Posted: March 3rd, 2021

ECON/AMS 11B WINTER 2014 Final Exam Instructions

ECON/AMS 11BWINTER 2014Final ExamInstructions• Please turn off all phones and other electronic devices.• There are 6 questions worth a total of 54 points. 100%=50 points.• No notes or books. A table of integration formulas is provided.• You may use a simple scientific calculator. No graphing or programmable calculators.• Read the questions carefully and check your answers.•For full credit—show all your work.Good Luck!!!NAME:Problem123456TotalScore/8/8/8/10/10/10/501ECON/AMS 11BFINAL EXAMSelected Integration FormulasBasic rules.uk+1+ C,k+11.uk du =2.1du = ln |u| + C.u3.eu du = eu + C.4.f (u) ± g(u) du =5.c · f (u) du = c ·k = −1.f (u) du ±g(u) du.f (u) du.Rational forms containing (a + bu).6.1du= ln |a + bu| + C.a + bub7.u duua= − 2 ln |a + bu| + C.a + bubb8.u2 duu2 au a2=− 2 + 3 ln |a + bu| + C.a + bu2bbb9.u2 duua22a= 2− 3− 3 ln |a + bu| + C.2(a + bu)bb (a + bu)bForms containing10.11.12.√a + bu.√2(3bu − 2a)(a + bu)3/2u a + bu du =+ C.15b2√u du2(bu − 2a) a + bu√=+ C.3b2a + bu√2(3b2 u2 − 4abu + 8a2 ) a + buu2 du√=+ C.15b3a + buExponential and logarithmic forms.eau+ C.a13.eau du =14.ueau du =15.un eau du =16.un ln u du =eau(au − 1) + C.a2un eau n−aaun−1 eau du .un+1 ln uun+1−+ C,n+1(n + 1)2n = −1.2WINTER 2014ECON/AMS 11BFINAL EXAM1. (8 pts) A firm’s marginal cost function is given bydc5q + 12=dqq+2and the firm’s fixed cost is $3000. Find the firm’s cost function.3WINTER 2014ECON/AMS 11BFINAL EXAMWINTER 20142. (8 pts) Find the Consumers’ surplus and Producers’ surplus at equilibrium for the market whose supplyand demand equations are given below.• Supply: p = 10 + 0.25q,• Demand: p = 180 − 0.1q 2 .4ECON/AMS 11BFINAL EXAM5WINTER 2014ECON/AMS 11BFINAL EXAMWINTER 20143. The average monthly demand for a ACME Widgets’ product is given by the relationQ = 4 ln(5Y 2 − 3p),where Q is the monthly demand, measured in 1000s of widgets; p is price of an ACME Widget, measuredin dollars; and Y is the average monthly household income in the market for the firm’s product, measuredin $1000s.(a) (5 pts) Find Q, Qp and QY when p = 25 and Y = 4.(b) (3 pts) Find the price-elasticity of demand when p = 25 and Y = 4.Round your answers to 2 decimal places.6ECON/AMS 11BFINAL EXAM7WINTER 2014ECON/AMS 11BFINAL EXAMWINTER 20144. (10 pts) A monopolistic firm produces two types of widgets, type A and type B widgets. It costs thefirm $8 per unit to produce type A widgets and $4 per unit to produce type B widgets, and their weeklyfixed cost is $2000. The demand functions for these products are given byQA = 400(PB − 2PA + 14)QB = 400(PA − PB ),where PA and PB are the selling prices per unit of type A and type B widgets, and QA and QB are thenumbers of type A and type B widgets that the firm sells in a week.Find the prices that the firm should set to maximize their weekly profit. Use the second derivative test tojustify your claim that the firm’s profit is maximized at the prices you found.8ECON/AMS 11BFINAL EXAM9WINTER 2014ECON/AMS 11BFINAL EXAMWINTER 20145. ACME Widget’s (AW) production function is given byQ = 10K 0.6 L0.4 ,where Q is the firm’s annual output, measured in widgets, K is the firm’s annual capital input and L isthe firm’s annual labor input. The price per unit of capital is pK = $5, 000 and the price per unit of laboris pL = $2, 000.(a) (6 pts) Find the levels of capital and labor input that AW should use to minimize the cost ofproducing Q0 = 4, 000 widgets. What is the minimum cost?(b) (2 pts) What is AW’s marginal cost? Explain your answer.(c) (2 pts) Use the envelope theorem and linear approximation to estimate the change in AW’s (minimum)cost of producing 4,000 widgets, if the price per unit of capital increases to $5,200 (assuming that allelse stays the same).10ECON/AMS 11BFINAL EXAM11WINTER 2014ECON/AMS 11BFINAL EXAMWINTER 20146. The Smith family’s utility function is given byU (x, y, z) = 12 ln x + 7 ln y + 5 ln z,where x, y and z are the quantities of X-goods, Y-goods and Z-goods that they consume per month. Theaverage prices of these goods are px = $15, py = $10 and pz = $5, respectively.(a) (7 pts) Find the quantities of X-goods, Y-goods and Z-goods that the Smith family should consumeeach month to maximize their utility, given that their monthly XYZ-budget is B = $3600. What istheir maximum utility?(b) (3 pts) By approximately how much will the Smiths need to increase their XYZ-budget if they wantto increase their monthly utility by 3 utils? Explain your answer.12ECON/AMS 11BFINAL EXAM13WINTER 2014ECON/AMS 11BFINAL EXAM14WINTER 2014

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