram showing the demand D and supply S curves for a good. Show the

equilibrium price by P1 and the equilibrium level of sales by Q1 .

(ii) On your diagram draw the line S T to show the new supply curve after an excise tax of T

is imposed on the good. Denote the new equilibrium price and quantity by 2P and Q2 .

(iii) Show clearly on your diagram consumer and producer surplus before and after the tax,

the government revenue and the excess burden (ie net welfare loss) from the tax.

Discuss the advantages and disadvantages of price ceilings and price floors.

Your discussion should include examples. Illustrate your answer with the aid of appropriate

diagrams.

Explain how the following examples of collusion between firms are detrimental to consumers:

(i) horizontal price-fixing agreements

(ii) agreements to share out markets

(iii) agreements to limit production

(iv) bid rigging.

Which of the following is NOT a reason why market forces fail to generate sufficient research and

development activity?

A Some firms may try to copy the ideas of other firms.

B Firms will try to gain a competitive advantage over other firms in the market.

C Firms may duplicate other firms' research.

D The benefit to the firm of a particular piece of research is uncertain.

Which of the following would NOT be likely to increase the amount of research performed?

A the introduction of a patent system

B increased funding to universities

C introduction of a tax on firms' research spending

D subsidies to firms conducting R&D

10.12 (i) Outline the reasons why the market may fail to provide an environment in which

technological change can thrive. [3]

(ii) Outline how the government may intervene in the market to encourage firms to

undertake research and development.

Suggest ways in which governments could regulate monopolies and oligopolies.

Determine the benefit 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 i = 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 5.3 with utilitj,r function a(x] = x - [till x2, [I at: x s: 5D. Determine the reserve, ,V, for i: = 1, 2, 3, and 4 such that the insurer, with wealth 11] at each duration, will be indifferent between continuing the risk while receiving premiums of 0.30360 (from Exercise 6.3) and paving the amount ,1! to a reinsurer to assume the risk. Consider a unit insurance issued to {D} on a fully continuous basis using the following assumptions: L De Moivre's law with to = 5 ii. i = ans iii. Principle Ill of Example 6.1.1 with a = ill. a. Display equations which can be solved for the exponential premium and the exponential reserve at t = l. b. Solve the equations of (a) for the numerical values for the exponential premium and exponential reserve. Numerical methods must be used to obtain these required solutions. on 7.2 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) = Axtin-1 - (A xtin-1)2 (8a x:7)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 = T t] and Var(,LT > t) in symbols of actuarial present values. Write prospective formulas for a. 20V(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 Uo = 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 uo 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. n 7.3 Write four formulas for 18V(A 40). Write seven formulas for 10 V(A 40:20). Give the retrospective formula for 20V(30/2 35)