How many firms will be operating in the long-run equilibrium

Assignment Help Econometrics
Reference no: EM131235603


Problem Set

Problem 1 (9.2 in the book)

Suppose a firm's production function is given by f (k, l) = kl - 0.8k2 - 0.2l2.

Problem 1.1 Fixing capital at k = 10, graph the marginal physical product of labor (MPl), as a function of l. At what l does MPl = 0?

Problem 1.2 Re-draw the MPl graph for k = 20.

Problem 1.3 Does this production function exhibit increasing returns to scale (IRS), decreasing returns to scale (DRS), or constant returns to scale (CRS)?

Problem 2 (9.4)

A single firm produces crayons in two locations. Location 1 has a production function given by q1 = 10√l1 and location 2 has a production function given by q2 = 50√l2, where l1 and l2 are the quantity of labor used in each location.

Problem 2.1 Given a fixed amount of total labor l, what allocation of labor between the two loca- tions maximizes total output? In other words, maximize q1 + q2 subject to l1 + l2 = l.

Problem 2.2 Derive a single production function f (l) that describes the firm's total output for a given total amount of labor l, assuming it always divides the labor optimally between locations.

Problem 3 (10.2)

Two partners, Mr. Jones and Mr. Smith, are producing a product. Let J be the hours of labor input from Jones, and S be the hours of labor input from Smith. The production function is simply f (J, S) = √(J · S). Smith's wage rate is $3 per hour, while Jones' wage rate is $12/hour. Suppose Smith has contributed S = 900 hours, but now refused to work any more.

Problem 3.1 How many hours will Jones have to work to achieve q = 150, q = 300, and q = 450?

Problem 3.2 What is the marginal cost of the 150th unit of output? Of the 300th unit? Of the 450th unit?

Problem 4 (11.2)

A firm has total cost function C(q) = 0.25q2. It sells its products in two countries. Demand in country A is given by qA = 100 - 2PA, and demand in country B is qB = 100 - 4PB (where PA is the price in country A and PB is the price in country B). Thus, total demand for this firm is qA + qB.

Problem 4.1 What is the firm's profit maximizing quantities to sell in each location? What are the resulting prices (PA and PB)?

Problem 5 (11.4)

A firm produces umbrellas at a cost of C(q) = 0.5q2 + 5q + 100. It chooses its output quantity at the beginning of the week. If it turns out to be a rainy week, umbrellas sell at a price of $30. If it's a sunny week, they sell for $20. The probability of it being a rainy week is 0.5 (meaning, 50%), and the probability of a sunny week is 0.5.

Problem 5.1 Write out the firm's expected profit function, denoted Eπ(q). (This is simply 0.5 times profit if sunny plus 0.5 times profit if rainy.)

Problem 5.2 What quantity q maximizes expected profits?

Problem 5.3 Suppose the owner is risk averse, where his utility for profits is given by u(π(q)) = √π(q). If he produces the expected-profit-maximizing quantity from the last problem, what will be his expected utility?

Problem 5.4 Give the first order condition for maximizing the owner's expected utility. (You don't have to solve for the maximum, but as an interesting math exercise you can try if you want.)

Problem 5.5 If the firm knew the weather in the coming week with certainty, what would be its optimal production plan?

Problem 6 (11.6)

Take a standard profit-maximizing competitive firm with profit function π(q) = R(q) - C(q, w, v).

Problem 6.1 Derive a the standard FOC for profit maximization. (This is simple; don't overthink it.)

Problem 6.2 Would a lump-sum tax of T (that doesn't depend on q) affect the profit-maximizing quantity of output?

Problem 6.3 Consider a corporate income tax, where the firm has to pay a fraction t of its profit to the government. Thus, it pays tπ(q) and keeps (1 - t)π(q). Would this tax affect the profit- maximizing quantity of output?

Problem 6.4 Would a tax of t dollars per unit of output affect the profit-maximizing quantity of output?

Problem 6.5 Would a tax on the labor input quantity (such as social security) affect the profit- maximizing quantity of output?

Problem 7 (Chapter 12)

Consider the smartphone market. There are many potential entrants in the long run. Economic costs for each firm are given by

C(q) = q3 - 20q2 + 200q + 1000,

where the $1,000 fixed cost is an opportunity cost representing the accounting profit the firm would earn if they were building weapons guidance systems instead (which is the next-most profitable use of their production technology). Market demand for smartphones is given by

QD = 1060 - 5p.

Problem 7.1 Below what price will all firms shut-down in the short run?

Problem 7.2 What is the long-run price? (Notice: costs don't depend on number of firms here.) You will need to use a computer program (such as Wolfram Alpha at to help solve a third-order polynomial. Your solution can be rounded to the nearest whole number.

Problem 7.3 With the current demand function, what will be the long-run total quantity produced in the market?

Problem 7.4 How many firms will be operating in the long-run equilibrium?

Problem 7.5 What are firms' accounting profits in the long run?

Reference no: EM131235603

What is the equilibrium of this scheme

A worker will be paid $3,000 if she gets at least 40 answers right and $2,500 otherwise. For either type, an hour of studying is as bad as giving up $20 income. What is the

What is cross-price elasticity of demand in firm and charm

data collected in the imaginary economy of Perturbia reveals that when the price of cham increased by 20%, the quantity of cham sold decreased by 30%, and the quantity of fi

What are the present worth values of drinking bottled water

If the average person drinks 2 bottles of water per day or uses 5 gallons per day in getting that amount of water from the tap, what are the present worth values of drinking

Which type of policy result in a higher level of net exports

The government is considering using expansionary fiscal or monetary policy to help get the economy back to full employment. Which type of policy will result in a higher leve

Who will pay each for the commuter service

Jane quit her job at IBM where she earned $50,000 a year. She cashed in $50,000 in corporate bonds that earned 10% interest annually to buy a mini-bus. Jane has decided to b

Will this attempt necessarily lead to less saving

How will the fall in consumer confidence affect consumption, investment, and private saving? Will the attempt to save more necessarily lead to more saving? Will this attempt

What is the probability that attendance is greater

The attendance at baseball games at a certain stadium is normally distributed, with a mean of 44,000 and a standard deviation of 2500. For any given game: a) What is the pro

What is present value of lifetime resource available to abby

A. If the interest rate is 15% for the time period for both borrowing and saving, what is the maximum she can borrow against her future income B. What is the present value o


Write a Review

Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd