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Question 1

A consumer has an income of E200 which can be spent either on Good X or on Good Y. Good X costs $20 per unit and Good Y costs $10 per unit. Good X is an inferior good and Good Y is a normal good. Read parts (i) to (iv) before answering: (i) Draw a budget line for the consumer. Label the quantities of Good X and Good Y at the points where the budget line meets the Good X and Good Y axes. (ii) Draw an indifference curve for Good X and Good Y at a point where the consumer is maximising satisfaction. Label the curve A, the quantity of X consumed as X1 and quantity of Y consumed as Y1. (ili) Show the effect on the budget line of an increase in the consumer's budget to $400. Label the quantities of Good X and Good Y at the points where the budget line meets the Good X and Good Y axes. (iv) Draw a new indifference curve for Good X and Good Y on the new f400 budget line at a point where the consumer is maximising his satisfaction. Label this new curve B, the quantity of X consumed as X2 and quantity of Y consumed as Y2.A consumer has an income of $500 which can be spent either on Good X or on Good Y. Good X costs f20 per unit and Good Y costs $25 per unit. Good Y is a normal good. Read parts (i) to (iv) before answering: (i) Draw a budget line for the consumer. Label the quantities of Good X and Good Y at the points where the budget line meets the Good X and Good Y axes and label the budget line B1.(ii) Draw an indifference curve for Good X and Good Y at a point where the consumer is maximising satisfaction. Label this original equilibrium position a, and the quantity of Good X consumed as X1. (iii) The price of Good X falls to f10 per unit. Draw a new budget line, label the quantity of Good X at the point where the budget line meets the Good X axis, and label the budget line B2. (iii) To identify the substitution effect of the price change, draw a new budget line that is parallel to the new budget line B2 (therefore reflecting new relative prices) but tangential to the original indifference curve A (therefore representing the original level of utility and real income), and label it B3. Label the tangency point b and the quantity of Good X at this point as X'. The movement from X1 to X' is the substitution effect. (iv) On the budget line B2, mark the following possible new equilibrium positions: c for a normal good d for an inferior but non-Giffen good e for a Giffen good and the resulting quantities of Good X demanded as X2c, X2d and X2e. (v) For the three types of goods listed above, identify the income effect and the overall price8.1 An explorer aged exactly 57 has just made a proposal to a life office for a whole life assurance with a sum assured of f10.000 payable at the end of the year of death. For lives accepted at normal rate, level annual premiums are payable until death under this policy. The explorer is about to undertake a hazardous expedition which will last three years. The life office estimates that during these three years the explorer will experience a constant addition of 0.02871 to the normal force of mortality, but after three years will experience normal mortality. The life office quotes a level extra premium payable for the first three years. Calculate this level extra premium on the following basis: normal mortality: A1967-70 ultimate interest: 3% per annum expenses: none 8.2 An impaired life aged exactly 55 wishes to effect a without profit endowment assurance for a sum assured of f1.000 payable at the end of 10 years or at the end of the year of earlier death. Level annual premiums are payable throughout the term of the policy. Special terms are offered on the assumption that the life will experience mortality which can be represented by: (a) for the first five years, a constant addition of 0.009569 to the normal force of mortality, and (b) for the remaining five years, the mortality of a life 8 years older. The life office quotes a level extra premium payable throughout the term. Calculate this level extra premium. Basis: normal mortality: A1967-70 ultimate interest: 376 per anmim expen969: hione