Question

Consider the firm with production function given by q = f ( L , K ) = L ^(1/4) K^(1/4). If w = r = 4, what is the change in the producer surplus when the price increases from $16 to $32? (round your answer to one decimal place if necessary)

Answer 1

Producer surplus is the area between the price and the supply curve. Hence, first we need to find out the supply curve. For that we need to minimize the cost of the firm, which is the firm's problem. This is because the supply curve is given by the marginal cost, i.e. P = MC

Hence our process includes:--- >>> minimize the cost >>> find total cost function >>> differentiate w.r.t Q to get MC>>>set P = MC which is supply curve >>>integrate over the price range to find out change in the producer surplus

calculations below:--