Midterm Exam #2 - Answers. November 24, 1997

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1 age 1 of 5 Name: Novembe 24, 1997 Instuctions: Answe all questions diectly on these sheets. oints fo the pats of each question ae indicated, and thee ae 84 points total. Budget you time. 1. [14 oints]he figue below shows the supply and demand cuve in the maket fo oanges. Also measued, on the vetical axis, ae an extenality, E, and a tax, t. he extenality is a positive extenal benefit aising fom consumption of oanges, a esult of thei ability to fend off the infectious common cold and theefoe impove the health of othes who come in contact with those who eat oanges. he tax, t, has been poposed in ode to aise evenue fo an unelated pupose. a) [4 points]find in the figue, dawing them if necessay, the cuves that indicate the maginal benefit to society and the maginal cost to Q 1 Q 0 $Q society of oanges, as functions of the quantity poduced. Label them MBS and MCS. If you need to add anything to the diagam in ode to do this, be sue to indicate what you have done. b) [2 points]identify in the figue the optimal level of output of oanges, and label it $Q. c) [4 points]stating fom the initial equilibium at Q 0 and 0, find the new equilibium that will aise if the tax, t, is levied on poduction. Label it Q 1 and 1. d) [4 points]identify and label in the figue the gain o loss to society due to the tax as a esult only of the extenality. hat is, ignoing the effects of the tax on poduces and consumes of oanges, by how much does the tax aise o lowe the welfae of society though its effects on those who come in contact with consumes of oanges? Indicate clealy whethe it is a gain o a loss. E 1 0 t Loss due to extenality E S=MCS D MBS Q

2 age 2 of 5 2. [45 points]he town of Gateway, South Dakota, cuent population 3,500, is consideing the constuction of a new wate teatment plant. he plant will take two yeas to build and would cost, at today s (Jan 1, 1998) pices, $300, in 1998 plus $ in he plant will begin opeating Jan 1, 2, and it will povide a benefit to the city s population, in today s pices, of $20 pe yea pe peson. Cost of opeation, at today s pices, will be the same egadless of the population: $ a yea. he plant is expected to opeate fo 20 yeas, stating Jan 1, 2. Unde each of the following sets of assumptions, calculate the pesent value of this poject. In each case, fist show the fomulas, with appopiate numbes plugged in but not evaluated, fo i) pesent value of constuction cost ii) pesent value of opeating cost iii) pesent value of benefits to population hen, evaluate the fomulas fo each, and combine them to get the total net benefit o cost, using you calculato if you like. (Most of the cedit will be given fo using coect fomulas with coect values in them, so be sue to make that clea.) a) [15 points]he nominal inteest ate is 8%, inflation is zeo, and population gowth is zeo. Ans: Real inteest ate = = 8% 0% = 8% C1 V ( CC) = C0 + = 300, + = 670, (Costs fo yeas 0 and 1, discounted by the eal inteest ate.) Cop V ( OC) 1 Cop ( ) = = 63, (Costs incued in the 20 yeas, numbeed 2,,. Fist tem is fomula fo constant cost in yeas 1,,. Second tem emoves the cost fo yea 1.) B V ( B) 1 B ( ) 70, , = 636, (Benefit is $20 3, $20 pe peson times 3,500 pesons in yeas 2,,. Fomula is same as fo opeating costs.) V ( NB) = V ( CC) + V ( OC) + V ( B) = 9 645

3 age 3 of 5 b) [15 points]he nominal inteest ate is 9%, inflation is 3%, and population gowth is zeo. Ans: Now = 9% 3% = 6%. Fomulas ae othewise the same as befoe: V ( CC) = 300, + = V ( OC) V ( B) = , V ( NB) = 4, 344 = 75, , = c) [15 points]he nominal inteest ate is 10%, inflation is zeo, and population of the town is expected to gow at the ate of 4% a yea, stating immediately. Ans: he benefit now gows at 4% a yea and the eal inteest ate is 10%. We have a fomula fo a gowing benefit, stating in yea 1 and ending in yea. It applies to a benefit that stats at a value B 1 in yea 1 and gows at a constant ate. Hee the benefit is $20 3,500 in yea 0 and will gow 4% aleady by yea 1, so B 1 =$70, (1.04)=$72,800. he fomulas fo costs ae the same as befoe: V ( CC) = 300, + = 663, V ( OC) = = 54, B V ( B) a ( a) B ( ) = 72, , 800 = 773, V ( NB) = 55, 715

4 age 4 of 5 3. [25 points]fo each of the policies in pats (a) and (b) below, by which a govenment could help the poo, calculate i) the cost to the govenment, ii) the benefit to the poo, iii) the cost o benefit to othes, and iv) the weight, $w, that would have to apply to the poo (if the weight is 1 fo eveyone else) in ode fo the policy to beak even (in the sense of its weighted net benefit being zeo). a) [8 points]he govenment gives checks fo $100 to each of 1 poo people, incuing administative costs of $20, plus $5 pe check. Cost to Govenment = CG = $ , = $125, Benefit to oo = B = $100 1 = $100, Benefit to Othes = BO = 0 Net Cost to Nonpoo 125, w$ = = = 125. Net Benefit to oo 100, b) [12 points]he govenment pays a subsidy of $1.00 pe can fo puchases of the luncheon meat, Spam, noting that pio to the policy, 300, cans of Spam ae sold each yea at a pice of $3.00 each and two thids of the buyes of Spam ae poo. Spam is known to be poduced at constant cost and sold pefectly competitively, and the elasticity of demand fo Spam is 2. Ans: Spam maket appeas at ight. Subsidy can be viewed as shifting the (hoizontal, since constant cost) supply cuve down by $1, loweing the pice fom $3 to $2, a 1/3 eduction. With demand elasticity of 2, the % change in quantity is twice the % change in pice, so a 1/3 eduction in pice causes quantity to incease by 2/3, to 500,. Govenment pays the subsidy of $1 on all cans, costing it $500,. Demandes gain consume suplus of the aea left of the demand cuve between the pices. wo thids of this is a gain to the poo, while one thid is a gain to S S D Q

5 age 5 of 5 othes: CG = $500, CS = (3 2)(300, + 500,)/2 = $ B = (2/3) CS = $266,667 BO = (1/3) CS = $133,333 Net Cost to Nonpoo 500, 133, 333 w$ = = = Net Benefit to oo 266, 667 a) [5 points]which of these policies tansfes esouces to the poo moe efficiently? Why? In this case, the diect payment (policy (a)) tansfes esouces moe efficiently. We can see this fom the fact that one needs a smalle exta weight on the poo, 1.25, in ode to justify that policy, as compaed on the weight on the poo needed to justify the Spam subsidy, Altenatively, this can be seen fom the fact that a lage pecentage of the net cost to the non-poo gets to the poo unde policy (a) (100/125= 80%) than unde policy (b) (266,667/366,667 = 73%), o that the leaky bucket coefficient fo (a) (20%) is less than (b) (27%).