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\f(c) Does the rm's production exhibit increasing, decreasing. or constant returns to scale? Justify your answer. (d) In the short run. the level of capital is xed at H = Ff. Formulate an expression for the shortrun optimal level of labor to produce y units of output. {e} In the long run. the Froman Sausage Company can vary both If and L. Set up the company's longrun costminimization problem using the Lagrangian and list the rst order conditions that characterize the optimal combination of inputs. (f) Formulate expressions for the rm's long-run costminimizing levels of labor and capital as a function of the output level y. Derive the Froman Sausage Company's longrun cost curve, clip). (g) Is there a protmaximizing level of output, 3;? Explain. (Hint: think about returns to scale) 3] Mr. Thatcher knows that the cost of publishing the newspaper The Inquirer is given by the function cIIyJ = 1H + 53; + Syz. where y is the number of copies published. (a) Find The Inquirer's xed cost and variable cost function 150(3)) (b) Derive the company's marginal cost curve, efgy]. and average sortable cost curve. .xivclgy]. (c) Suppose the xed cost is a sunk cost. If the price of the newspaper is p = 11, how many copies should be produced? (d) 'What is the revenue from publishing The Inquirer? \"That is the total prot?l 4] The Seahaven 1Ifending Machine Company is a uniformpricing monopolist with cost function 0(a) = 1'23; and the demand curve for the company's product is F[y] = 1m] - 13; (a) Formulate an expression for the Seahaven Vending Machine Company's marginal rev enue curve. M'Rliyj, and marginal cost curve, :1-fC{y]. {b} Find the monopolist's optimal quantity and price in this market and what the optimal quantity and price would be if this market were perfectly competitive. {c} Draw a diagram {with y on the horizontal axis} labeling the perfectly competitive out come as fl, and the monopolist outcome as B. Include the marginal cost, marginal revenue, and demand curves in your diagram and shade the area that represents the deadweight loss from monopoly. (d) Calculate the consumer surplus in this market under the monopoly. what the con sumer surplus would be under perfect competition. and what the deadweight loss from monopoly is. (e) Suppose the Seahaven 1'v'ending Machine Company could engage in rstdegree price discrimination. 1What would the consumer surplus and deadweight loss from monopoly be with this type of price discrimination in place