List of top Microeconomics Questions on Production and cost asked in GATE XH-C1

A Cobb-Douglas type short-run production function is given by \[ q = 2\sqrt{L \overline{K}} \] where \( q, L \) and \( K \) are the output, labour and capital, respectively. \( K \) is fixed at \( \overline{K} \). The unit price of \( L \) is \( w \) and the unit price of \( K \) is \( r \). It is given that \( w = 12 \). Considering the above information, which of the following statements is/are CORRECT?

The long-run cost function of all identical firms in a perfectly competitive industry is given by: \[ C = 25q - 3q^2 + 1.5q^3 \] The market demand function is: \[ P = 2500 - 0.25Q \] The number of firms in the industry at equilibrium is _________ (in integer).