Homework #1 Microeconomics (I), Fall 2010 Due day: 7 th Oct., 2010

Transcription

1 組別 姓名與學號 Homework #1 Microeconomics (I), Fall 2010 Due day: 7 th Oct., 2010 Part I. Multiple Choices: 60% (5% each) Please fill your answers in below blanks B A B C B C A D B C C C 1. Which of the following statements is true about a market economy? A. With a large enough computer, central planners could guide production more efficiently than markets. B. Market participants act as if guided by an invisible hand to produce outcomes that maximize social welfare. C. Taxes help prices communicate costs and benefits to producers and consumers. D. None of above. 2. Microeconomics is: A. The study of the economic choices individuals and firms make to allocate the scarce resources and how those choices create markets. B. The study of the economy as a whole, examining factors such as inflation, unemployment, gross national product, consumption, government spending, trade, investment, etc. C. The study of how to earn money. D. None of above. 3. Which of the following is normative statement? A. Economists have a higher life expectancy than do miners. B. Economists deserve to have lower life insurance rates than do miners. C. Economists receive higher pay, on average, than do miners.. D. Economists pay more taxes, on average, than do miners. 1

2 4. What is the main reason of using models and mathematics in economics analysis? A. Because it makes economics seems cool! B. Because many economists are bad in writing. C. Because we need to simplify the too complicated real world for analysis. D. All of above. 5. Consider the demand function Q=a-bP. The effects of other determinants of Q is reflected in: A. The slope of the function. B. The intercept of the function. C. In both the slope and the intercept of the function. D. Neither the slope nor the intercept of the function. 6. As the price of a good decreases, the change in the quantity supplied can be shown by: A. Shifting the supply curve leftward. B. Shifting the supply curve rightward. C. Moving down along the same supply curve. D. Moving up along the same supply curve. 7. When two goods are substitutes, a shock that raises the price of one good causes the price of the other good to: A. Increase B. Decrease C. Remain unchanged D. Change in an unpredictable manner 8. The supply function of milk is Q= P, then the inverse supply function is: A. P= Q B. P=-120+(Q/40) C. P=-3+(Q/40) D. P=3+(Q/40) 9. If the demand function is Q=-4P+10, which set of following equilibrium prices and quantities is inelastic? 2

3 A. (P*, Q*) = (1.25, 5) B. (P*, Q*) = (1, 6) C. (P*, Q*) = (2, 2) D. (P*, Q*) = (0, 10) 10.Suppose the elasticity of demand of a firm s product is -1.5, and the firm is going to cut the price for 10%, if so, the revenue of the firm will: A. Increase 1.5% B. Decrease 1.5% C. Increase 3.5% D. Decrease 3.5% 11.Suppose one man purchases a good increase from 8 to 10 as his income rises from 100 to 110. the income elasticity of demand of him is: A. 2 B C. 2.5 D The above figure shows a graph of the market for pizzas in a large town. How many pizzas will be supplied (Q s ) and demanded (Q d ) if the price is 7? A. (Q s, Q d ) = (0, 140) B. (Q s, Q d ) = (60, 60) C. (Q s, Q d ) = (40, 70) D. (Q s, Q d ) = (70, 40) 3

4 Part II. Problems: 40% 1. Suppose the individual demand function for apple juice (in liter per month) in a village with 20 peoples is: q i =-2P+52; i=1, 2,, 20 And the supply function is given by: Q s =150P-2000 In above equations, q i mean individual demand and Q means total quantity of apple juice; P means price in dollars per liter of apple juice. i) Please find the equilibrium price and (total) quantity; (6%) ii) If someday another 10 peoples moved into the village, suppose their demand curve for apple juice is q j =-P+36; j=1,2,,10. Try to find the new equilibrium price and (total) quantity. (10%) ANS: i) Q d = Σq i = 20 (-2P+52) = -40P+1040 Solve Q s = Q d 150P-2000 = -40P+1040 P*=16 Put P* back to demand or supply function, will get Q*=400 Therefore, (P*, Q*) = (16, 400) ii) First calculate the new aggregates demand function of 10 new peoples: Q d n = Σq j = 10(-P+36) = -10P+360 Then add the aggregates demand function which we get from i) to complete the full demand function: Q d f = -40P (-10P)+360 = -50P+1400 Solve Q s = Q d f 150P-2000 =-50P+1400 P* = 17 And put P* back to Q s or Q d f, we will get Q*=550 Therefore, the new equilibrium price and quantity = (P*, Q*) = (17, 550) 4

