advanced microeconomics, uncertainty Question:Suppose that a risk neutral competitive firm has to make its output (y) decisionbefore it observes the uncertain output price, p. Assume that p is a random variablewhose mean is E(p) = 2 and whose variance is Var(p) = 4. Assume that p is alwaysgreater than 1 (this ensures that there is always a strictly positive solution for y,regardless of what p is). Let the cost function be given by C = y + y². How muchis the firm willing to pay for information about p?Use below provided example case to solve above question8.2 Example of Calculation of Value of Information. Consider the choice of output. Let the cost function be C = C(y).• Case 1: choose output before the price is known.• Case 2: choose output after the price is known.• Let C = y².• Case 1:• Case 2:Note: SOC OK.. Calculate profits:• Thus, expected profits are:Note: the second-order condition (SOC) is OK.• Calculate expected profits:• But, remember that:EVPI = E{max(py – C(y)}YThus, using this, we get:EVPI = E{max(py – y²)} – max E(py - y²)YYmax E(py - y²)Ymax uy —YπT (μ)=max py - y²Yπ(p)ܝ ܕ | ܠvar (p)E(p²)==μYр =Y ==P/²/2TIT-max E(py - C(y))Yp²==FOC2yNIE=22E[π(p)] = = E(p²)FOC2y=E(p²) - μ²var(p) + µ²11E[ñ(p)] − ñ(µ) = ½{var(p) + µ²³] — — µ² = ²/var(p) > 0• This is the amount of money the firm is willing to pay for information on p.● It is willing to pay this, although it is risk-neutral.• What about the case of a risk-averse firm?(80)(81)(82)(83)(84)(85)(86)(87)(88)(89)(90)(91)(92)(93)(94)

Cost function : C(y) = y + y2 There are two cases to be considered to find the maximum price that…

Suppose that a risk neutral competitive firm has to make its output (y) decision before it observes the uncertain output price, p. Assume that p is a random variable whose mean is E(p) = 2 and whose variance is Var(p) = 4. Assume that p is always greater than 1 (this ensures that there is always a strictly positive solution for y, regardless of what p is). Let the cost function be given by C = y + y². How much is the firm willing to pay for information about p?

Suppose that a risk neutral competitive firm has to make its output (y) decision before it observes the uncertain output price, p. Assume that p is a random variable whose mean is E(p) = 2 and whose variance is Var(p) = 4. Assume that p is always greater than 1 (this ensures that there is always a strictly positive solution for y, regardless of what p is). Let the cost function be given by C = y + y². How much is the firm willing to pay for information about p?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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