Answer to Question #236218 in Macroeconomics for Abyssinia

Question

7.    Given that a perfectly competitive firm incurs TC=200+Q2-40Q and market demand is equal to P=3000-10Qd and market supply is equal to P=1000+4Qs where Qd and Qs are quantity demand and quantity supply respectively .Then

A.   What is the profit maximizing level of output

B.   What is the equilibrium level of price

C.   What is the MR of the firm

D.   What is the maximum profit at equilibrium level

E.    Draw the graph showing the equilibrium level

F.    Is the firm at short run or long run? How do you know? 

Answer 1

The given demand and supply equation:

$P = 3000 − 10Qd\\Qd= 300 − 0.1P\\P= 1000 + 4Qs\\Qs= 250 + 0.25P$

a)

Equate quantity demanded and quantity supplied:

$Qd=Qs\\ 300 − 0.1P =250 + 0.25P\\50=0.35P \\ P =142.85$

The market determined price is $142.85.

A perfectly competitive firm produces at the point at which price equals marginal cost (MC).

Marginal cost (MC) is the first derivative of total cost and is calculated as follows:

$MC =\frac{ ∂TC}{∂Q}\\=2Q − 40$

Equate price and marginal cost:

$P=MC\\ 142.85 = 2Q −40 \\182.85 =2Q \\Q=91.425$

Equilibrium unit of output is 91.425,

b)

The profit is calculated as follows:

$Qd=Qs\\ 300 − 0.1P =250 + 0.25P\\50=0.35P \\ P =142.85$

equilibrium level of price is $142.85.

c)

The marginal revenue of a perfectly competitive firm is equal to price $142.85.

d)

$Profit =TR − TC\\=(P×Q) − (200 + Q^2−40Q)\\=(\$142.85×91.425) − (200 + (91.425)^2 −40(91.425))\\=\$13060.06125 −\$12215.530625\\= \$844.530625$

Profit is $844.530625.

e)

The graphical representation is as follows:

The price line intersect the marginal cost curve at point e corresponding to which equilibrium quantity produced by perfectly competitive firm is 91.425 units.

f)

The firm is in the short run because in the long run each perfectly competitive firm makes the normal profit but here the firm is making super normal profit which is only possible in the short run.