Market demand for certain product, QD = 900p-1 . Each firm’s production function ?? = ??...

Market demand for certain product, QD = 900p-1 . Each firm’s production function ?? = ?? 0.5 . Suppose the price of labor is w = 2.

(a) Suppose there is only one firm in the market. Derive the firm’s supply curve and solve for the competitive equilibrium price and quantity. Calculate the firm’s profit.

(b) Now, suppose that there are two firms, whose output levels are denoted by q1 and q2. Solve for the competitive equilibrium price and quantities produced by each firm. Compare the results with part (a).

Solutions

Expert Solution

Given,

QD = 900_p-1

qi = Li = 0.5

Suppose the price of labor is W = 2.

a) Derive the firm's supply curve and solve for the competitive equilibrium price and quantities.

Calculate the firm's profit.

We know that,

W/P = MP_L

It is the marginal product of labor.

b) Now suppose that there are two firms whose output levels are denoted by q1 and q2 .

To solve:

The competitive equilibrium price and quantities produced by each firm.

p = 42.42

Q = 900/ 42.42

Q = 21.21

Here due to increase the number of firm price of each firm is lower compose to in one part a. But equilibrium quantity is higher as more as spelling market.

Rahul Sunny answered 1 year ago

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