Answer the questions below:

Suppose a firm in monopolistic competition is in long-run equilibrium. What is the effect on the

firm's output, price and profit in the short run and in the long run of:

(i) a rise in the firm's fixed costs of production, eg an increase in rent [5]

(ii) a decrease in the firm's variable costs of production, eg a reduction in wages.

8.7 Outline the key feature that distinguishes:

(a) monopolistic competition from perfect competition

(b) oligopoly from monopoly.

Compare and contrast oligopoly, monopolistic competition and perfect competition in terms of:

(a) the products that they offer

(b) the level of profits that they make.

Discuss the relative benefits to consumers of the four main market structures.

Consider the following payoff matrix for two firms, A and B. The payoffs show the profit resulting

from various combinations of low-price and high-price strategies.

Firm B

High price Low price

Firm A

High price (50, 50) (10, 80)

Low price (80, 10) (20, 20)

(i) State which strategy would maximise joint profit.

(ii) Determine the dominant strategy for each firm and state whether there a dominant

equilibrium.

(iii) State whether this game has a Nash equilibrium.

(iv) Explain what happens to the payoff table if Firms A and B introduce a price matching

clause (ie a promise to match the lowest price offered by a competitor) into their

contracts with customers.

(iv) State which strategy firms would choose in this situation.

Prove that the variance of the loss associated with a single premium whole life insurance is less than the variance of the loss associated with an annual premium whole life insurance. Assume immediate payment of claims on death and continuous payment of benefit premiums. Show that (1 + day ) dx P(A,) dAx dx = p (x). n 6.3 On the basis of the Illustrative Life Table and an interest rate of 6%, calculate values for the annual premiums in the following table. Note any patterns of inequalities that appear in the matrix of results. Fully Continuous Semicontinuous Fully Discrete P(A35:10) P(A 35:10) P35:101 P(A 35:30) P(A 35:30) P35:30 P(A35:60) P(A 35:60) P 35:60 P(A35) P(A 35) P 35 P(A 35:30) P(A 35-30) P 35:30 P(A 35.10) P(A 35:10) P 35:10 Show that 20 2:30 - x:20) = 20P(20/10Ax). Generalize Example 6.3.1 where *9x = (1 - r)rk k = 0, 1, 2, ... ; that is, derive expressions in terms of r and i for A,, ax, P., and 2A, - (A.) 1 / (d a . ). 6.4 Using the information given in Example 6.4.1, calculate the value P. Jsing various formulas for am, first under the assumption of a uniform dis- ribution of deaths in each year of age, show that the ratio a xiin (6.4.2) can be expressed as the reciprocal of each of (a) and (b). As an alternative, if the development of (5.4.10) is followed show that the ratio is the reciprocal of (c). a. an" - B(m)P x:A b. a(m) - B(m)(Pin + d) c. 1 m - 1 2m Pan + d). Refer to Example 6.4.1(b) and directly calculate A 50:20 P(2)(A 50:20) a 50:20 using the Illustrative Life Table for the actuarial present values in the nu- merator and the denominator. If pl (12) x:20 = 1.032 PT:201 and Prag = 0.040, what is the value of P(2? on 6.5 Arrange in order of magnitude and indicate your reasoning: P(2)( A 40:25), P( A 40:25), Pli(A 40:25), P(A 40:25), P121( A 40:25). Given that ad 99 7(12) 100 evaluate P(12(A,) Pill(A) If P(A ) = 0.03, and if interest is at the effective annual rate of 5%, calculate the semiannual benefit premium for a 50,000 whole life insurance on (x) where premiums are apportionable. Show that A .. - Ax (m) pim(A n ) - P((An) = P(A . ) = P(A :)