Let's consider a littering (or pollution) externality. Albert and Berta both have Cobb-Douglas utility uA=xA1xA2-2xB2 and...

Let's consider a littering (or pollution) externality. Albert and Berta both have Cobb-Douglas utility u_A=x_A¹x_A²-2x_B² and u_B=x_B¹x_B²-x_A². Good 2 is candy, where after each candy bar they absent-mindedly throw the rapper away in the middle of the beautiful street. Berta always forgets and so has a large externality on Albert, while Albert sometimes remembers so has a small externality on Berta. This effect is captured in their utility functions. If endowments are w_A=(4,4) and w_B=(10,2), find equilibrium price of good 2 (letting p₁=1) and simplify to one decimal point.

Expert Solution

NOTE: PLEASE GIVE UPVOTE IF YOU LIKE MY ANSWER.IT HELPS ME A LOT THANK YOU.

ekkarill92 answered 1 year ago

Person A and B both have Cobb-Douglas preferences, uA = (x1A)2/5 · (x2A)3/5 and uB =...

Person A and B both have Cobb-Douglas preferences, uA = (x1A)2/5 · (x2A)3/5 and uB = x1B · x2B . Their endowments are wA = (0, 2) and wB = (4, 0). Find their demand functions and use market clearing to derive equilibrium price for good two, p2 (set p1=1, and enter your answer as a simplified decimal).

Consider an economy with the following Cobb-Douglas production function:

Chapter 7, Labor Market Regulation (3 points):• Consider an economy with the following Cobb-Douglas production function:Y =k^1/3L^2/3The economy has 1,000 units of capital and a labor force of 1,000 workers.(a) Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock (Hint: Review Chapter 3.)(b) If the real wage can adjust to equilibrate labor supply and labor demand, what is the real wage? In this equilibrium, what are employment, output, and...

Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l...

Cobb-Douglas...again Consider the Cobb-Douglas production function function of the form, q(k, l) = k α l 1−α (a) Determine the relation between α and the marginal product of k and l. For what values of α is the marginal product for each input: (i) increasing, (ii) constant, and, (iii) decreasing. (b) Show that the marginal rate of technical substitution (MRTS) is equal to α 1 − α l k . For what values of α is MRTS decreasing in k?...

Consider the following Cobb-Douglas utility function: U(x,y) = 10 + 22xy, where x denotes the quantity...

Consider the following Cobb-Douglas utility function: U(x,y) = 10 + 22xy, where x denotes the quantity of apples and y denotes the quantity of pears. Income is m; the price for one apple is px and the price for one pear is py. b) By applying the Lagrangian method, derive the optimal demands for apples and pears. c) What is the impact of an increase in the price of apples on the optimal demand for pears? What is the impact...

Once again, consider the Cobb-Douglas production function ? = ?? ?? ? . a) This time,...

Once again, consider the Cobb-Douglas production function ? = ?? ?? ? . a) This time, derive the conditional input demands ? ∗ (?, ?, ?) and ? ∗ (?, ?, ?) and the associated long-run cost function ?(?, ?, ?) under the assumption that ? + ? = 1. b) Describe the average cost and marginal cost functions. How do they depend on output q and factor prices w and r? Explain. c) Continuing to assume ? + ?...

Consider the Cobb-Douglas production function ?=??^??^??^? where ?, ?, ?, ? are positive constants and ?+?+?<1....

Consider the Cobb-Douglas production function ?=??^??^??^? where ?, ?, ?, ? are positive constants and ?+?+?<1. Let ? be the amount of labor, ? the amount of capital, and ? be the amount of other materials used. Let the profit function be defined by ?=?−(??+??+??) where the costs of labor, capital, and other materials are, respectively, ?, ?, and ?. Determine whether second order conditions for profit maximization hold, when the profit function is defined by ?=?−(30?+20?+10?) with ?=5?^0.3?^0.4?^0.2.

Assume a Cobb-douglas utility function of 2 goods x and y given by U = x...

Assume a Cobb-douglas utility function of 2 goods x and y given by U = x 0.5y 0.5 and an initial income I of 100. Let initial price be px = 4 and py = 1. Now vary the price of x from 1 to 7 in steps of 1. So you have 7 prices for x. px = {1, 2, 3, 4, 5, 6, 7} For each of these px, py REMAINS the SAME at 1. In the excel...

Solve the optimization problem for a Cobb-Douglas utility function with three goods: U(x1, x2, x3) =...

Solve the optimization problem for a Cobb-Douglas utility function with three goods: U(x1, x2, x3) = x c 1x d 2x f 3 , where c, d, f > 0.

Substitution and Income Effect (Calculation) Suppose that the consumer's utility function is Cobb-Douglas U(x; y) =...

Substitution and Income Effect (Calculation) Suppose that the consumer's utility function is Cobb-Douglas U(x; y) = xy. She initially has $100 income and the prices that she faces are px = py = $2: a. Compute her demands for x and y. b. Now suppose that px decreases to $1 while py remains unchanged. Compute her new demands for x and y. c. What is the total (price) effect on the consumption of x? d. What is the substitution effect...

Which of the following utility functions is a Cobb-Douglas? Group of answer choices U(x,y) = ln(x)...

Which of the following utility functions is a Cobb-Douglas? Group of answer choices U(x,y) = ln(x) + 4y U(x,y) = 2x + 4y U(x,y) = ln(x) + 4ln(y) U(x,y) = min{x, 4y} None of the above

Question