Intermediate Microeconomics I

Materials allowed: pens, pencils, erasers, rules, non-programmable calculators. Everything else must be left in front or in the back of the room. Please use provided booklet to answer all questions. Please note if I cannot read your answers, I cannot mark it. If you do not show all your steps, you cannot get partial marks. Please note, there is a bonus question, but of course, you don't need to solve that one. Please make sure to show all your steps. Good luck!! Question 1 (3 points): Assume that the market demand for tuna cans is Qte 75-1.25 x p + 1.5x psc +1.75Y (where ptc price of tuna cans and psc price of sardine cans). Further assume ptc = $2.5, psc = $3.35, and Y = $400. a) (1 points) Calculate the price elasticity of demand for tuna cans. b) (1 points) Calculate cross-price elasticity for tuna cans and identify whether the goods are substitutes or complements. c) (1 points) Calculate income elasticity of tuna cans. Question 2 (6 points): If the individual's preferences can be represented by the utility function u(x, y) = 5x0.2 0.65. a). (1 points) Write the Lagrangian function for the constraint optimization problem. b). (2 points) Write down the first order conditions for optimum. c). (2 points) Find demand functions. d). (1 points) Are x and y normal goods? Explain. Question 3 (5 points): If the individual preferences can be represented by the utility function U(x, y) = min(, 3y). a) (3 points) what are the demand functions? b) (1 points) Are those goods normal? c) (1 points) Are they complements or substitutes? Explain. Question 4 (2 points): Compute the MRTS (marginal rate of technical substitution) for the following production functions: a) (0.5 points) q(L,K) = 2.25 In(L) + 2.5ln (K) b) (0.5 points) q(L, K) = 5L ^ 0.25 * K ^ 0.75 (auints) q(L, K) = 2L ^ - 5 + 7K ^ 3 Question 5 (6 points): Anne's utility function from spending weekends away (W) and enjoying eating out (E) is given by the function U(W, E) = W ^ 0.4 * E ^ 0.6 Last year the price of a weekend away was $300.00, and the price of earing out was $50.00. Thus year, the price of eating out has risen to $75.00; and the price out weekends away has stayed the same. Both years, Anne's budget for enjoying those two items is $1,600. Calculate the change in Anne's consumer surplus from eating out resulting from the change in the price of eating out. Question 6 (3 points): Paul's Math Tutoring Centre has the following production function: q = 6L - 2L ^ 2 where q is the number of students trained in calculus and L is the quantity of tutors Paul employs. a) (1.5 points) Derive the MPL (marginal product of labour) and APL (average product of labour) b) (1.5 points) Draw MPL and APL on the graph (place L on horizontal axis). Label the graph properly. Bonus Question (2.5 points): Alison lives in a small town where she plans to hire workers to help her make candy. Her production function for candy is q = 7.5L * K ^ (1/3) She begins producing with K = 27 The cost of capital is $50 per unit. The wage depends on the number of workers she employs. Specifically, w(L) = 5 + 12L a) Does Alison's production function exhibit diminishing marginal return to labor? Explain. b) Derive Alison's short-run cost function. c) Derive Alison's Marginal Cost function. d) Does the relationship w/MP = MC hold? Show this explicitly. Question 6 (3 points): Paul's Math Tutoring Centre has the following production function: q = 6L - 2L ^ 2 where q is the number of students trained in calculus and L is the quantity tutors Paul employs. 2) (1.5 points) Derive the M*P_{L} marginal product of labour) and A*P_{L} average product of labour) b) (1.5 points) Draw M*P_{L} and A*P_{L} on the graph (place L on horizontal axis). Label the graph properly. Bonus Question (2.5 points): Alison lives in a small town where she plans to hire workers to help her make candy. Her production function for candy is q = 7.5L * K ^ (1/3) She begins K = 27 The cost of capital is $50 per unit. The wage depends on the number of workers she employs. Specifically, w(L) = S + 12L a) Does Alison's production function exhibit diminishing marginal return to labor? Explain. b) Derive Alison's short-run cost function. c) Derive Alison's Marginal Cost function. d) Does the relationship w/MP-MC hold? Show this explicitly. Question 1 (3 points): Assume that the market demand for tuna cans is overline Q ^ (tc) = 75 - 1.25p ^ (tc) + 1.5p ^ (sc) + 1.75Y (where pt price of tuna cans and p ^ (sc) - p ^ (tc) =\$2.5, p ^ (sc) =\$3.35. and Y =\$400. pats) Calculate the price elasticity of demand for tuna cans. b) (1 points) Calculate cross-price elasticity for tuna cans and identify whether the goods are substitutes or complements. c) (1 points) Calculate income elasticity of tuna cans.