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Econ 4351: Lecture 2 Practice Exam 1 Dr. Myoung Lee Spring, 2014 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 Practice Exam 1 Dr. Myoung Lee Spring, 2014 University of Missouri 1. (22pts) The inverse demand curve for product X is given by: 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: PX = 500 + 5 QX. 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. . (b) (4) Determine the equilibrium price and quantity sold of X. Equate supply and demand to calculate Q. 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. (c) (4) Calculate the cross price elasticity. (1)Determine whether X and Y are substitutes or complements. At PY =$10, QX =20 2332010yXXyPQdPdQQPEYX Since 23YXPQE, 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 = XXXXdPdQQP = 10120600 = - 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, (= XXQP ). 40 80 Q P 800 400 Unit Elastic, Ed = -1 |Ed| =1 at P=$400, Q=40 Ed =𝑷𝑸𝐝𝐐𝐝𝐏=𝟒𝟎𝟎𝟒𝟎𝟏𝟏𝟎= -1 Elastic part of D - ∞ < Ed < - 1 |Ed| >1 Inelastic part of D -1< Ed < 0 |Ed| <1Econ 4351: Lecture 2 Practice Exam 1 Dr. Myoung Lee Spring, 2014 University of Missouri 2. (4pts) Suppose that there are 500 identical consumers in the market for fruit baskets. An individual demand is given by P = 50 – ½ qi. Derive the total market demand curve for fruit baskets. Q = 500X qi <=5001i 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) 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. 1000,10000,1012pppQPdpdQd This is the same functional form of: AppApQPdpdQd1, which is a constant. Where, 1ApdpdQ. Where 1 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) Pceiling Interest Rate Shortage Free mkt PEcon 4351: Lecture 2 Practice Exam 1 Dr. Myoung Lee Spring, 2014 University of Missouri 5. (4pts) Suppose the market for widgets can be described by the following equations: Demand: P = 11 - Q Supply: P = 2Q + 1 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. (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) 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) Yes (c) (2) At what rate of exchange would Gavin be willing to stay put at his consumption level? 2 Gorditas for 1 Coke 7. (4pts) Explain, using mathematical notation and the basic assumptions about preferences, why two indifference curves cannot intersect, as shown below. Good YGood XACBU1U2 Gorditas 5 10 15 20 25 30 35 40 40 35 30 25 20 15 10 5 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

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