Question

1. Consider the national market for Tesla Model S all-electric luxury car with the inverse demand given by P=120-0.75*Qd and inverse supply given by P=15+0.25Qs. (Note: the price is in thousands of US$ and quantity is in thousands of cars). a. Calculate the equilibrium price and quantity and draw a graph to represent them. (Label clearly everything on the graph to obtain maximum points) b. Calculate the Total Surplus at the equilibrium point and provide a succinct argument as to why the equilibrium represents an efficient allocation of resources in this market. c. Consider now that the price of Tesla Model S decreases by $10 (thousands) below the equilibrium price I. Will there be any efficiency losses (.e. decrease in Total Surplus)? Calculate the new Total Surplus and find the Deadweight Loss.

please show work

Answer 1

Answer:

considering the national market for test model S all-electric luxury car with the inverse demand

a)

Given by:-

P = 120 -0.75 * QD

Now, When  

P=0 => 120 -0.75 * Qp = 0

=> Qp = 160

When

Qp = 0 => p = 120

Now inverse supply

p=15+0.25 Q5

When

p=0 => 15 +0.25 Qs = 0

=> 0.25 Qs = -15

Qs = -60

When

Qs = 0 => p= 15

Now we can draw demand and supply curve

Now equilibrium occurs when demand equals supply and at equilibrium  

Qs = Qd = Q

hence ,

120 – 0.75Q = 15 +0.25Q

=> -0.75 -0.25Q = 15 – 120

=> -Q= -105

SOI = 0 <=

and equilibrium price will be found by substituting Q=105 in either demand or in supply equation.

Hence

p= 120 – 0.75 Q

= 120 - 10.75 + 105)

= $41.25

aprice Supply 7695 - 41.25 31.25PL is Demand . -60 P 65 105 118.33 160 quantity

b)

Now, consumer supply at equilibrium is the area below the demand curve and above equilibrium price

p= $ 41.25 i.e. areaof triangle ABC

= * base * height

== *(105 -0) * (120 -41.25)

= $ 4134.38

and producer supply is the area above the supply curve and below price i.e. area of triangle ABC

== + (41.25-15) + (105-0)

= $1378.13

Hence, total supply

= (consumersupply + producer supply)

= $141.34.38 + 1378.13)

= $ 5512.51

This is an efficient allocation of resources because at the equilibrium price where quantity demanded becomes equal to the quantity supplied, there is no loss or dead weight loss in the economy.

e)

If price of Tesla model decreases by $10(towards below the equilibrium price)

New price will be

= $141.25-10) = $31.25

(i)

Now at price of $31.25 quantity demanded

p= 120 – 0.75 QD

=> 31.25 = 120 – 0.75QD

Qp = 118.33

AND quantity supplied

p=15+0.25 Qs

=> 31.25 = 15+0.25Qs

=> Qs = 65

Now consumer supply

areaof A AMN + areaofO MNOP

Now to get point M,we substitute quantity

Q=65 in the demand equation and solve for the price.

Hence,

p= 120 +0.75 QD

P=1210 * (0.75*65) = 71.25

areaofO MNOP = (71.25 – 31.25) * (65 - 0)

=$ 2600

and area of A AMN = = * base * height

(65-0) + (120-71.25

= $1584.38

Hence total consumer supply

  

= $( 2600 + 1584.38)

= $41.8438

Now producer supply

area of A POD

(65-0) + (31.25-15)

= $528.13

Hence total supply= consumer supply+producer supply

= $(4184.38 + 528.13)

= $ 4712.51

dead weight loss = area of A NCD

= * base * height

$=\frac{1}{2} *(105-65)*(71.25-31.25)$

Hence total supply demand by $=\$(5512.51-4712.51)$

Note:-

If you do not get anything in this solution, please put a comment and I will help you out.

=> $Q_{D}=160$

when
OD=0