Question

3. Swedish Automobiles Are the Best (SAAB) sells two types of cars: a combi and a sedan. Based on past trends, the inverse demand equation for cars is estimated as PC = 40 - 0.05QC where QC is the number of combi cars sold per year and PC is the price per combi car (in thousands of dollars). The price equation for sedans is: PS = 30 - 0.1QS. In turn, SAAB pays $10 (thousand) to produce each combi car and $8 (thousand) to produce each sedan.

a. Determine the profit-maximizing outputs of combi cars and sedans for SAAB and the respective price they should charge for combi cars and sedans.

b. Compute the total profit earned from combi cars and sedans combined using the quantities computed in part a

c. Suppose now that SAAB’s capacity is limited to a total of 260 vehicles per year. Determine the profit-maximizing quantities of and prices for combi cars and sedans for SAAB with this new constraint.

d. Compute the total profit earned from combi cars and sedans combined using the quantities computed in part c

e. SAAB is considering an expansion of their production facility, which would increase their current capacity (of 260) by as much as 80%. This expansion would also increase their annual fixed cost by $700 (thousand). Should SAAB expand (motivate your answer using profit data)?

Answer 1

Answer : Given , PC = 40 - 0.05QC; PS = 30 - 0.1QS ; Cost per combi car = 10; TC ( Total Cost ) for combi car = 10QC ; Cost per sedan car = 8; TC for sedan car = 8QS . NOW, TRC (TOTAL REVENUE) = PC*QC = (40 - 0.05QC)*QC = 40QC - 0.05QC^2; MRC ( MARGINAL REVENUE ) = TRC / QC = 40 - 0.1QC; MCC= TC / QC = 10;

TRS = PS * QS = ( 30 - 0.1QS)*QS = 30QS - 0.1QS^2; MRS = TRS / QS = 30 - 0.2QS ; MCS = TCS/QS = 8

a) At equilibrium MRC = MCC => 40 - 0.1QC = 10 ... (i)

=> 0.1QC = -10 + 40 =30

=> QC = 30/0.1 = 300

PC = 40 - 0.5(300) = -110

Again , at equilibrium MRS = MCS => 30 - 0.2QS = 8 ... (ii)

=> 0.2QS = 22 => QS = 22/0.2 = 110

PS = 30 - 0.1 (110) = 19

Therefore, profit maximizing outputs are QC = 300 and QS = 110 .

Prices are PC = -110 and PS = 19.

b) TRC = 40*300 - 0.5 (300)^2 = 12000 - 45000 = -33000

TCC = 10*300 = 3000.

Therefore, Profit for Combi = TRC - TCC = -33000 - 3000 = - 36000. Firm faces loss here.

TRS = 30*110 - 0.1 (110)^2 = 3300 - 1210 = 2090

TCS = 8*110 = 880.

Therefore, Profit for Sedan = TRS - TCS = 2090 - 880

= $1210.

c) Given, QC + QS = 260 => QC = 260 - QS

From equation (i) , we get ,

40 - 0.1 (260 - QS) = 10 => 40 - 26 + 0.1QS = 10

=> - 0.1QS = 4 => QS = 4/-0.1 = - 40.

PS = 30 - 0.1*(-40) = 40 + 4 =44

Again, QS = 260 - QC

From equation (ii) we have,

30 - 0.2(260 - QC) = 8 => 30 - 52 + 0.2QC = 8

=> -0.2QC = -30 => QC = 150

PC = 40 - 0.05*150 = 32.5

d) TRC = 40*150 - 0.05 ( 150 )^2 = 6000 -1125 = 4875

TCC = 10*150 = 1500

Therefore, Profit for Combi = TRC - TCC = 4875 - 1500

= $3375

TRS = 30*(-40) - 0.1 (-40)^2 = - 1200 - 160 = - 1360

TCS = 8*(-40) = - 320

Profit for Sedan = TRS - TCS = - 1360 - ( -320) = - 1040. The firm faces loss here.