Answer all the questions below:

Explain with the aid of a diagram what limit pricing means.

9.2 Define third-degree price discrimination and outline the conditions that must hold for a firm to be

able to practise third-degree price discrimination.

(i) Using supporting diagrams show how a profit-maximising firm will practise third-degree

price discrimination by dividing its market into two distinct markets A and B with different

demand elasticities. Show the price in the market with inelastic demand (Market A) and

in the market with a more elastic demand (Market B) and the overall output of the firm

made up of demand in both Market A and Market B.

(ii) Give an example of second-degree and third-degree price discrimination.

A firm that produces a main product and a by-product will maximise profits if it:

A decides on the viability of producing the by-product after it has made the decision to

produce the main product.

B selects the level of output of the by-product where marginal cost of the by-product equals

its marginal revenue.

C selects the combined output where the combined marginal cost equals the combined

marginal revenue.

D uses cost-based pricing for the main product and the by-product.

9.5 (i) Draw a graph showing the four stages of the product life cycle.

(ii) Describe the stages of the life cycle of basic mobile phones.

(iii) Explain the pricing policies of the basic mobile phone companies during the cycle,

including the later introduction of more sophisticated smart phones.

. The single premium is returned at the end of 10 years if (65) reaches age 75, is given by 100,000 ; (12) * (12) = 100,000(B) 65:10 $ 65:10. where (B) denotes the answer to part (b) of this exercise. An insurance issued to (35) with level premiums to age 65 provides . 100,000 in case the insured survives to age 65, and . The return of the annual contract premiums with interest at the valuation rate to the end of the year of death if the insured dies before age 65. If the annual contract premium G is 1.14 where u is the annual benefit pre- mium, write an expression for T. If 15P45 = 0.038, P45:15) = 0.056, and A 60 = 0.625, calculate P 45:15) . A 20-payment life policy is designed to return, in the event of death, 10,000 plus all contract premiums without interest. The return-of-premium feature applies both during the premium paying period and after. Premiums are an- nual and death claims are paid at the end of the year of death. For a policy issued to (x), the annual contract premium is to be 110% of the benefit pre- mium plus 25. Express in terms of actuarial present-value symbols the annual contract premium. Express in terms of actuarial present-value symbols the initial annual benefit premium for a whole life insurance issued to (25), subject to the following provisions: . The face amount is to be one for the first 10 years and two thereafter. . Each premium during the first 10 years is 1/2 of each premium payable thereafter. . Premiums are payable annually to age 65. . Claims are paid at the end of the year of death. Let L, be the insurer's loss on a unit of whole life insurance, issued to (x) on a fully continuous basis. Let L2 be the loss to (x) on a continuous life annuity purchased for a single premium of one. Show that L, = L, and give an ex- planation in words. An ordinary life contract for a unit amount on a fully discrete basis is issued to a person age x with an annual premium of 0.048. Assume d = 0.06, A* = 0.4, and 2A, = 0.2. Let L be the insurer's loss function at issue of this policy. a. Calculate E[L]. b. Calculate Var(L).as an annual premium. Interpret your result. On the basis of the Illustrative Life Table and an interest rate of 6%, calculate the components of the two decompositions a. 1,000 P50:20 = 1,000(P 30:20) + P 50-20) b. 1,000 P50-20 = 1,000 (P 30:20 + $ 20 Consider the continuous random variable analogue of (6.6.3), W =. UT 1 STI 0 =T <>