Question

Suppose the market demand function is Q = 120 – 2P, and the marginal cost (in dollars) of producing the product is MC = Q, where P is the price of the product and Q is the quantity demanded and/or supplied.

- How much would be supplied by a competitive market? (Hint: In a perfect competition, the profit maximization condition is MR=P=MC)

- Compute the consumer surplus and producer surplus. Show that the economic surplus is maximized.

Answer #1

Demand function;

Q = 120 - 2P

2P = 120 - Q

P = 60 - Q/2

where P is the price of the
product

Q is the quantity demanded and/or supplied.

Marginal cost;

MC = Q

a) The equilibrium condition is;

P = MR = MC

60 - Q/2 = Q

60 = Q + Q/2

60 = (2Q+Q)/2

120 = 3Q

**Q = 40**

Therefore, quantity supplied by a competitive market will be;
**Q = 40**

b) The supply curve in a competitive market will be the marginal cost in short run;

P = MC

P = Q

The consumer surplus will be;

CS = 1/2 * 40 * (60-40)

= 20 * 20

**CS = 400**

The producer surplus will be;

PS = 1/2 * 40 * 40

= 20 * 40

**PS = 800**

Total economic surplus;

TES = CS + PS

= 400 + 800

TES = 1200

Economic surplus is maximised when marginal benefit from consuming a good is equal to its marginal cost of producing;

P = MC

which is at the point where;

Q = 40

MC = 40

P = 60 - Q/2

= 60 - 40/2

= 60 - 20

P = 40 = MC

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