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4. For the total cost function TC(y) = 3y2 + 7y + 24, y...
2y (9 points) Given the initial value problem y' => y (xo) = yo. Use the...
2y (9 points) Given the initial value problem y' => y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where xo + 0, b) no solution exists if y (0) = yo # 0, and c) an infinite number of solutions exist if y (0) = 0.
The cost of producing y is c(y) 5 +7y. Demand for y is given by 0...
The cost of producing y is c(y) 5 +7y. Demand for y is given by 0 if p > 10 y(p) - -10 if p E (8,10 20 if p E [0,8 a) What are the monopoly price, quantity, profit, and total surplus? b) Suppose the monopoly can price discriminate between the two following sub-markets: 0 if p>10 0 if p >10 7 ifpE (8,10] 10 if p e [0, 8] Y2(p) 3 if pE (8,10 if p E [0,8]...
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)
A monopolist has demand function Q(P)-ap-ε (with lel > 1) and total cost function TC(Q)-cQ (a)...
A monopolist has demand function Q(P)-ap-ε (with lel > 1) and total cost function TC(Q)-cQ (a) Show that the demand elasticity is -e (b) Find the firm's optimal price as a function of c and ε. (c) What happens to price as є ічі.e. є approaches 1 from the right side of the number line)? (d) What is the monopoly's profit-maximizing output?
Exponential(). That is Y has a density function of the form 7. Let Y Ay f(y)...
Exponential(). That is Y has a density function of the form 7. Let Y Ay f(y) = de"^9,y> 0 where 0. Show that: (a) If a >0 and b > 0, then P(Y > a + b|Y > a) = P(Y > b) (b) E(Y) 1/A
#8. (2 points +0.5 bonus) Suppose a cost function takes the form: TC = 2 +...
#8. (2 points +0.5 bonus) Suppose a cost function takes the form: TC = 2 + 2q - 3q2 + #8.a> (2 points) Derive fixed cost FC, marginal cost MC, variable cost VC, average total cost ATC, and average variable cost AVC. #8.b> (Bonus 0.5 point) Draw MC, ATC, and AVC together. You can use Wolfram Alpha to help you. We have some sample syntax in Slides #8 and #9 on Canvas. Alternatively, you can draw these by hand. To...
Let X and Y b Var(Y) (1) If a, b,c and d are fixed real numbers,...
Let X and Y b Var(Y) (1) If a, b,c and d are fixed real numbers, = E(X), μγ E (Y),咳= Var(X) and e ranclom variables. with y a) show Cov(aX +b, cY +d)- ac Cov(X,Y) (b) show Corr(aX + b, cY + d)-PXY for a > 0 and c > 0.
Question 2: Supply Suppose that Jessica faces the following total cost function: C(y) = 2y2 +...
Question 2: Supply Suppose that Jessica faces the following total cost function: C(y) = 2y2 + y + 200 Note that 200 denotes the fixed cost component. Use this information in answering this p submission question. (a) Find the Marginal cost function, Average Cost function, Average Variable cost functi Average fixed cost function. Once you obtain these, sketch them on the grid below. AC, AVC, AFC, MC (b) Derive the short run supply function for Jessica. Suppose p = 61....
Any help would be appreciated! Problem 4 Let (X, Y)~ N and Z = X1(XY >...
Any help would be appreciated!
Problem 4 Let (X, Y)~ N and Z = X1(XY > 0}-X1(XY < 0} (1) Find the distribution of Z (2) Show that the joint distribution of Y and Z is not bivariate normal.
> The graph shown is of the function y 1 1 4 1 1 1 1...
> The graph shown is of the function y 1 1 4 1 1 1 1 2 TT TO + 34 -2 T ! 1 -4 1. y = cotx b. y = csc X c. y = tan x d. y = sec x
2y (9 points) Given the initial value problem y' => y (xo) = yo. Use the existence and uniqueness theorem to show that a) a unique solution exists on any interval where xo + 0, b) no solution exists if y (0) = yo # 0, and c) an infinite number of solutions exist if y (0) = 0.
The cost of producing y is c(y) 5 +7y. Demand for y is given by 0 if p > 10 y(p) - -10 if p E (8,10 20 if p E [0,8 a) What are the monopoly price, quantity, profit, and total surplus? b) Suppose the monopoly can price discriminate between the two following sub-markets: 0 if p>10 0 if p >10 7 ifpE (8,10] 10 if p e [0, 8] Y2(p) 3 if pE (8,10 if p E [0,8]...
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)
A monopolist has demand function Q(P)-ap-ε (with lel > 1) and total cost function TC(Q)-cQ (a) Show that the demand elasticity is -e (b) Find the firm's optimal price as a function of c and ε. (c) What happens to price as є ічі.e. є approaches 1 from the right side of the number line)? (d) What is the monopoly's profit-maximizing output?
Exponential(). That is Y has a density function of the form 7. Let Y Ay f(y) = de"^9,y> 0 where 0. Show that: (a) If a >0 and b > 0, then P(Y > a + b|Y > a) = P(Y > b) (b) E(Y) 1/A
#8. (2 points +0.5 bonus) Suppose a cost function takes the form: TC = 2 + 2q - 3q2 + #8.a> (2 points) Derive fixed cost FC, marginal cost MC, variable cost VC, average total cost ATC, and average variable cost AVC. #8.b> (Bonus 0.5 point) Draw MC, ATC, and AVC together. You can use Wolfram Alpha to help you. We have some sample syntax in Slides #8 and #9 on Canvas. Alternatively, you can draw these by hand. To...
Let X and Y b Var(Y) (1) If a, b,c and d are fixed real numbers, = E(X), μγ E (Y),咳= Var(X) and e ranclom variables. with y a) show Cov(aX +b, cY +d)- ac Cov(X,Y) (b) show Corr(aX + b, cY + d)-PXY for a > 0 and c > 0.
Question 2: Supply Suppose that Jessica faces the following total cost function: C(y) = 2y2 + y + 200 Note that 200 denotes the fixed cost component. Use this information in answering this p submission question. (a) Find the Marginal cost function, Average Cost function, Average Variable cost functi Average fixed cost function. Once you obtain these, sketch them on the grid below. AC, AVC, AFC, MC (b) Derive the short run supply function for Jessica. Suppose p = 61....
Any help would be appreciated!
Problem 4 Let (X, Y)~ N and Z = X1(XY > 0}-X1(XY < 0} (1) Find the distribution of Z (2) Show that the joint distribution of Y and Z is not bivariate normal.
> The graph shown is of the function y 1 1 4 1 1 1 1 2 TT TO + 34 -2 T ! 1 -4 1. y = cotx b. y = csc X c. y = tan x d. y = sec x
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