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# PP Chapters 1-3 Answer Key-1 - PRACTICE PROBLEM SET#1...

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Unformatted text preview: PRACTICE PROBLEM SET #1 ANSWER KEY Chapter 1. 2. The constraint is that the individual must achieve a level of'satisfaction, S, of at least ten, otherwise she dies. Algebraically, this constraint can be written as (FCW2 210. ‘ The objective function is a representation of what the consumer tries to achieve. In this case, she is trying to minimize her total expenditure on F and C (i.e., she wants to minimize PFF + PCC). The variables under the consumer’s control are the amounts of each good that she purchase-s. Therefore, the endogenous variables are F and C, and the exogenous variables are 5, Pc, and PF. The constrained optimization problem can be written as Min PFF + PcC wrt F, C subject to (FC)”2 210. 3. The maximization problem is Max 100W2 wrt L subject to L 56. The solution to this problem is at point A on the graph, where the vertical line intersects the horizontal axis at L = 6. In Other words, the vertical line represents the constraint while the curve represents the objective. Point A corresponds to the highest level of output that can be achieved given that total daily work time cannot exceed 6 hours. - 6) Chapter 2 2. Quantity demanded is a speciﬁc quantity on the demand curve. A change in price will cause the quantity demanded to change (i.e., a movement along the curve). Demand is the entire curve. It represents a functional relationship ' between price and quantity demanded. A change in one of the determinants of demand (eg. preferences, income, prices of related goods, etc.) will change demand (i.e., shift the entire curve). Quantity supplied is a specific quantity on the supply curve. A change in price will cause the quantity supplied to change (Le, a movement along the curve). Supply is the entire curve. It represents a functional relationship between price and quantity supplied. A change in one of the determinants of supply (eg. costs, number of suppliers, sellers’ expectations of future price, etc.) will change supply (i.e., shift the entire curve). 3. Qd = —P + 20 + I/100 Qd=Qs ‘ -Pe + 20 +1/100 = 2Pe- 40 + 6T 50 + I/100—6T= 3 Pa P.3 = 20 + I/300 — 2T <—- Reduced Form Equation Qe = -[20 + 1/300 -2T] + 20 + I/100 e = 2T + 21/300 <— Reduced Form Equation I = 1200 , T = 4 . 4; 51 Qd=-P+20-+12 - Qa = -P + 32 <— Demand p = _Qd + 32 <— Inverse Demand Q5=2P—40+24 35”,. Q5 = 2P - 16 <— Supply _ p = 1/2Qs + 8 <— Inverse Supply P,3 = 20 + I/300 — 2T Pa = 20 ‘+ 1200/300 — 2(4) = \$16- Qe = 2T + 21/300 . _ Qe = 2(4) + 2(1200)/300 = 16 If T increases to 5, this will increase supply. An increase in supply causes a decrease in price and an increase in quantity. as QS=2P'40+30 32 Q; = 2P — 10 <— New Supply P = VZQs + 5 <— New Inverse Supply Pe=20+I/300—2T §:=:—_ w... Pa = 20 + 12001300 - 2(5) = \$14 Qe = 2T + 21/300 Qe = 2(5) + 2(1200)/300 = 18 If I decreases to 900 instead, this will decrease demand (since the good is a normal good). A decrease in demand causes a decrease in price and a decrease in quantity (from the original). ‘ d: Qd = -P + 20 + 9 r 32 Qd = -p + 29 <— New Demand 29 p = —Qd + 29 <— New Inverse Demand 5 Pe=lb Pe=20+I/300—2T . /" Pa = 20 + 900/300 — 2(4) = \$15 “5 g. I _| I Qe = 2T + 21/300, I . D' D Qe = 2(4) + 2(900)/300 =14 a; as a Initially, you used equilibrium analysis. Then you used comparative statics. 4. Qd=100-5P Q5 = 50 + 5P Qd = Q5 100 - 5Pe = 50 + SR; lOPe = 50 P, = 5 (\$500) Qe = 100 — 5(5) Q,. = 75 (750,000) A price ceiling at \$100 (P = 1) would cause Qd (1) = 95 and Q5 (1) z ‘55. Therefore, it creates a shortage of 40 (or 400,000) units. 