(A) A consumer's utility function is given by U(x, y) = xy P = 2, and...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
(A) A consumer's utility function is given by U(x, y) = xy P = 2, and Income M = 100. y 1/21/2 where P = 1, x - What quantity of good x can be purchased if the consumer allocates their entire income to good x? Good y? Find the optimal consumption bundle (x, y) and corresponding optimal utility level U What is meant by the rationality condition in consumer utility-maximization? (B) Now suppose P = 2with P = 2, and Income M = 100. y What quantity of good x can be purchased if the consumer allocates their entire income to good? Good y? Find the new optimal consumption bundle (x,y") and corresponding optimal utility level U What additional income (i.e. compensating variation) is needed by the consumer to reach the previous utility level U given these new prices? For the results in part A and part B, illustrate the budget constraint, indifference curve, and optimal bundles on an appropriately-labeled diagram Question 2 A firm's production function is given by f(K, L) = K¹/32/3. Assume that the factors of production of the firm are fully employed. The cost of capital (rent) is 10 and cost of labor (wages) is 5. The firm has an available budget of 100. - What is the factor mix (i.e. optimal bundle) of capital and labor used by the firm to maximize profits? Calculate the slope of the isoquant at a point Sketch an appropriately-labeled diagram showing the firm's budget constraint, isoquant, and factor mix What is the significance of the marginal rate of technical substitution (MRTS)? Why is the MRTS negative? Is this firm exhibiting decreasing returns to scale, constant returns to scale, or increasing returns to scale? Question 3 Consider a perfectly competitive market with a demand function given by Q = 100 - 2P, where Q represents the total quantity and Pis the market price. The firm's marginal cost is MC = 10. Calculate the equilibrium price P and quantity Q in this competitive market What decision rule will the firm use to decide output? Can a firm in a competitive market charge more than the market price for a good? Explain intuitively what happens to the firm's profits if they were to do so. Provide an example of a perfectly competitive market and a good (A) A consumer's utility function is given by U(x, y) = xy P = 2, and Income M = 100. y 1/21/2 where P = 1, x - What quantity of good x can be purchased if the consumer allocates their entire income to good x? Good y? Find the optimal consumption bundle (x, y) and corresponding optimal utility level U What is meant by the rationality condition in consumer utility-maximization? (B) Now suppose P = 2with P = 2, and Income M = 100. y What quantity of good x can be purchased if the consumer allocates their entire income to good? Good y? Find the new optimal consumption bundle (x,y") and corresponding optimal utility level U What additional income (i.e. compensating variation) is needed by the consumer to reach the previous utility level U given these new prices? For the results in part A and part B, illustrate the budget constraint, indifference curve, and optimal bundles on an appropriately-labeled diagram Question 2 A firm's production function is given by f(K, L) = K¹/32/3. Assume that the factors of production of the firm are fully employed. The cost of capital (rent) is 10 and cost of labor (wages) is 5. The firm has an available budget of 100. - What is the factor mix (i.e. optimal bundle) of capital and labor used by the firm to maximize profits? Calculate the slope of the isoquant at a point Sketch an appropriately-labeled diagram showing the firm's budget constraint, isoquant, and factor mix What is the significance of the marginal rate of technical substitution (MRTS)? Why is the MRTS negative? Is this firm exhibiting decreasing returns to scale, constant returns to scale, or increasing returns to scale? Question 3 Consider a perfectly competitive market with a demand function given by Q = 100 - 2P, where Q represents the total quantity and Pis the market price. The firm's marginal cost is MC = 10. Calculate the equilibrium price P and quantity Q in this competitive market What decision rule will the firm use to decide output? Can a firm in a competitive market charge more than the market price for a good? Explain intuitively what happens to the firm's profits if they were to do so. Provide an example of a perfectly competitive market and a good
Expert Answer:
Related Book For
Vector Mechanics for Engineers Statics and Dynamics
ISBN: 978-0073212227
8th Edition
Authors: Ferdinand Beer, E. Russell Johnston, Jr., Elliot Eisenberg, William Clausen, David Mazurek, Phillip Cornwell
Posted Date:
Students also viewed these mathematics questions
-
The FTC instituted proceedings against the Soft Drink Bottling Company, alleging violations of laws prohibiting unfair methods of competition. The complaint against Soft Drink Bottling challenged the...
