Question

In: Economics

Given the following demand and supply equations for chicken sandwich:

Qd = 200 - 2P

Qs = 20 + 0.25P

What is the demand faced by each seller if this is perfectly competitive market?
What is the demand elasticity for the seller in (d) above? Draw a sketch of each seller’s demand curve in (e).
What will the price of chicken sandwich be if there is only one seller?
How many chicken sandwiches will be sold if there is only one seller?

Expert Solution

a)

Set Qd=Qs for equilibrium

200-2P=20+0.25P

2.25P=180

P=$80

Each seller is price taker in perfectly competitive firm. So, demand for an individual seller will be a horizontal line at P=$80 i.e.

P=$80

b)

Since demand faced by individual perfectly competitive firm is horizontal line, demand for a competitive firm is perfectly elastic.

Price elasticity of demand=infinity

c)

Demand curve is given by

Q=200-2P

2P=200-Q

P=100-0.5Q

Total Revenue=TR=P*Q=100Q-0.5Q^2

Marginal Revenue=MR=dTR/dQ=100-Q

Supply curve is given by

Q=20+0.25P

0.25P=-20+Q

P=-80+4Q (Marginal Cost)

It is the marginal cost curve of a monopolist

Set MR=MC for profit maximization

100-Q=-80+4Q

5Q=180

Q=36

P=100-0.5Q=100-0.5*36=$82 (Price if there is only one seller)

d)

Output if there is only one seller=36 (Refer part c)

Rahul Sunny answered 2 years ago

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