Explain the game theory?

Good Y has a cross-price elasticity of demand with respect to Good X of 0.5. 100 units of Good Y

are demanded when Good X costs $50. Using the 'original' formula for cross-price elasticity of

demand between two points (ie arc elasticity), a rise in the price of Good X to $75 will lead to a

change in the demand for Good Y to:

A 150 units.

B 125 units.

C 75 units.

D 50 units.

4.7 The income elasticity of demand for a normal good:

A must be less than 1.

B must be greater than 1.

C must be positive.

D could be anything.

Describe three factors that will make the demand curve for a good more price-elastic, other

things being equal.

Shadow markets are most likely to be associated with:

A price ceilings which cause excess demand.

B price ceilings which cause excess supply.

C price floors which cause excess demand.

D price floors which cause excess supply.

4.10 A price floor set above the market equilibrium price is likely to cause:

A excess supply.

B excess demand.

C a decrease in price and a decrease in the quantity traded.

D an increase in price and an increase in the quantity traded.

Discuss the advantages and disadvantages of price ceilings.

Your discussion should include examples and be illustrated with appropriate diagrams.

If the demand for Good X is price-inelastic and the supply of Good X is price-elastic, then the

burden of a sales tax on Good X will be borne:

A equally by buyers and sellers.

B more heavily by buyers.

C more heavily by sellers.

D by neither buyers nor sellers.

Obtain formulas for the evaluation of a life annuity-due to (I) with an initial payment of 1 and with annual payments increasing thereafter by a. 3% of the initial annual payment b. 3% of the previous year' 5 annual payment. Express [D)x as an integral and prove the formula 3 - _ _ (Dha = \"as Give an expression for the actuarial accumulated value at age 70 of an annuity with the following monthly payments: - 100 at the end of each month from age 30 to 40 - 200 at the end of each month from age 40 to 50 - 500 at the end of each month from age 50 to 60 - 1,000 at the end of each month from age 60 to 70. Derive a simplied expression for the actuarial present value for a 25-year term insurance payable immediately on the death of [35), under which the death benet in case of death at age 35 + t is s3, 0 5 t E 25. Interpret your result. Derive a simplied expression for the actuarial present value for an 31-year term insurance payable at the end of the year of death of (x), under which the death benet in case of death in year k + 1 is rm 0 i: k a: n. Interpret your result. . Obtain a simplied expression for {12) {12) (man [Islam- . Consider an 11-year deferred continuous life annuity of 1 per year as an in- surance with probability of claim, "p1, and random amount of claim, a" a. Here T has p.d.f., 1P1\" p.1{n + t]. Apply (2.2.13) to show that the variance of the insurance equals 2 _ _ ' 2 UN up: (1 max) aim + at\" War ungW and verify that this reduces to (5.2.21). . Write the discrete analogue of the variance formula in Exercise 5.37. b. Show that the actuarial present value can be expressed as 2 affi- k=1 If in Exercise 5.23 the yearly income does not cease at age I + u but continues at the level a while (I) survives therafter, the actuarial present value is de- noted by \"El tag\". a. Display the present-value random variable, Y, for this annuity as a function of the K and I random variables. 13. Show that the actuarial present value can be expressed as I'Il 2 salm- r=o Verify the formula scam + Ta?\" = as, where T represents the future lifetime of (I). Use it to prove that ads), + (Di), = ax. where (fish is the actuarial present value of a life annuity to (at) under which payments are being made continuously at the rate of t per annum at time t. {m} + . . . From :13 = rig\") + 11%\") a', show that the assumption of umforrn distri- bution of deaths in each year of age leads to w 1' n 1 1 \"an-E = 10;; [am + u up, 111+\" + (E W) u up: AIM} m 5.5 Establish and interpret the following formulas: a. 1 = 11\"" Sig\") + xix b_ 1 = dun} lm} + Ax c. 3:? = (we as a. as = (BMW-l) as e. 3:13,} = (1 + am\" 353. Let H(m) = aw $53\"). Prove that H{m) 2: 0 and lim H{m) = 0. M allaueous For 0 E t E 1 and the assumption of a uniform distribution of deaths in each year of age, show that __ (1 + ith'r' - t{1 + i) b. \"a: = u*[(1 + as, to +13]