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Explanation for part c)
As compared to part a) a change in probability distribution of prices, increases the optimal output, this is due to logarithmic utility function, which exhibits a risk averse individual.
such that even though expected price remains same, the optimal changes, due to concavity of the ln function.
3. Optimal Production under Uncertainty. Assume a firm owner is an expected utility maxmizer and has...
3. Optimal Production under Uncertainty. Assume a firm owner is an expected utility maxmizer and has NM utility function u(x) = ln(x) where x is final wealth. She has initial wealth of w, a constant unit cost of production, c = 5, and fixed costs of co= 2. She faces a maximum production capacity of y = 20. (a) The output price is uncertain: with probability p= .5 the price is 3 and otherwise the price is 9. What is...
2 Perfect substitutes Consider an agent with perfectly substitutable utility over R The agent has total wealth w>0 1. Suppose the agent faces linear prices and that P1くPi for every i > 1, what is the agent's optimal consumption bundle? What fraction of her wealth does she spend on each good? Show that the tangency conditions for optimality are satisfed for the bundle you've found. 2. Suppose instead she faces the same linear price for every good. Describe the set...
2. A competitive firm must decide on how much labor L to employ in production of output Y. Suppose that Y = 0 In(L) with probability T, and Y =0,In(L) with probability 1-2, where 0<x<1 and > > 0. Thus, the marginal product of labor is a random variable. Each unit of labor costs w and each unit of output is sold at the market price P. Both wage and output price are known to the firm. The firm has...
Assume that Sam has following utility function: U(x,y) = 2√x+y. Assume px = 1/5, py = 1 and her income I = 10. (e) Draw an optimal bundle which is the result of utility maximization under given budget set. (Hint: Assume interior solution). Define corresponding expenditure minimization problem (note the elements for expenditure minimization problem are (i) objective function, (ii) constraint, (iii) what to choose). (f)Describeaboutwhatthedualityproblemis. Definemarshalliandemandfuction andhicksiandemandfunction. (Hint: identifytheinputfactorsofthesefunctions.) (g) Consider a price increase for the good x from...
1- Suppose that a firm producing commodity with the following production function: Y = 20X,X2 Then, assume that the maximum amount the firm can spend on these two inputs is $100 and price of commodities are as follow: Xi = 4, X2 = 5 a. Use Lagrange Multiplier to determine the optimal production level at this firm. b. What is the meaning of shadow price? How you can interpret it using the solution of part a? 2- Assume the following...
An industry has 100 firms with identical production function. In the short run, each firm has fixed costs of $200. There are 2 variable factors in the short run and output is given by y=(min{x1,3x2})(1/2) . Suppose ω1=5, ω2=4. Obtain the industry supply curve in the short run.
Suppose that for a particular firm the only variable input into the production process is labor and that output equals zero when no workers are hired. In addition, suppose that when the firm hires 2 workers, the total cost of production is $2,000. When the firm hires a total of3 workers, the total cost of production is $2,500. In addition, assume that the variable cost per unit of labor is the same regardless of the number of units of labor...
1. If each competitive firm in an industry has the short run cost function TC=50+5q+q2, and MC=5+2q. The market price is $35. a. What is the profit maximizing output level for each firm? b. What are the profits? c. Now, suppose that fixed costs were $250 instead of $50, so the firm faces the short run cost function TC=250+5q+q2. How does this change affect the firm’s output decision and profits? Should the firm continue to operate in the short run?
2. Suppose the firm has the one variable production function Q=L?. Assume that the wage rate is w= 20 and that the firm has fixed costs of 10. Finally, assume that the firm is a price taker and the market price is 2. a) Show that this production function exhibits increasing returns to scale. Show that the marginal product of labor is increasing. Illustrate the production function. Is it convex, concave or neither? b) Find the variable and total cost...
A firm has a production function defined as y = 8L1/4K3/4. The firm faces costs of $20 wage, $60 rental rate of capital, $2 per unit produced, and a $42 fixed cost. Find the cost function, and average total cost, average variable cost, and marginal cost functions.