5. Point price elasticity looks at elasticity at a speciﬁc price. All: price elasticity looks at an “average" elasticity between two prices. Point price elasticity is a more accurate measure. EQdy = an/aP ' P/Qd QC] = -P + 20 + 1/100 I = 1200, P = 6 EQdJ: = "1 - 6/26 = -0.2308 I = 1200, P = 2 EW = —1 - 2/30 = -0.0667 I = 1400, P = 20 EQdJ = an/BI j P/I = 1/100 - (1400/14) = 1 6. de= 30—2P,+ 1.5P,—3P,+ .51 and P)( = 3, FY: 8, 19,: 4, andI= 20 de = 30 — 2(3) + 1.5(3) — 3(4) + .5(20) = 34 Ede,px = anx/an - lax/QC,x = -2 - 3/34 = —3/17 Ederz = anx/apz - Pz/Qdx = -3 - 4/34 = 45/17 Equ,1= anx/BI - I/de = 0.5 - 20/34 = 5/17 Ede.Pv = anx/apy - Py/de = 1.5 - 3/34 = 6/17 7. Because of the Law of Demand, price and quantity change in opposite directions. Therefore, since total revenue (TR) is P - Qd, the effect of a price change on TR depends on the relative size of the changes. The price elasticity gives us information on the relative size of the changes. (Note that the amount of revenue collected is the same as the amount spent. 50 consumer expenditures equal total revenue.) When demand is elastic, the quantity effect is larger than the price effect, in percentage terms. Therefore, if price is increased, quantity demanded will decrease by a larger percentage. So TR will fall. 0n the other, if price is decreased, quantity demanded will increase by a larger percentage. So TR will increase. When demand is inelastic, the opposite is true. The price effect is larger than the quantity effect, in percentage terms. Therefore, if price is increased, quantity demanded will decrease by a smaller percentage. So TR will increase. On the other, if price is decreased, quantity demanded will increase by a smaller percentage. 50 TR will fall. If the government is trying to raise funds through an excise tax, they will raise more money on items whose quantity demanded does not decrease substantially when the tax is imposed. An excise tax will increase price, and if the good has an inelastic demand, this price increase will generate a smaller percentage decrease in quantity demanded than if it were elastic, therefore generating more revenue. Chapter 3 2. a. Violates completeness b. Violates nonsatiation c. No violations d. Violates nonsatiation 3. See your class notes or the text for the deﬁnitions. A diminishing MRS implies that the indifference curves are convex which basically means that the slope of the indifference curve gets ﬂatter as the individual consumes more and more of the good on the x—axis. (1) U = xx2 Mm=ﬁ MRsx, = y2/2xy = y/Zx Convex since it decreases as x increases (and y decreases) (2) U = X1/2y1/2 MUx = (1/2)x'1/2y1/2 Muy = (1/2)x1/2y'1/2 MRSx,y = [(1/2)X'1’2y1’2]/[ (1/2)x1/2y-1/2] = W Convex since it decreases as x increases (and y decreases) (3) U=5x+3y MUX=5 MUY=3 MRS,“ = 5/3 Not convex. The indifference curves are linear since the slope is constant. (4) U = x1’4y3’4 MUx = (1/4)x‘3/4y3/4 MUV = (3/4)x1/4y'1’4 MRSx,y = [(1/4)x-3/4y3/4]/[ (3/4)X1/4y~1/4] = Y/3X Convex since it decreases as x increases (and y decreases) (5) u = taxi/2 + 2y MUX = 3x11”- MUy = 2 MRS” = 3x'1’2/2 = 3/2x1/2 Convex since it decreases as x increases (and y decreases) 4. If we put horror movies on the x—axis and all other goods on the y-axis, this statement implies that the individual would be willing to give up more units of y in order to consume additional horror movies. This would mean an increasing MRS“. The indifference curves would therefore be concave rather than convex. All OWE? 6:22:16 H’ error H0 v‘ I ‘58 5. See your class notes for an explanation of this. NA b. With alcohol on the horizontal axis and non-alcohol on the vertical, these preferences would imply that for the same level of alcohol consumption, Smith’s MRSAM would be lower than Jones’. Since Smith prefers non-alcohol to alcohol, the number of units of non-alcohol he would be willing to give up to get alcohol (which is what MRSAM measures) is lower than what Jones, who prefers alcohol, would be willing to give up. ...
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