A producer has the following technology y = K+L a) Show that the production function exhibits decreasing returns to scale (provide formal argument). b) Find analytically (the variable) cost function given prices of inputs wK = 1 and wL = 2 (formula). Plot the cost function in the graph. c) Assuming fixed cost F = 1 find analytically yMES and ATCMES (give two numbers) and plot a supply of the firm, marking a threshold for non-zero production. d) Determine the number of firms operating in the industry if demand is D(p) = 40p, firms are competitive and there is free entry in the market. (one number)