Reference no: EM131392661
In this exercise, you will explore the equilibrium of a market in which we know the cost function of the firms, as well as the demand function of consumers. You will first analyze the short-run equilibrium, and then the long-run equilibrium. Each firm in the industry has the same technology with cost function c(y)=k^2 +2y +y^2 where y is the quantity produced and k is some positive fixed cost. You should think of this cost function as coming out of a standard cost minimization problem with respect to the inputs.
(a) Derive the average cost c(y)/y, the average variable cost and the marginal cost c'(y) for y > 0. Graph all these cost curves in an appropriately labeled diagram.
(b) Draw the supply function in the graph, and write down the equation that represents it, y(p).
(c) Derive the aggregate supply function Y^S(p) by adding up the supply y(p) over the J firms that are in the market. Write down the expression for Y^S(p)
(d) Consider now the demand side of the market. For simplicity, assume a linear demand function: Y ^D(p) = A-Bp, where A and B are positive numbers, and Y^D represents the total quantity demanded in the industry. Assume that this comes from aggregation of the individual demand functions derived from maximization. Find the short-run equilibrium price p by equating Y^D and Y^S. You can assume that A and B are such that we are on the increasing part of the supply function, i.e. quantity produced is strictly positive. Find the short-run equilibrium industry production Y^*=Y^D(p^*) = Y^S(p^*).
(e) Under what conditions for A,B,J and k the firms will indeed produce a positive quantity of output? We maintain this assumption for the next items.
(f) In the short-run, what happens to Y^* and p^* as the fixed cost k increases? What is the intuition?
(g) Consider now the long-run equilibrium, in which firms are allowed to enter the market. Solve for the number of firms J^* that will enter into the market.
(h) How does the number of firms J^* depend on k, A and B?
(i) What is the equation of the long-run supply curve? Is it horizontal, increasing or decreasing?
|
What will be the equilibrium level of labor
: Suppose that there are 100 identical firms, each with the following technology: f = K^1/4 L^1/2. Suppose also that in the short run K =1,with r = 1, and P = 4. For the short run: Calculate the MPL and each firm's demand for labor. Calculate each firm..
|
|
Calculate the average molecular speed
: A process temperature is found to change by 33.4°F. Calculate the change in °C. A change in temperature does not involve a scale shift.
|
|
Find the resistance
: Temperature is to be controlled in the range 350°C to 550°C. What is this expressed in °F?- find the resistance at 25°F?
|
|
Budget hearing process
: Why is it important for government agency's budget hearing process and governing body's efforts to obtain input from key stakeholders and the public before making final decisions?
|
|
Explore the equilibrium of market
: In this exercise, you will explore the equilibrium of a market in which we know the cost function of the firms, as well as the demand function of consumers. You will first analyze the short-run equilibrium, and then the long-run equilibrium. Draw the..
|
|
What is the audit importance of each of the given exceptions
: What is the audit importance of each of these exceptions? What follow-up procedures would you use to determine more about the nature of each exception?
|
|
Develop a compelling presentation to the operations manager
: Both the operations manager and the warehouse manager have been impressed with your argument in making a case of supply chain management and quality management within the company. The operations manager in your department wants you to conduct a fo..
|
|
Calculate an exact dynamic model
: Calculate the error in the mass moment of inertia of the approximate model as a percentage of the original mass moment of inertia.
|
|
Using the normative criteria of good tax structure
: In 1991, Congress imposed a 10 percent excise tax on the portion of the retail price of certain items that exceeded the following: $35,000 for automobiles, $150,000 for yachts, and $20,000 for jewelry and furs. Evaluate theses taxes using the normati..
|