5 2. Suppose that the market demand for cigarettes in New York City is Q=2000(P -2 ) and that the inverse market supply curve of cigarettes in the city is P=1.5P w, where P w is the wholesale price of cigarettes. (That is, retailers sell cigarettes at 1.5P w, a price that is 50% higher than what retailers pay for the cigarettes.) i) Assume that the New York retail market for cigarettes is competitive. Calculate the equilibrium price and quantity of cigarettes as a function of the wholesale price. Let Q* represent the equilibrium quantity. Find dq*/dp w.(6%) ii) Now suppose that the government impose a $3 specific tax on each pack of cigarettes, for all cigarettes possessed for sale or use in New York City. The tax is paid by the retailers. Show using both math and a graph how the introduction of the tax shifts the market supply curve. How does the introduction of the tax affect the equilibrium retail price and quantity of cigarettes? (8%) iii) With a specific tax (says $T) in place, calculate the equilibrium price and quantity of cigarettes as a function of wholesale price. How does the presence of the quantity tax affect dq*/dp w? (10%) ANS: i) Because the supply curve is simply a horizontal line P=1.5P w So the P*=1.5P w. Then recall the demand function: Q=2000(P -2 ), so what we need to do is replace P with P*=1.5P w, hence we get Q*=2000[(1.5P w ) - 2 ], and get Q*=(8000/9)(P w ) -2 Final, using basic calculus to find dq*/dp w, and we will find dq*/dp w = (-2)(8000/9)(P w -3 )=(-16000/9)(P w -3 ) and of course you can use chain rule to find it: dq*/dp w = (dq*/dp w ).(dp w /dp) = (-2)2000(P -3 ).(1.5) = -6000(P -3 ) If we put P=1.5P w back we will still can get dq*/dp w = (-16000/9)(P w -3 ); either one is correct. (but express in P w is 5

6 recommended) ii) Because a unit tax imposed, so the new price = old price + tax, and it is also the supply function. P t = P+3 = 1.5P w +3 Q*=(8000/9)(1.5P w +3) -2 < (8000/9)(1.5P w ) -2 In below diagram, we can have a better view: Original equilibrium point = e 1 Original equilibrium retail price and quantity = (P 1, Q 1 ) $3 unit tax imposes, shifting the supply curve upward. (S S t ) The new equilibrium point = e t New equilibrium retail price and quantity = (P t, Q t ) => price increased and quantity decreased iii) Firstly, calculate P* and Q* Because with tax, so P*=(1.5P w +T) and Q*=(8000/9)(1.5P w +T) -2 Secondly, the question is ask to find: or dq*/dp w = (-2)(8000/9)(1.5P w +T) -3 (1.5) = -(8000/3)(1.5P w +T) -3 = d[(-8000/3)(1.5p w +T) -3 )] / dt = (-4)(-8000/3)(1.5P w +T) -4 (1) =(32000/3)(1.5P w +T) -4 >0 6

7 Recall dq*/dp w = -(8000/3)(1.5P w +T) -3 <0 So if T increase, (dq*/dp w ) will also increase, and because dq*/dp w is less than 0, hence it means (dq*/dp w ) will closer to 0 when T increase. That actually means more tax on cigarettes will make the quantity of demand less sensitive on the wholesales price. 7