Assume the demand for a particular product is given by p = 120 - q and firms produce at linear costs c(q) = cq = 80q. Suppose a new production technology lowers marginal costs to 60, i.e., firms can produce with c(q) = cq = 60q, if they spend K. The innovation is protected by a patent, i.e., only the firm who adopts the innovation can produce at the lower cost. Take the perspective of a social planner who wants to maximize the social surplus, i.e., the sum of consumer surplus and producer profit in this market. (i) Derive the formula for the consumer surplus. (ii) What is the price and the quantity a social planner chooses without innovation? How big is the social surplus? (iii) What is the price and the quantity a social planner chooses with innovation? How much does the social surplus increase with this innovation? (iv) Suppose K = 600. Is the innovation worthwhile from a social planner perspective? What if K = 1500? How does your answer change if you consider multiple periods?

Suppose that the inverse demand for aloe juice in Greece is given by P = 100 – 2Q, where P is the price per bottle (1000ml) of aloe juice and Q is the total quantity, i.e., number of bottles, supplied in the market. There are two aloe juice manufacturers in Greece, Aloe Health and Aloe Wealth, operating under similar cost conditions. Each manufacturer's cost function is C(q) = 4qi, i =1,2, where q¡ is the manufacturer's individual quantity produced and Q = qı + q2. (a) Based on demand conditions every year, they decide, independently of each other, the quantity of aloe juice that will be supplied, letting the market determine the price per bottle. Find the equilibrium price and each firm's profit in this market. %3D (b) Consider that the above two manufacturers form a cartel, agreeing to fix their total quantity in such a way that the market maintains a collusive price. For simplicity, the eventual cartel directory will determine the target total-quantity and price pair, and each firm…

A large number of firms enter the Swedish market for the game Padel. For simplicity assume that they all act as price takers and let the cost function for each of them be given by C(q)=1000+0.4*q² where q is the number of customers served. a) In the long run free entry should drive profit to zero. At this point p=MC=ATC. Intuitively why is this the case?   b) The condition in c) implies that in a free entry equilibrium with firms that have the same cost function each firm's production will be given by the lowest point in the average total cost curve. How much does each firm produce in the free entry equilibrium? What is price in this equilibrium? (Hint: You can either differentiate the expression for average cost to determine its minimum or you can look for the minimum point using your graph in b).   c) Assume that overall demand is given by Q-1200-2*P. How many firms will there be in equilibrium?

Optimization Problem #5

R(x)= -0.956x^2 + 157x C(x)= 50.8x + 73.4 P(x)= R(x) - C(x) P(x)= -0.956x^2 + 106.2x - 73.4 What are the break-even points?  What is the profit at the break-even points? What number of widgets sold will yield positive profit? Determine the number of widgets that you should try to sell in order to maximize profit.  What is the maximum profit?

An industry has the following cost function: C(X, Y ) = 1500+20X +20Y . Market demands for the 2 goods are given by PX =80−X, and PY =140−2Y Suppose the government wished to use two part tariffs in these markets, and suppose further that two part tariffs are feasible. Imagine that there are 10 consumer in each market. Solve for a set of two part tariffs (one for each martket) that pay the firm zero profits in total, yet achieves efficiency.

Suppose the Boston to Philadelphia airline route is serviced by three airlines – US Airways (Firm A) and JetBlue (Firm B) and Continental (Firm C). The demand for airline travel between these two cities is Q = 150 – p. The cost function is C(Q) = 30Q. The cost function is the same for all three airlines. Assume that the three airlines are making investments in airline capacity. In other words, they are simultaneously choosing quantity. (Cournot Competition) Derive US Airways’ residual demand function given JetBlue’s output, qB, and Continental’s output, qC. What is the Marginal Revenue for US Airways? Derive US Airways reaction function Derive the market equilibrium quantity, Q*, price, p*, and Profit.

A pharmaceutical company is the only producer of a particular drug. It sells that drug in two countries, one rich and the other a development country. The inverse demand for the drug in the rich country is pr(qr) = 20 – 2qñ, and in the developing country it is pp(qp) 10- qp. The total cost of production is C(qR, qp) = (qr+qp)². What is the profit-maximizing quantity in the rich country, qR? (a) qR = 1 (b) qR = 3 (c) qR = 6 (d) qR 8 (e) qR 14

​Katie's Quilts is a small retailer of quilts and other bed linen products. Katie currently purchases quilts from a large producer for ​$100 each and sells them in her store at a price that does not change with the number of quilts that she sells. Katie is considering vertically integrating by making her own quilts. If the fixed cost of vertically integrating is ​$25,000 and she can produce quilts at Homework: Homework 7 (Lecture 6) Save Score: 0 of 1 pt 6 of 10 (8 complete) HW Score: 80%, 8 of 10 pts Text Question 4.2 Ques ​$50 per​ quilt, her total cost of producing​ quilts, q, herself is C=25,000+50q. How many quilts does Katie need to sell for vertical integration to be a profitable​ decision? For vertical integration to be​ profitable, Katie must sell at least nothing quilts. ​(Enter your response rounded to the nearest whole​ number.)

A firm is producing computer monitors. The market price per monitor is P1=$450. The cost function is given by C(Q) = 1,500 + 2.8Q2.  New information indicates that the new market price is P2=$130. Given this information, what are the optimal profits at the new price?