3. (10 points) Consider the utility function U(q;θ) = q1−θ−1, where 0 < θ < 1 is a utility parameter.
(a) Compute the marginal utility function, MU(q; θ) = U0(q; θ).
(b) Show that MU(q; θ) is decreasing.
Homework Answers
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3. (10 points) Consider the utility function U(q;θ) = q1−θ−1,
where 0 < θ < 1...
Please answer 6 and 7. Question 3 and 4 are referenced for the questions asked. Thank...
Please answer 6 and 7. Question 3 and 4 are referenced for the
questions asked. Thank you!
4. (20 points) Consider the demand function D(p;m) mP, where > 0 is consumers' average income. The supply consists of a monopoly, whose revenue from sales is given by R(p;mpD(p;m) (a) (5 points) Compute the elasticity function, E(p;m)-D'(p;m) b) (5 points) Find the value of p such that E(p; (c) (5 points) Compute the marginal revenue function, MR(p; m) R'(p; (d) (5 points)...
2 Utility Functions (2 Points) Consider the utility function u(c) where c denotes consumption of some...
2 Utility Functions (2 Points) Consider the utility function u(c) where c denotes consumption of some arbitrary good and ơ (the Greek letter "sigma") is known as the "curvature parameter" because its value governs how curved the utility function is and is treated as a constant. In the following, restrict your attention to the region c > 0 (because "negative consumption" is an ill-defined concept) a. (0.50 Points) Plot the utility function for σ 0, Does this utility function display...
Consider a utility function u(x,y) = Xayb, where 0くaく1 and 0 < b 〈 1. Also...
Consider a utility function u(x,y) = Xayb, where 0くaく1 and 0 < b 〈 1. Also assume that x,y>0 7.1. Derive the marginal utility of x and the marginal utility of y and state whether or not the assumption that more is better is satisfied for both goods. 7.2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x?What does it mean in words? 7.3. What is MRS.y? 7.4. Suppose a, b- Wht...
3. Consider the following utility function, u (1, 2) min br 0<a1 and b>0 (a) [15...
3. Consider the following utility function, u (1, 2) min br 0<a1 and b>0 (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? consumption goods normal goods? (b) [ 15 points Derive the Hicksian demand functions. Does the icksian demand increase with price?
1. Consider a utility function u(x1, x2) = x1 + (x2)^a where a > 0. (a)...
1. Consider a utility function u(x1, x2) = x1 + (x2)^a where a > 0. (a) Show that if a < 1, then preferences are convex. (b) Show that if a = 1, then preferences have perfect substitutes form. (c) Show that if a > 1, then preferences are concave. (d) For each case, explain how you would solve for the optimal bundle.
5, (20 points) Consider the following cost function: c(q:F)-F +109 + 뚤, where F > 0...
5, (20 points) Consider the following cost function: c(q:F)-F +109 + 뚤, where F > 0 represents the fixed cost F = c(QF). (a) (5 points) Compute the marginal cost function, MC(q) (q; F) b) (5 points) Show that the marginal cost function MC() is increasing. (c) (10 points) Recall the average cost function, AC(q; F) - Find (F the value of q (given F) at which AC(q; F) MC(4)
Consider my utility(U) function for Q: U 60Q-30? (a) At what Q do I maximize U?...
Consider my utility(U) function for Q: U 60Q-30? (a) At what Q do I maximize U? (b) Graph the U function and directly below it graph my demand function for Q. (c) At the market price of PM 32, compute my: Total Utility (TU); Expenses (outlays); and Consumer Surplus (CS)
Suppose that all agents in the economy have the following utility function U(c,l)=( c(1-θ) /(1- θ...
Suppose that all agents in the economy have the following utility function U(c,l)=( c(1-θ) /(1- θ ))-l where c is consumption, l is the supply of labor, and θ a fixed parameter. Suppose that individuals only have labor income, with an hourly wage of w and a tax rate of t. Thus, the budget constraint of the agent is w(1-t) l=c . We will assume here that θ = 0.5 and w = 1. The elasticity of the labor supply with...
Let X1, ..., Xn be a sample from a U(0, θ) distribution where θ > 0...
Let X1, ..., Xn be a sample from a U(0, θ) distribution where θ > 0 is a constant parameter. a) Density function of X(n) , the largest order statistic of X1,..., Xn. b) Mean and variance of X(n) . c) show Yn = sqrt(n)*(θ − X(n) ) converges to 0, in prob. d) What is the distribution of n(θ − X(n)).
1. For a utility function u(x) the measure of Absolute Risk Aversion is defined as Alca)...
1. For a utility function u(x) the measure of Absolute Risk Aversion is defined as Alca) = uchun Consider the utility function u(x)=1-e-axi where a is some positive parameter. Show that this utility function is for risk-averse consumer (concave utility/negative second derivative). Show that this utility function exhibits Constant Absolute Risk Aversion. Find the value of this constant.
Please answer 6 and 7. Question 3 and 4 are referenced for the
questions asked. Thank you!
4. (20 points) Consider the demand function D(p;m) mP, where > 0 is consumers' average income. The supply consists of a monopoly, whose revenue from sales is given by R(p;mpD(p;m) (a) (5 points) Compute the elasticity function, E(p;m)-D'(p;m) b) (5 points) Find the value of p such that E(p; (c) (5 points) Compute the marginal revenue function, MR(p; m) R'(p; (d) (5 points)...
2 Utility Functions (2 Points) Consider the utility function u(c) where c denotes consumption of some arbitrary good and ơ (the Greek letter "sigma") is known as the "curvature parameter" because its value governs how curved the utility function is and is treated as a constant. In the following, restrict your attention to the region c > 0 (because "negative consumption" is an ill-defined concept) a. (0.50 Points) Plot the utility function for σ 0, Does this utility function display...
Consider a utility function u(x,y) = Xayb, where 0くaく1 and 0 < b 〈 1. Also assume that x,y>0 7.1. Derive the marginal utility of x and the marginal utility of y and state whether or not the assumption that more is better is satisfied for both goods. 7.2. Does the marginal utility of x diminish, remain constant, or increase as the consumer buys more x?What does it mean in words? 7.3. What is MRS.y? 7.4. Suppose a, b- Wht...
3. Consider the following utility function, u (1, 2) min br 0<a1 and b>0 (a) [15 points] Derive the Marshallian demand functions. (Explain your derivation in details.) Does the Marshallian demand increase with price? consumption goods normal goods? (b) [ 15 points Derive the Hicksian demand functions. Does the icksian demand increase with price?
5, (20 points) Consider the following cost function: c(q:F)-F +109 + 뚤, where F > 0 represents the fixed cost F = c(QF). (a) (5 points) Compute the marginal cost function, MC(q) (q; F) b) (5 points) Show that the marginal cost function MC() is increasing. (c) (10 points) Recall the average cost function, AC(q; F) - Find (F the value of q (given F) at which AC(q; F) MC(4)
Consider my utility(U) function for Q: U 60Q-30? (a) At what Q do I maximize U? (b) Graph the U function and directly below it graph my demand function for Q. (c) At the market price of PM 32, compute my: Total Utility (TU); Expenses (outlays); and Consumer Surplus (CS)
1. For a utility function u(x) the measure of Absolute Risk Aversion is defined as Alca) = uchun Consider the utility function u(x)=1-e-axi where a is some positive parameter. Show that this utility function is for risk-averse consumer (concave utility/negative second derivative). Show that this utility function exhibits Constant Absolute Risk Aversion. Find the value of this constant.
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