-
A consumption matrix C and a demand vector d are given. In each case, find a feasible production vector x that satisfies equation (2). 0.5 0.2 0.1 3 0.2 , d = C = | 0 0.4 2 0.5
-
A consumption matrix C and a demand vector d are given. In each case, find a feasible production vector x that satisfies equation (2). 0.1 0.4 1.1 0.1 1.1 C = | 0 0.2 0.2 , d 3.5 0.3 0.2 0.3 2.0
-
Find the laurents series f(z)= 1/(z-1)(z-2) (i) |z| <1 (ii) 1 2
-
In Exercises 15, use the frequency distribution to find the (a) Class width, (b) Class midpoints, (c) Class boundaries. Cleveland, OH High Temperatures (F) Class Frequency, f 20 30. 19 31 41 . 43...
-
Which account is debited by the IFI when the amount of shareholders Zakah exceeds their distributable profits? a. Cash/Bank b. Payables c. Receivables d. Zakah expense
-
What are the pressures on managers to report biased ecological impact information to stakeholders? How might these be alleviated?
-
On January 1, 2013, Plains Power Company overhauled four turbine engines that generate power for customers. The overhaul resulted in a slight increase in the capacity of the engines to produce power....
-
11-33 Special Order Green Grow Inc. (GGI) manufactures lawn fertilizer. Because of the product's very high quality, GGI often receives special orders from agricultural research groups. For each type...
-
Nancy Nanny opened a child-care facility on January 1, Year 1. Use the Chart of Accounts below to complete the requirements on the following pages for Nancy Nanny Child Care. NANCY NANNY CHILD...
-
The financial report of a listed corporation in Hong Kong shows the following accounting policies in respect to the valuation of its asset items in the financial accounts: Goodwill Goodwill on...
-
Shown below is D. Diesel Company's adjusted trial balance at the end of its annual accounting period (December 31, 2022). Account Debit Credit Cash $15,000 Accounts Receivable 15,000 Office Supplies...
-
6. A jellyfish is floating in a water-filled aquarium 1.00 m behind a flat plane of glass 6.00 cm thick and having an index of refraction of 1.50. a. Where is the image of the jellyfish located? b....
-
Parex Ltd., a listed Canadian company that follows IFRS, acquired 90% of outstanding shares of sheet information and other information are as below: balance Cash and receivables Parex Carrying value...
-
Compute each of the following integrals. (a) (4x+3)dx 8t+2 (b) f =dt 2t2+t (c) fecos(t) sin(t)dt (d) fu(u3+5) du (e) fx 1xdx - (f) sin(2x + x) + x sin(2x + x)dx (g) fo x+1dx
-
Given the picture to the right: a) What is the force exerted by the women in each hand in this push-up position? b) If at the top of her push up position her centre of mass is 0.240 m off the ground,...
-
please round to 2 decimal places A solution is prepared at 25 C that is initially 0.38 Afin methylamine (CH, NH,), a weak base with K, -4.4 10 and 0.019 Min methylammonium bromide (CH, NH, Br)....
-
The polar coordinates of a point are given. Find the rectangular coordinates of the point. (-1, - /3)
-
If 1 cup of cream having a density of 1005 kg/m 3 is turned into 3 cups of whipped cream, determine the specific gravity and specific weight of the whipped cream.
-
The diameter of the eye of a stationary hurricane is 32 km and the maximum wind speed is 160 km/h at the eye wall, r = 16 km. Assuming that the wind speed is constant for constant r and decreases...
-
A 1.5-kg block A rests on a 1.5-kg block B and is attached to a spring of constant 180 N/m. The coefficients of friction between the two blocks are 0.35 s = and 0.30 k = and the coefficients of...
-
Show that for an ideal gas, \(\left(\frac{\partial E}{\partial V} ight)_{T}=0\), and for a van der Waals gas, \(\left(\frac{\partial E}{\partial V} ight)_{T}=\frac{a n^{2}}{V^{2}}\).
-
Explain some important methods for the estimation of the fugacity coefficient of a pure substance.
-
Estimate the residual entropy, enthalpy and internal energy at 298 K and 10 bar for nitrogen obeying the van der Waals equation of state, given that T c = 126.2 K and P c = 34.0 bar.
Study smarter with the SolutionInn App