/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 6 Would a lump-sum profits tax aff... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Would a lump-sum profits tax affect the profit-maximizing quantity of output? How about a proportional tax on profits? How about a tax assessed on each unit of output? How about a tax on labor input?

Short Answer

Expert verified
Answer: The profit-maximizing quantity of output will not change for lump-sum profits tax or proportional tax on profits, as these taxes do not affect the firm's marginal cost or marginal revenue. For taxes assessed on each unit of output or taxes on labor input, the profit-maximizing quantity of output will change due to shifts in the marginal cost curve.

Step by step solution

01

1. Lump-sum profits tax

A lump-sum profits tax is a fixed amount of tax that is independent of the firm's level of output or profits. Since it doesn't change based on output, it will not affect the firm's marginal cost or marginal revenue. Therefore, it will not change the profit-maximizing quantity of output.
02

2. Proportional tax on profits

A proportional tax on profits is a tax that is a percentage of the firm's profits. In this case, the tax will affect the firm's overall profit, but it will not change the firm's marginal cost or marginal revenue. Hence, the profit-maximizing output level remains unchanged.
03

3. Tax assessed on each unit of output

A tax assessed on each unit of output is a per-unit tax. This tax will increase the marginal cost of production, shifting the marginal cost curve upward. As a result, the profit-maximizing output level will change. To determine the new profit-maximizing quantity of output, we need to find the new intersection point between the marginal cost curve (including the tax) and marginal revenue curve.
04

4. Tax on labor input

A tax on labor input will affect the firm's total cost of production, as it raises the cost of labor. This leads to a higher variable cost that will affect the firm's marginal cost. Consequently, the marginal cost curve will shift upward. Like with the tax assessed on each unit of output, we need to find the new intersection point between the marginal cost curve (including the tax) and marginal revenue curve to determine the new profit-maximizing quantity of output.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91Ó°ÊÓ!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

This problem has you work through some of the calculations associated with the numerical example in the Extensions. Refer to the Extensions for a discussion of the theory in the case of Fisher Body and General Motors (GM), who we imagine are deciding between remaining as separate firms or having GM acquire Fisher Body and thus become one (larger) firm. Let the total surplus that the units generate together be \(S\left(x_{F}, x_{G}\right)=x_{F}^{1 / 2}+a x_{G}^{1 / 2},\) where \(x_{F}\) and \(x_{G}\) are the investments undertaken by the managers of the two units before negotiating, and where a unit of investment costs \(\$ 1 .\) The parameter \(a\) measures the importance of GM's manager's investment. Show that, according to the property rights model worked out in the Extensions, it is efficient for GM to acquire Fisher Body if and only if GM's manager's investment is important enough, in particular, if \(a>\sqrt{3}\)

With a CES production function of the form \(q=\left(k^{\rho}+l^{\rho}\right)^{\gamma / \rho}\) a whole lot of algebra is needed to compute the profit function as \(\Pi(P, v, w)=K P^{1 /(1-\gamma)}\left(v^{1-\alpha}+w^{1-\sigma}\right)^{\gamma /(1-\sigma)(\gamma-1)},\) where \(\sigma=1 /(1-\rho)\) and \(K\) is a constant a. If you are a glutton for punishment (or if your instructor is), prove that the profit function takes this form. Perhaps the easiest way to do so is to start from the CES cost function in Example 10.2 b. Explain why this profit function provides a reasonable representation of a firm's behavior only for \(0<\gamma<1\) c. Explain the role of the elasticity of substitution ( \(\sigma\) ) in this profit function. What is the supply function in this case? How does \(\sigma\) determine the extent to which that function shifts when input prices change? e. Derive the input demand functions in this case. How are these functions affected by the size of \(\sigma ?\)

John's Lawn Mowing Service is a small business that acts as a price-taker (i.e., \(M R=P\) ). The prevailing market price of lawn mowing is \(\$ 20\) per acre. John's costs are given by total cost \(=0.1 q^{2}+10 q+50\) where \(q=\) the number of acres John chooses to cut a day. a. How many acres should John choose to cut to maximize profit? b. Calculate John's maximum daily profit. c. Graph these results, and label John's supply curve.

Young's theorem can be used in combination with the envelope results in this chapter to derive some useful results. a. Show that \(\partial l(P, v, w) / \partial v=\partial k(P, v, w) / \partial w\). Interpret this result using substitution and output effects. b. Use the result from part (a) to show how a unit tax on labor would be expected to affect capital input. c. Show that \(\partial q / \partial w=-\partial l / \partial P\). Interpret this result. d. Use the result from part (c) to discuss how a unit tax on labor input would affect quantity supplied.

The market for high-quality caviar is dependent on the weather. If the weather is good, there are many fancy parties and caviar sells for \(\$ 30\) per pound. In bad weather it sells for only \(\$ 20\) per pound. Caviar produced one weck will not keep until the next week. A small caviar producer has a cost function given by $$C=0.5 q^{2}+5 q+100$$ where \(q\) is weekly caviar production. Production decisions must be made before the weather (and the price of caviar) is known, but it is known that good weather and bad weather each occur with a probability of 0.5 a. How much caviar should this firm produce if it wishes to maximize the expected value of its profits? b. Suppose the owner of this firm has a utility function of the form \\[ \text { utility }=\sqrt{\pi} \\] where \(\pi\) is weekly profits. What is the expected utility associated with the output strategy defined in part (a)? c. Can this firm owner obtain a higher utility of profits by producing some output other than that specified in parts (a) and (b)? Explain. d. Suppose this firm could predict next week's price but could not influence that price. What strategy would maximize expected profits in this case? What would expected profits be?

See all solutions

Recommended explanations on Economics Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.