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Unformatted text preview: EC 301, Spring 2014 Practice questions and answers for Midterm 1 Instructor: Prof. Arijit Mukherjee 1. Suppose that the demand function for the Toyota Camry is given by Qd = 500 -12PC + 10PH - 5PG + 0.0001M, where PC is the price of the Toyota Camry (in thousands), PH is the price of the Honda Accord (in thousands), PG is the price of gas (per gallon) and M is income. Further, suppose the supply curve for the Toyota Camry is given by QS = 20PC - 55. a. What is the demand curve for the Toyota Camry if the price of the Accord is $25,000, gas is $2 per gallon and income is $50,000? ANSWER: The demand curve is obtained by plugging the values of PH, PG, and M into the demand function given above. That is, the demand curve for Toyota Camry is (note that the unit for both PC and PH are in thousands of dollars. So when the price is $25,000, PC is 25.) Qd = 500 -12 PC + 10 X 25 – 5 X 2 + 0.0001 X 50,000 i.e., Qd = 745 - 12PC. b. What is the equilibrium price and quantity in the market for Toyota Camry? ANSWER: In equilibrium, Qd = QS, i.e., 745 - 12PC = 20PC – 55. Solving for P we get P = $25,000. Plugging this value in Qd = 745 - 12PC we get Q = 445. c. Is demand elastic or inelastic at the equilibrium price? ANSWER: Recall that price elasticity is (slope of the demand function) X (pricequantity ratio). The demand function suggests that the slope is –12. Also, in equilibrium, the price quantity ratio is 25/445. Hence, the elasticity is -12 x (25/445) = -0.66, which implies that demand is inelastic. d. What is the cross price elasticity of demand at equilibrium with respect to Honda Accord’s price? ANSWER: The slope with respect to PH is 10. So, as show above, the cross price elasticity can be computed as 10 x (25/445) = .56. EC 301, Spring 2014 Practice questions and answers for Midterm 1 e. What is the income elasticity of demand for Camry at equilibrium? ANSWER: The slope with respect to M is 0.0001. So, as show above, the cross price elasticity can be computed as 0.0001 x (50,000/445) = .11. 2. Suppose that you can schedule a worker up to four hours per day. The benefit function is given by B(H) = 500H - 22.5H2 and the cost function is given by C(H) = 100 + 15H2. The corresponding marginal benefit and marginal cost functions are given by MB(H) = 500 - 45H and MC(H) = 100 + 30H. What is the best choice of hours for this worker? ANSWER: Setting MC=MB gives 500 - 45H = 100 + 30H, so H = 5.3, which exceeds the four hours per day the worker can be scheduled. At H = 4, MB = 320 and MC = 220. Since MB > MC at H = 4, the worker should be scheduled for 4 hours. 3. Ben and Matt both love Simpsons and The Family Guy. Ben’s utility from watching a half-hour episode of Simpsons is 30 and from a half-hour episode of The Family Guy is 15. Matt’s utility from watching a half-hour episode of Simpsons is 10 and from a half-hour episode of The Family Guy is 20. Which of the following statements are correct and why? a. Ben prefers watching Simpsons to watching The Family Guy ANSWER: True. Ben’s utility is 30 from Simpsons and 15 from Family Guy. The higher is the utility the more preferred is the consumption bundle b. Matt prefers watching The Family Guy to watching Simpsons ANSWER: True. Matt’s utility is 10 from Simpsons and 20 from Family Guy. The higher is the utility the more preferred is the consumption bundle c. Matt prefers watching The Family Guy twice as much as he likes watching Simpsons EC 301, Spring 2014 Practice questions and answers for Midterm 1 ANSWER: False. Utility is ordinal. So we cannot answer a question that asks: “how much more” does Matt prefer Family Guy to Simpsons? d. Compared to Ben, Matt is a bigger fan of The Family Guy ANSWER: False. Utility is ordinal. So utilities cannot be compared across different consumers. 4. John spends all his money on X and Y. Suppose John has $20 to spend. Draw John’s budget line in each of the following scenarios: a. Price of X is $1/unit and price of Y is $2/unit. Y 10 0 b. 20 X John’s dad gives him 10 units of X as gift. The market price for X and Y are still the same as above EC 301, Spring 2014 Practice questions and answers for Midterm 1 c. Price of Y is still the same but X is available on a deal: if John signs up for the deal he has to pay $5 to the seller for X but he gets the first 10 units of X at no additional charge. The subsequent units of X are still sold at $1/unit. Y 10 New budget line with deal on X 7.5 Budget line in part (a) 10 0 d. X 25 Price of X is still the same as in part (a) above, but the seller of Y offers a rebate: the first 5 units of Y are sold at $2/unit but then all subsequent units are sold at 50% discount. Y 15 10 New budget line with discount 5 Budget line in part (a) 0 10 20 X 5. Nicole's income is $1,000 per month. She spends all of it on shoes (S) and books (B). Shoes cost $50 and books cost $25. Her marginal rate of substitution for shoes with books is MRSSB = 2B/3S. Illustrate her utility-maximizing combination of shoes and books and draw her price-consumption curve if the price of books rises to $30. EC 301, Spring 2014 Practice questions and answers for Midterm 1 ANSWER: Given the prices of books and shoes and Nicole’s income, her budget constraint is $50S+$25B = $1,000. At the utility-maximizing combination of shoes and books, MRSSB = = PS/PB, i.e., 2B/3S = $50/$25, which implies that B = 3S. Substituting this into the budget constraint yields $50S+$25B = $50S+$25 (3S) = $50S+$75S = $1,000, or $125S = $1,000. Solving this equation gives S = 8. Since B = 3S, B = 24. Her initial utility-maximizing combination of shoes and books is represented by point A in the figure below. Now, if the price of books rises to $30, then Nicole’s new utility-maximizing bundle must solve MRSSB = 2B/3S = PS/PB = $50/$30, which implies that B = 2.5S. Also, the new budget constraint is: $50S+$30B = $1,000. Substituting this into the budget constraint yields $50S+$30S = $50S+$30 (2.5S) = $50S+$75S = $1,000, or $125S = $1,000. Solving this equation gives S = 8. Since B = 2.5S, B = 20. Her initial utility-maximizing combination of shoes and books is represented by point B in the figure below. One obtains the price consumption curve by joining the points A and B. EC 301, Spring 2014 Practice questions and answers for Midterm 1 ...
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