16:10 ← BEC 3701 - Assignments-... KWAME NKRUMAH UNIVERSITY TEACHING FOR EXCELLENCE SCHOOL OF BUSINESS STUDIES DEPARTMENT OF ECONOMICS AND FINANCE ADVANCED MICRO-ECONOMICS (BEC 3701) Assignments INSTRUCTIONS: Check instructions below: LTE 1) Let u(q1,q2) = ln q₁ + q2 be the (direct) utility function, where q₁ and q2the two goods. Denote P₁ and P2 as the prices of those two goods and let M be per period money income. Derive each of the following: a) the ordinary or Marshallian demand functions q₁ = d₂ (P₁, P₂, M) for i = 1,2 [3 Marks] b) the compensated or Hicksian demand functions q₁ = h₂ (P₁, P2, M) for i = 1,2 [3 Marks] c) the Indirect Utility Function uº = v(P₁, P2, M) [3 Marks] d) the Expenditure Function E(P1, P2, U°) [3 Marks] e) Draw a diagram of the solution. There should be two graphs, one above the other; the first containing the indifference curves and budget constraint that characterize the solution to the consumer's choice problem; the second characterizing the demand functions [3 Marks] 2) Consider the following information about Simon lungu's choices; When prices are (4,6), lungu chooses the bundle (6,6) call it observation A and when prices are (6,3), he chooses the bundle (10,0), observation B. Based on this information, a) Sketch (in a graph) each of lungu's budget constraints and choices. [2 Marks] b) Is the consumer's behaviour consistent with the model of maximizing behaviour? [2 Marks] c) Is lungu's behaviour consistent with the Weak Axiom of Revealed Preference? [2 Marks] 3) A chemical plant has the following production function: In the short run, capital, K, is 100. The rental rate of capital is 20 and labour cost is 10. i. Find the fixed cost, variable cost and total cost equations. [2 Marks] ii. Find the average fixed cost, average variable cost, average total cost and marginal cost equations. [3 Marks] iii. At what quantity will average cost reach a minimum? [2 Marks] iv. If a per unit subsidy of 10 is in place, will it affect your answer in (c)? If so, what is the new level? [2 Marks] 4) BigTree Beaverages company manufactures three products Fruiticana, Fruitop and Vatra water. Suppose The required raw material per piece of product Fruiticana, Fruitop and Vatra water is 2kg, 1kg, and 2kg. Assume that the total weekly availability is 50 kg. In order to produce the products, the raw materials are processed on a machine by the labour force and on a weekly the availability of machine hours is 30. Suppose that the available total labour hour is 26. The following table illustrates time required per unit of the three products: Product Labour Hour Machine Hour Fruiticana 0.5 1 Fruitop 3 Vatra water 2 1 1 Further, suppose that the profit per unit from the three are K25, K30 and K40 respec the BigTree's dual problem and determine the optimum values of the dual variables. [2 5) An individual purchases a dozen eggs and must take them home. Although making trips home is costless there is a 50 percent chance that all. te trin will be broken during