Question

1)

Suppose a perfectly Competitive market had Demand given as: P = 225 -.03Q and Supply Given as: P = 15 + 0.04Q. What are the equilibrium values for P and Q?

Now suppose demand is still P = 225 -.03Q but the industry has one firm with a marginal cost given by: MC = 15 + .04Q. What are the equilibrium values for P and Q in this case? How do the values pf P and Q in Pure Monopoly compare to your result for perfect competition?

2) Suppose you operate a business in a perfectly competitive market. The market price of the good is: P = 30 and your marginal cost is 5 + .02Q. You have Fixed Costs of: FC =5000. Find your profit maximizing value for Q and determine how much profit you make.

Answer 1

(1) The demand and supply in the perfectly competitive market are,

Demand: P = 225 - 0.3.Q

Supply: P = 15 + 0.04.Q

Now, at equilibrum the supply and the demand are equal. Hence,

225 - 0.3Q = 15 + 0.04Q

or, 0.34.Q = 210

or, Q* = 617.65

Putting Q* in the demand curve we get

P* = 225 - 0.3×Q* = 225 - 0.3×617.65

or, P* = 39.7 ~ 40

Hence, the equilibrum values are

P* = 40 and Q* = 617.65.

✓ Now, the demand curve is same as before i.e.

P = 225 - 0.3.Q

The industry has one firm with Marginal Cost

MC = 15 + 0.04.Q

Hence, at equilibrum,

  P = MC

or, 225 - 0.3.Q = 15 + 0.04.Q

or, 0.34.Q = 210

or, Q* = 617.65

And, putting Q* in demand curve we get

P* = 225 - 0.3×617.65 = 39.7

or, P* = 40

In this case the equilibrum values in the competitive industry are same as before i.e.

P* = 40 and Q* = 617.65.

✓ If the market is monopoly, then at equilirbum, the Marginal Cost should be equal to Marginal Revenue.

The market demand is

P = 225 - 0.3.Q

Hence, Total Revenue is

TR = P.Q = (225 - 0.3.Q).Q

or,

Hence, Marginal Revenue is

MR = d(TR)/dQ

or, MR = 225 - 0.6.Q.........(1)

And, Marginal Cost is

MC = 15 + 0.04.Q.........(2)

Hence, at equilibrum

MR = MC

or, 225 - 0.6.Q = 15 + 0.04.Q

or, 0.64.Q = 210

or, Qm = 328.125

Puttimg Qm in the demand curve we get

Pm = 225 - 0.3.Q = 225 - 0.3×328.125

or, Pm = 126.5625

I am not rounding off the values as they look fine.

Hence, the equilibrum values in the monopoly market are

Pm = 126.5625 and Qm = 328.125

Comparing between Monopoly and Perfect Competition: ​​​​​​

At the competitive industry, P* = 40 and in the monopoly market Pm = 126.5625.

• Monopoly price is much higher than competitive price.

At the competitive market, Q* = 617.65 and in the monopoly market Qm = 328.125.

• Monopoly quantity is much lower than the competitive quantity.

(2) The market price of the good is

P = 30..........(1)

The marginal cost is given as

MC = 5 + 0.02.Q........(2)

Fixed cost is given as

FC = 5000........(3)

Now, from the marginal cost, we can calculate the total cost by integrating the marginal cost with respect to Q.

Hence,

or, ........(4)

Now, at equilibrum in the competitive market, the Price equals Marginal Cost. Hence,

P = MC

or, 30 = 5 + 0.02.Q

or, Q* = 1250

Hence, the profit maximizing value of Q is

Q* = 1250.

Now, Total Revenue is

TR = P×Q* = 30×1250

or, TR = 37500

And, Total Cost or TC at Q=1250 is

  

or,

or, TC = 26875

Hence, Maximum profit of the firm is

π = TR - TC

or, π = 37500 - 26875

or, π* = 10625

Hence, the firm makes profit of

π* = 10625.

Hope the solutions are clear to you my frirnd.