Answer Key - Assignment # 1
Question 1 [20 pts] – See file Assign1_AK1.xls attached.
Question 2 [ 25 pts]
(By “structure of demand”, we mean to analyzethe elasticity of demand).
(a)[5pts]
At p = 7.5, Q = 150, and the consumer surplus is:
CS = CDA = {(10-7.5)* 150 }/ 2 = $187.5 (thous.)
The consumer surplus of $187,500 represents the excess consumers are willing to pay to consume 150,000 lbs units of cheddar cheese at the price of $7.5/lb.
(b)[5pt]
Given the above information, the point elasticity of the demand for cheddar cheese when we move from A to B is:
Eown-price = [(QB – QA)/QA]/[(PB – PA)/PA]
= [(225-150)/150]/[(6.25-7.5)/7.5] = -3
(Remember in the denominator we use the quantity/price before change. We are calculating own-price elasticity which relates the change in quantity demanded of one good with the change in the price of that same good).
(c)[5 pts]
Consumer surplus will increase by the area of DEBA, which is calculated as follows:
CS = DEBA = CS2 – CS1 = CEB – CDA = ((10-6.25)* 225 –(10- 7.5)* 150)/2 = $234.375 (thous.)
(d)[10pt]
Income elasticity is calculated as follow:
Eincome = [(Q2 – Q1)/Q1]/[(Y2 – Y1)/Y1]
In which: Y1 and Y2 are theinitial andnew incomes correspondingly.
Income increases by 10%, so sales increase by (Q2 – Q1)/Q1 = Eincome * (Y2 – Y1)/Y1 = 1.5*.1 = .15 or 15%. . Or Q2 = Q`1 (1+.15) = 258.75 (thous. lbs)
We know the slope of the original demand curve is (10-7.5)/150=1/60
So we can find the new intercept of the demand curve as (x-6.25)/258.75=1/60 or x=10.5625
Then the increase in CS is given as ((10.5625-6.25)*258.75-(10-6.25)*225)/2=136.0547
Question 3. [25 pts]
(a)[5pts]
CS = CDA = [(40-22.5)*100]/2 = $875 (mil.)
(b)[10pts]
Given cash rebate, the price per unit of hybrid reduces by $2,500; and you estimate that the sales of the GM SUV will fall. This implies that GM SUV and Ford Escape are substitutes, as proven by a positive cross-price elasticity of demand for GM SUV with respect to Ford Escape price as shown below:
Ecross-price = (80-100)/100]/ [(-2.5/25)]
= 2
(c)[5pts]
The cash rebate reduces the price of hybrid per unit The demand curve for Ford Escape shifts in parallel to the right. At any price price, consumers now are able to consume more The consumer surplus increases.
Demand for Ford Escape is PFord = a + bQFord
Before cash rebate program
At Q = 0, P = 45 a = 45; At Q = 250, P = 25 b = -0.08
PFord = 45- 0.08 QFord
The consumer surplus at P = 25 is CSo = GKH = (45-25)*250/2 = $2,500 (mil.)
With cash rebate:
The consumer’s price per unit of Ford Escape is PFord – 2.5 = 45 – 0.08 QFord
Or PFord = 47.5 – 0.08 QFord
Now at P = 25, Qnew = (47.5-25)/0.08 = 281.25 (thous)
The corresponding consumer surplus is: CS1 = G’KH’ = (47.5-25) * 281.25/2 = $3164.06 (mil.)
Consumer surplus increases by CS = G’GHH’ = CS1 – CSo = $664.06 (mil.)
(d)[5pts]
Before cash rebate program
PGM = c + dQGM
At Q = 0, P = 40 c = 40; At Q = 100, P = 22.5 d = -0 .175
PGM = 40 -0.175QGM CSo = CDA = (40-22.5)*100/2 = $875 (mil.)
Given cash rebate program
The shift in demand for Ford Escape due to cash rebate results in a decline in demand for GM SUV Demand for GM SUV shifts to the left as shown in the graph below.
Now: PGM = c – t – 0.175QGM
At A’: QGM = 80, PGM = 22.5 (GM SUV price does not change)
t = 40 – 0.175*80 - 22.5 = 3.5.
So: PGM = 36.5 – 0.175QGM CS1 = C’DA’ = (36.5-22.5)*80/2 = $560 (mil.)
Consumer surplus for GM SUV’s consumers changes by:
CS = CC’A’A = CS1 – CSo
= 560 - 875
= - $315 (mil.)
Consumer surplus for GM SUV’s consumers reduce by $315 mil.