Quiz 2 Ec21 S2015 Solutions.pdf

Quiz 2 Ec21 S2015 Solutions.pdf - Economics 21 Spring 201 5...

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Unformatted text preview: Economics 21 , Spring 201 5 Prof. Luttmer Solutions to Quiz 2 1. Short Answer Questions (21 points) a. [10 points!] Suppose the income elasticity of demand is 2. At an income of $2,000, the quantity demanded is 50 units. At which level of income will the quantity demanded be 54? As always, show how you arrived at your answer. No credit for correct answer if you don ’t Show how you arrived at it. Income elasticity of demand = (percent change in quantity demanded)/(percent change in income) The percent change in quantity demanded is +8%. Hence, the percent change in income must have been +4% (because each percentage point increase in income leads to a 2 percentage points increase in quantity demanded if the income elasticity is 2). A 4 percent increase in income from a base of $2,000 is a 4*$20 increase, so the final income level is: $2,080. b. [3 points] As you know, Dartmouth is moving forward with a new housing policy based on residential communities. What to you personally is the equivalent variation of this new policy? Explain how you arrived at your answer using the definition of equivalent variation. The equivalent variation of a policy is the amount of money I would need to give you instead of the policy so that you would be as well off as with the policy. Your answer would depend on how much you like the new policy. Whether you like the new policy does not just depends on financial consideration but also, and probably predominantly in this case, on social considerations such as whether you can build good friendships and spend time with friends. E. g., if I gave you a choice between either (i) the current housing system plus $566 in cash OR (ii) the new residential community housing system, and you think both options make you exactly as well off, then your EV is +$566. If you like the residential community housing system less than the current system, your EV would be negative. To get full credit you would need to give your EV in dollars (and what that dollar amount is depends on your preferences). 0. [3 points] Draw an Engel curve for an inferior good. Give values to two points on the curve: specify a number on the X-axis and the on the Y-axis for two points on the Engel curve. Be sure to label the axes (as always). The curve needs to be downward sloping with Income on the Y-axis and the quantity of the good on the X-axis. You’re free to pick any two points. (1. [5 points]. See next page for the question. Page 1 of 5 d. Ganiru’s indifference curves for Munchkins (M) and Coffee (C) are given in the figure below. If he consumes 20 oz of coffee and 7 munchkins, his utility level is 17.6. The price of a Munchkin is $1.00. In a separate figure, draw his compensated (=Hicksian) demand curve for Coffee between a price of coffee of $1.00/ounce and $0.20/ounce for utility level u=17.6. Show at least 3 price— quantity points on his compensated demand curve where you give the numerical value of the price and the corresponding quantity. If you mess up this graph, there is an extra graph on the next page. Beclearwhwhgmphlshouldgmde Coffee versus Munchkins 25; m .E x .C u 3 2 Page 2 of 5 2. Taxing Rice (12 points) Suppose the uncompensated demand for rice is given by: x(p,y) = 100 ~ 20p + y/ 10, where p is the price of rice, y is income, x is the quantity of rice demanded. Suppose y=2000. a. What is the quantity of rice demanded at p=10? { ’2 F0 LIA-3‘ > x(10, 2000) = 100 — 20*10 + 2000/10 = 100 b. Find the equation for the linear approximation of the compensated (=Hicksian) demand curve going through the quantity you found in (a) at p=10. ( 6 PUMA/S) Use the Slutsky equation in derivative form to find the derivative of the compensated demand curve: dh/dp = dx/dp + x dx/dy = - 20 + 100/10 = -10 Thus, the linear approximation is: h(p) = a — 10p Find the constant “a” by noting you are finding the compensated demand curve going through the point (price=10, quantity=100). h(p)=a— 10p 100 =a—10*10 9a=200 So: h(p) = 200 — 10 p 0. Suppose the compensated demand for rice at a utility level corresponding to a consumption of 100 units of rice and 1000 units of all other goods is h(p) = 150 — 5 p. (Note: this equation may be different from the one you found in part b even if your part b answer is correct). Further suppose that the supply of rice is perfectly elastic at p=6 but that the government taxes rice by 4/unit, so that consumers pay p=10. What is the true (EV-based) DWL of the tax on rice? ( Lf pan/13$ > The DWL triangle is -0.5(change in compensated quantity)*(change in price). The price change is 4. Hence, the compensated change in quantity is 4 times dh/dp, so it is 4*(-5) = -20. The DWL is therefore -0.5*4*(-20) = 40. ‘3 FYI? W {$01 dt‘qqAaa‘ (Moi MCQCQ :WCQC-B Page 3 of 5 3. Fighting Obesity (12 points) Consider a country Where citizens only consume two goods: Food (F) and Clothing (C). Suppose the price of a unit of food is 1 and the price of a unit clothing is 6. Suppose that the supply of food and the supply of clothing are both perfectly elastic. Each citizen has an income of $140. a. [2 points] In the graph on the next page, draw a citizen’s initial budget constraint and label this curve BCo. Also indicate the bundle of F and C that the citizen chooses and denote this bundle by A. The budget line BCO intersects the Y-axis at l40/6=23.3 and the X—axis at 140/ 1:140. (The blue line) The country adopts a draconian policy to fight obesity: it levies a 215% tax on food (so the new price of food is 3.15) but gives every citizen a grant of $100 (so that each citizen now has a total income of $240) b. [2 points] In the graph on the next page, draw the citizen’s budget constraint when the new policy is in place and label this curve BC1. Also indicate the bundle of F and C that the citizen now chooses and denote this bundle by B. Please make sure that it is unambiguous where this new budget constraint lies, for example by using a different color or a diflerent type ofline such as a dashed line. The budget line BC1 intersects the Y-axis at 240/6=40 and the X-axis at 240/3.15=76.2. (The green line) c. [3 points] What is the EV to the citizen of the new policy? Show the EV in the graph on the next page and give a numerical answer below: To find the EV, you need to find the change in income under the old policy (so with the old prices) such that the individual is as well off as under the new policy. Changing income under the old policy shows up graphically as a parallel shift in the original budget constraint. You have to shift the budget constraint until it is tangent to the indifference curve that goes through bundle B because this is the indifference curve that corresponds to the new utility level. The shifted budget constraint is the red line. It is shifted down, so the person is worse off, which means the EV is negative. It is shifted down by about 5 units of food (from 23.3 to 18.3), so the EV is minus 5 units of food times the original price offood (6). EV = - $ 5 * 6 = -$30 (1. [3 points] What is the EV—based DWL of the new policy? Show the EV-based DWL in the graph on the next page and give a numerical answer below: . To find out how much the government spends on the new policy (=grant minus tax revenue), we need to find out how much more expensive bundle B is at the original prices than bundle A. The easiest way to do this is to draw a line through bundle B that is parallel to the original BC. You can then read of the Y-axis that bundle B is as expensive as 26.3 units of C. Bundle A costs as much as 23.3 units of C. Hence, bundle B is 3 units of C more expensive than bundle A. This means that the government is spending on net 3*6=18 on the policy. Thus, the new policy costs the government $18, but makes the person $30 worse off. This means the policy “wastes” $48. More formally, the EV-based DWL = $48. e. [2 points] On the graph on the next page Show: (i) by how much the quantity demand of food changes (and in which direction) due to the income effect of this policy and (see graph) (ii) by how much the quantity demand of food changes (and in which direction) due to the substitution effect of this policy (see graph). Page 4 of 5 Units of Food d O O F S U S r e V g .m Cloth 5 7 mEfoU 96 3E: ...
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