Question

Q3. Market demand: P-8000-4y I. Perfect competition with market supply P 500 A. Find the market equilibrium price and quantity. y B. Find the profit maximizing quantity for a firm with cost function C 100,000 200y 2y2. C. How much profit the firm would make?

Answer 1

Given

Demand

P = 8000 - Y / 4

Supply

P = 500 - Y / 8

1) Market equilibrium price and quantity

Equilibrium is where both demand and supply are equal so equating both demand and supply equation

8000 - Y / 4 = 500 - Y / 8

64000 - 2Y = 4000 + Y

60000 = 3Y

20000 = Y

Equilibrium quantity is 20000

Also, the equilibrium price can find out by putting the value of the quantity in any of the equations

P = 8000 - Y / 4

P = 8000 - 20000 / 4

P = 3000

Equilibrium price is 3000

2) Given cost function is C = 100000 + 200Y + 2Y²

First thing we need to do is to recognize that in perfect competition, profit maximization requires that the firm produce the amount of output consistent where the price equals the marginal cost.

P = MC

We have price which is 3000 so we have to find MC function

Now from the above TC function, MC function can find out through the differential.

There are some properties of differential

1) C = xⁿ

  
_dc

example -

C = x³

C = 3x²

2) if an equation has constant then after differential it will be 0

Now to the question

C(Y) = 100000 + 200Y + 2Y²

TC = 100000 + 200Y + 2Y²

$MC(Y) = \frac{dC(Y)}{dY}$

MC (Y) = 0 + (1)200Y^1-1 + (2)2Y^2-1

MC = 200 + 4Y

Now we have MC function and we know P = MC

3000 = 200 + 4Y

Y = 700

Profit maximizing output is 700

3) For calculating profit

Profit = TR -TC

TR = Price x Quantity

TR = 3000 x 700

TR = 2100000

For calculating the total cost, we have the cost function

C = 100000 + 200Y + 2Y² .

and we have the value of Y as 700 so putting 700 in the cost function

C = 100000 + 200(700) + 2(700)² .

C = 1220000

Profit = TR - TC

Profit = 2100000 - 1220000

Profit = 880000