- QUESTION THREE (20 MARKS) The following trial balance was extracted from the books of Rydone, a sole trader, at 31^st December 2021: Ksh Ksh. Provision for bad debts General Expenses Bank balances Motor van at cost/Provision for depreciation Proceeds on sale of van Motor expenses Freehold premises at cost Rent received Provision for depreciation on buildings The following matters are to be taken in to account: 1. Stock in trade at 31^st December 2021 was Ksh . 9.884 2. Rates paid in advance at 31^st December 2021, Ksh.40 3. Rent receivable due at 31^st December 2021, Ksh.250 4. Lighting and heating due at 31^st December 2021, sh.85 5. Provision for doubtful debts to be increased to Ksh.388 6. Included in the amount for insurance Ksh.172 is an item for Ksh82 for motor insurance and this amount should be transferred to motor expenses. 7. Depreciation has been and is to be charged on vans at an annual rate of 20% on cost. 8. Depreciate buildings Ksh.500 9.On 1^st January 2021 a van which had been purchased for Ksh.1,000 on 1^st January 2018 was sold for Ksh250 . The only record of matter is the credit of Ksh.250 to "Proceeds of sale on van" account. Required: A Statement of Profit and Loss for the year ended 31^st December 2021 and a Statement of Financial Position as at date using vertical format.
- a) Graphically and mathematically, show that in short runs profit maximization , firm price of marginal product is equal to input price. (8mks) b) A monopolist faces the following markets with the following demand functions Q=b_(0)-dot (b)_(1)P Show mathematically and illustrate diagrammatically the slope of the MR is twice the slope of AR (6mks) c) Derive the relationship between marginal urility and marginal rate of substitution (6mks) d) Suppose utility function of a consumer is given by II=f(x_(1)x_(2))=x^2/3x_(2)^1/2 Trice of commodity X_(1) is Ksh 10 per unit and price of commodity X_(2) is Ksh 15 per unit.How many units of two commodities, will he buy given that his income is equal to Ksh 450 (10mks) ESTION TWO (20MKS) 1) Mathematically, derive the relationship between price elasticity and marginal revenue of a firm. (6mks) ii) A. monopolist has the following total cost function Q=10div 5Q if the price elasticity for his product is -2 find out what price he will fix for his product.
- 38. A calculator company produces a handheld calculator and a scientific calculator. Long -term projections indicate an expected demand of at least 150 scientific and 100 handheld calculators each day. Because of limitations on production capacity, no more than 250 scientific and 200 handheld calculators can be made daily. To satisfy a shipping contract, a minimum of 250 calculators must be shipped each day. If each scientific calculator sold , results in a 20 dollars loss, but each handheld calculator produces a 50 dollars profit; then how many of each type should be manufactured daily to maximize the net profit?
- 30. Didierlimited manufactures three products; tables, sideboards and chairs which require special material, timber and labour. In a given week, there are 92 units of special material, 116 pieces of timber and 140 hours of labour. The requirements of special materials are 2 units, 4 units and 2 units , for a + sideboard and chair respectively Manufacturing a table or a sideboard requires 2 hours of labou while a chair requires 4 hours. Timber requirements are 4 pieces, 2 pieces and 2 pieces for a tai sideboard and a chair respectively. At least 2 tables and 4 chairs must be made. The profit contributions are £30,£40,£20 for a table, sideboard and chair respectively. Formulate the underlying LP and solve it to advice Didier limited how to maximize profits.
- jii) Discuss if x. is a normal good to Mary's can Discuss the differences between the following terms'as used in ecor 2mics(use graph where iec ssary); i) Feasible allocation and Pareto efficient ellocation (2mks) ii) Shysiky and Hicksian substitution effect yii) Retuin to scale and Marginal product (3mks) (2mks) b) Mary has a utility function u(x_(1)x_(2))=x_(1)^1/xx_(2) i) Calculate the Marshallian demand sfarictions ii) Assuming that the initial price of x_(1) is given by P_(i)=4 and the initial income is given by m=160 Now essume that the price of x_(1) increase to p_(1)'=5 . Calculare the income and - substitution effect based on shisky equation. (8mks) -c) Determine the return;to scale of Britannia company production function is given as follows (6mks) . (2mks) (3mks)
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