1. As a result of the 1979 – 1980 energy crisis, government policy makers originally estimated that American consumers would have to reduce their consumption of gasoline by about 30%. (a) What measures could be undertaken to reduce gasoline consumption? What are the pros and cons of each measure? (b) If by 1982 the quantity of gasoline consumed by each vehicle dropped by 8% in the face of a 40% increase in price, what is a rough measure of the coefficient of price elasticity of demand for gasoline? To achieve the needed 30% reduction in gasoline consumption, what increase in the price of gasoline does your estimate of the price elasticity of demand require? (c) How did the administration in Washington attempt to solve this problem?
2. Using indifference curve analysis, derive an elastic demand curve of commodity X for a reduction in Px, while keeping constant the price of Y and the consumer’s tastes and money income.
3. (a) Given the following TPL, find the APLand MPL.
L 1 2 3 4 5 6 7
TP 2 6 12 16 18 18 16
(b) On the same set of axes, plot the TPL, APL, and MPLschedules and indicate on the figure the stages of production for L and K; where does the law of the diminishing returns for L begin to operate? Where will a rational producer produce? Why? (c) If both L and K are variable, and TO¼ $12, PL¼ $1, and PK¼ $2, plot the isocost. What is its slope? On the same graph, draw an isoquant which shows the equilibrium point where the producer uses 6L and 3K. Express the condition for producer equilibrium in terms of the MRTSLK, MPL, MPK, PL, and PK.
4. (a) Given the following TVC schedule and TFC¼ $12, (a) find TC, AFC, AVC, AC, and MC for the various levels of output.
Q 1 2 3 4 5 6
TVC $6 8 9 10.5 14 21
(b) Plot on the same graph the AVC, AC, and MC schedules of part (a). What is the relationship between AVC, AC, and MC? (c) Draw a figure clearly showing the relationship between the typical SAC, SMC, LAC, LMC.
5. Redraw the figure of Problem 2 and show on it the Hicksian and Slutsky substitution and income effects and derive the Hicksian and the Slutsky demand curves. Which is a better measure of the substitution and income effects? Why?
6. For a Cobb-Douglas production function, (a) write its formula in terms of L and K,aandb, and indicate the economic meaning of each component of the formula. (b) Sketch the typical TPL, APL, and MPL curves. To which stage of production do they refer? (c) Ifa¼ 1.5 and b¼ 0.5, sketch the expansion path with isoquants Q¼ 100 and Q ¼ 400. What is the value of (e subst.)LK?
Optional
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Answers
1. (a) One way to reduce gasoline consumption is rationing. Such a policy could cut gasoline consumption by the required 30% but would also lead to black markets and a huge bureaucracy to enforce rationing. As a result, rationing was not adopted but was reserved as a policy of last resort only. Another way to reduce gasoline con-sumption is by increasing the price of gasoline. The advantage of this policy is that it works through the price mechanism rather than replacing it (as in the case of rationing). The disadvantage is that because the coefficient of price elasticity of demand is very low, a huge price increase would be required to achieve the needed 30%
cutback in the quantity of gasoline consumed.
(b) When the amount of gasoline demanded per vehicle dropped 8% in the face of a price increase of 40%, the coeffi-cient of price elasticity of demand for gasoline was roughly
e¼ %DQ
%DP¼ (8%) (þ40%)¼ 0:2
This is a very rough measure because it assumes that everything else remained constant, which was clearly not the case. To achieve the 30% reduction in gasoline consumption, the required price increase would have to be roughly
%DP ¼%DQ e ¼30%
0:2 ¼ 150%
(c) The Administration in Washington, while stressing conservation, believed that deregulation and the resulting sharp increase in gasoline prices would stimulate new exploration which would lead to a large increase in dom-estic petroleum extraction. Thus the Administration stressed the supply side to attempt to solve this problem while previous efforts relied mostly on the demand side.
2. In the top panel of Fig. M-1, point A on budget line 1 and indifference curve I is the original consumer equilibrium point. When Pxfalls, equilibrium is at point B, where indifference curve II is tangent to budget line 2. The move-ment from point A to point B (Q1Q4) is the total of the substitution and income effects of the fall in Pxand gives dx(the usual demand curve) in the bottom panel. Because the slope of the price consumption curve is negative between points A and B, dxis price-elastic.
Fig. M-1
3.
(b) The law of diminishing returns for L begins to operate where MPLbegins to decline. A rational producer will produce at stage II for L and K, where the AP and MP of L and K are both positive but declining. The producer will not produce in stage I for L because MPKis negative. Similarly, the producer will not produce in stage III for L because MPLis negative. See Fig. M-2.
(c) The slope of the isoquant is
()TO=PK
That is, at equilibrium, the slope of the isoquant equals the slope of the isocost.
(b) AC¼ AVC þ AFC. Since AFC declines continuously as output expands, the AC curve reaches its lowest point at a higher level of output than the AVC curve. The MC curve crosses the AVC and AC curves at their lowest point.
The reason for this is that for the AVC and the AC to fall, the MC must be lower, and for the AVC and AC to rise, the MC must be higher. Thus, MC¼ AVC and MC ¼ AC at the lowest AVC and AC. See Fig. M-4.
(c) See Fig. M-5.
Fig. M-4
Fig. M-5
5. In the top panel of Fig. M-6, real income is kept constant according to Hicks by shifting budget line 2 down and parallel to itself (budget line 3) until it is tangent to the original indifference curve I at point C. The movement from A to C (Q1 Q2) is the Hicksian substitution effect shown on the Hicksian demand curve in the bottom panel. Q2Q4is then the Hicksian income effect. In the top panel, real income is kept constant according to Slutsky by rotating budget line 1 through point A until it is parallel to budget line 2. This gives budget line 4, which is tangent to indifference curve III at point D. The movement from A to D (Q1Q3) is the Slutsky substitution effect shown on the Slutsky demand curve in the bottom panel. Q3 Q4 is then the Slutsky income effect. The Slutsky method is a better measure of the substitution effect because, as with the income effect, it puts the consumer on a higher indifference curve and because it can be obtained from observed prices and quantities without the need to know the exact shape of the indifference curve.
6. (a) Q¼ ALaKb, where Q¼ output, and L and K ¼ inputs. A,a, and b are positive parameters determined in each case by the data. The greater the value of A, the more advanced is the technology. a and b measure the output elasticity of L and K, respectively. There are constant, increasing, or decreasing returns to scale to the extent thata þ b ¼ 1, a þ b . 1, or a þ b , 1, respectively.
(b) See Fig. M-7. The TPL, APL, and MPLrefer only to stage II of production (i.e., the Cobb-Douglas production function is not defined for stage I or III of L and K ).
(c) In Fig. M-8, doubling the inputs of L and K quadruples output. e subst.LK¼ 1 for a Cobb-Douglas.
Fig. M-6
Fig. M-7
Fig. M-8
MIDTERM EXAMINATION 183