Econ 4351 Lecture 2 Spring 2014 Practice Exam 1 Dr Myoung Lee University of Missouri Name SOLUTION Student Number Total Points earned 100pts ECON 4351 PRACTICE EXAM 1 SPRING 2014 You have 75 minutes to answer the following questions Directions You should have nothing on your desk at this time other than the exam pencils and an eraser Do not expect me to read your mind The exam will be graded based ONLY on what you write in the space provided Please show your work step by step for every question in order to get full credit Even correct answers will get zero points if you do not show your work Your handwriting must be legible and you must make sure that I can follow your logic Econ 4351 Lecture 2 Spring 2014 1 22pts The inverse demand curve for product X is given by Practice Exam 1 Dr Myoung Lee University of Missouri PX 500 10 QX 30 PY where PX represents the price in dollars per unit QX represents the rate of sales in pounds per week and PY represents the selling price of another product Y in dollars per unit The inverse supply curve of product X is given by Let PY 10 a 8 Draw the market demand curve for X Label the axes and intercepts At what PX QX combination is the demand unit elastic Show how you get the price and quantity Discuss how the price elasticity of demand changes along the demand curve PX 500 5 QX Elastic part of D Ed 1 Ed 1 Unit Elastic Ed 1 Ed 1 at P 400 Q 40 Ed 1 P 800 400 Inelastic part of D 1 Ed 0 Ed 1 40 80 Q b 4 Determine the equilibrium price and quantity sold of X Equate supply and demand to calculate Q c 4 Calculate the cross price elasticity 1 Determine whether X and Y are substitutes or complements 500 10QX 30PY 500 5 QX 500 10QX 30 10 500 5 QX 15QX 300 units per week QX 20 At QX 20 PX 500 10 20 30 10 600 per unit At PY 10 QX 20 Since the goods X and Y are substitutes 1 From the cross price elasticity above you know that a decrease of 10 in the price of Y will result in a 15 or decrease of 15 change in the quantity sold of X d 3 Calculate the price elasticity of demand when current price of PX is 600 At PX 600 QX 20 Ed 3 2 You an economist are hired to analyze the total spending on good X by consumers What happens to total spending if PX rises Rising PX will result in a decrease in the total spending 2332010 yXXyPQdPdQQPEYX23 YXPQEXXXXdPdQQP 10120600 XXQP Econ 4351 Lecture 2 Spring 2014 2 4pts Suppose that there are 500 identical consumers in the market for fruit baskets An individual Practice Exam 1 Dr Myoung Lee University of Missouri demand is given by P 50 qi Derive the total market demand curve for fruit baskets qi q1 q2 q499 q500 500 qi where qi 100 2 P P 100 2qi so 500 X 100 2 P 2 50 000 1000P OR P 50 1 1000Q 2 Q 500X qi 3 5pts Suppose that the demand curve for comic books is expressed as Q 10 000 P Find the price elasticity of demand This demand function has a unitary elasticity This is the same functional form of which is a constant Where Where 4 4pts Usury laws place a ceiling on interest rates that lenders such as banks can charge borrowers The interest rate is the price of a loan Graph a binding usury law on the market for loans and describe the effects of the law on the quantity of loans supplied and the quantity of loans demanded The usury law will result in more loans being demanded and fewer loans being supplied In order for the price ceiling on interest rates to be a binding it has to be below free market interest rate 2 Shortage will occur 2 Interest Rate Free mkt P Pceiling Shortage 5001 i1000 10000 1012 pppQPdpdQd AppApQPdpdQd11 ApdpdQ1 Practice Exam 1 Econ 4351 Lecture 2 Spring 2014 5 4pts Suppose the market for widgets can be described by the following equations Supply P 2Q 1 Demand P 11 Q Dr Myoung Lee University of Missouri where P is the price in dollars per unit and Q is the quantity in thousands of units Suppose the government imposes a tax of 1 per unit to reduce widget consumption and raise government revenues What will the quantity traded What price will the buyer pay What amount per unit will the seller receive We know that Pb Ps t Pb Ps 1 1 Hence Pb 11 Q Ps 1 11 Q Ps 10 Q Ps 2Q 1 1 10 Q 2Q 1 3Q 9 Q traded 3 1 Ps 10 Q 7 Pb 7 1 8 1 6 6pts Gavin is currently consuming 20 Gorditas and 20 Cokes a week A typical indifference curve for Gavin is depicted below Coke 5 10 15 20 25 30 35 40 Gorditas 7 4pts Explain using mathematical notation and the basic assumptions about preferences why two indifference curves cannot intersect as shown below 40 35 30 25 20 15 10 5 a 2 If someone offered to trade Gavin one extra Gordita for every Coke he gave up would Gavin want to do this Yes or no b 2 What if it were the other way around for every Gordita Gavin give up he would get an extra Coke Would he accept this offer Yes or no No Yes c 2 At what rate of exchange would Gavin be willing to stay put at his consumption level 2 Gorditas for 1 Coke Two of the following reasons should be given 2 According to transitivity assumption if C A and A B then C B The graph violates the transitivity assumption because B and C are on different indifference curves 2 Since C contains more of Y C must be preferred to B If C B from C A and A B then it also violates more is better than less assumption 2 Completeness is violated since consumer can t compare two baskets B and C Thus indifference curves cannot intersect as shown in the graph Good YGood XACBU1U2 Econ 4351 Lecture 2 Spring 2014 8 6pts Discuss four basic assumptions about preferences Do not simply list the properties Explain Practice Exam 1 Dr Myoung Lee University of Missouri them using the preference notation Completeness The consumer s preference has a ranking over any 2 market baskets 1 1 e g or Transitivity The consumer s preference is consistent If A is at least as good as B B is at least as good as C then A is at least as good as C 1 e g 1 then and More is better than less Nonsatiation 1 Convexity MRS decreases 1 9 4pts What is the Equi marginal principle Explain in your own words Use the equation that was given …