Question

In: Economics

Consider an industry with identical firms and production function y= (x12 + x22)1/2 The demand function...

Consider an industry with identical firms and production function y= (x1² + x2²)^1/2

The demand function is qD (p) = a − bp, where a > 0, b > 0. Compute the long run equilibrium number of firms in the market, and the quantity of output that each firm produces.

Expert Solution

Assuming that the production function is

Each firm's cost minimization problem is to minimize where w and r are price of factors and respectively, subject to the constraint that

At equilibrium, the Marginal Rate of Technical Substitution (MRTS) = Ratio of the factor prices

Hence, the cost function of the firm is

Each firm's profit function is

The is the quantity of output produced by one firm. In the long run, let there be n such firms. The total output is:

Substituting the value of Q in the market demand function:

Rahul Sunny answered 1 year ago

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