Consider a firm with the production function given by y = L^1/2K^1/2, where y is the output, L is the labour input, and
Posted: Fri Jul 01, 2022 7:55 am
Consider a firm with the production function given byy = L^1/2K^1/2,where y is the output, L is the labour input, and K is the capitalinput. The firm is in a competitiveindustry, and hence, the firm takes the price of the output asgiven. Also the factor markets arecompetitive and hence, the firm takes the prices of the inputs asgiven.Currently, the price of the labour is $5, the price of the capitalis $10.(a) If the firm were to produce y = 100, how many units of thelabour and capital is it goingto hire?(b) Now consider any positive amount of the output (y). Find thecost-minimizing labour andcapital inputs. Note that they must be a function of y.(c) Derive the cost function based on (b).