Econ 480, Assignment 2

1- A firm manufactures a gadget. Firm chooses: (i) How many gadgets to make, and (ii) Howmuch to spend advertising them. Marketing department claims that the market price is givenby = 10? ? , Where A is the amount spent on advertising, and Q is the quantity sold.Advertising “pushes up” the demand curve, but at a diminishing rate. Some advertising isrequired to make the product known. Additional advertising contributes to sales less.Production department claims that the production costs are equal to () = 5. How manygadgets should the firm make and how much should it spend advertising? Which solution is theoptimum answer? Note the market is not competitive and firm’s actions have effect on themarket price through the demand curve described above.2- Do the following productions have increasing, decreasing, or constant returns to scale? Kstands for capital, L for labor and a & b are positive numbers.(a) = 4 0.5 0.5 ; (b) = 0.5 0.6 ; (c) = 2 + 2 ;(d) = 4 + 2;3- Consider the demand function x = 1-p, where x is the quantity demanded and p is the price.(a) Find the revenue function as a function of p. What value of p maximizes total revenue?What is the maximum value of revenue?(b) What is the consumer surplus at price p? What is the relationship between consumersurplus and price?(c) What is the price elasticity of demand at p = 0.44- Consider a competitive industry with two firms, one with cost function 1 () = 2 , andother with cost function 2 () = 2 2 . Find the industry supply function.5- Market demand for certain product, QD = 900p-1. Each firm’s production function = 0.5 .Suppose the price of labor is w = 2.(a) Suppose there is only one firm in the market. Derive the firm’s supply curve and solve forthe competitive equilibrium price and quantity. Calculate the firm’s profit.(b) Now, suppose that there are two firms, whose output levels are denoted by q 1 and q2. Solvefor the competitive equilibrium price and quantities produced by each firm. Compare theresults with part (a).6- U.S. consumers have a demand function for umbrella which has the form QD = 90-p.Umbrellas are supplied by U.S. firms and U.K. firms. For simplicity, we assume there is a single representative firm in each country that behaves competitively. The cost function for producing2umbrella in each country is () = ?2 .(a) What is the aggregate supply function for umbrella? What is the equilibrium price andquantity sold?(b) The domestic industry lobbies for protection and Congress agrees to input a $3 tariff onforeign umbrellas. What is the new U.S. price for umbrella paid by the consumers?(c) How many umbrellas will foreign firms supply? How many umbrellas will domestic firmssupply?7- A competitive industry is composed of identical firms each with cost function C = 1 + 2 Q2,where C denotes cost and Q is the level of output. The government imposes a fixed fee of $1per year on each firm that operates in this competitive market. What happens to output, theoptimal scale of a firm, and price if there is free entry into the market?8- In the above question, suppose instead of imposing the $1 fixed fee, the governmentimposes a tax of $1 per unit of output. What happens to the optimal scale of firms? We againassume all firms are identical and any firm can enter the market.