A firm’s technology is represented by f(x1,x2) = x1x2.. Derive the conditional input demands for input...

A firm’s technology is represented by f(x_1,x₂) = x₁x_2.. Derive the conditional input demands for input 1 and 2 and write down the total cost function.

Expert Solution

Rahul Sunny answered 2 years ago

Charlie’s utility function is U(x1, x2) = x1x2, where x1 and x2 are the Charlie’s consumption...

Charlie’s utility function is U(x1, x2) = x1x2, where x1 and x2 are the Charlie’s consumption of banana and apple, respectively. The price of apples is $1, the price of bananas is $2, and his income is $40. (a) Find out the Charlie’s optimal consumption bundle. (Note that Charlie’s utility function is Cobb-Douglas.) (b) If the price of apples now increases to $6 and the price of bananas stays constant, what would Charlie’s income have to be in order to...

1. Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's...

1. Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's consumption of banana and apple, respectively. The price of apples is $1, the price of bananas is $2, and his income is $40. (a) Find out the Amy's optimal consumption bundle. (Note that Amy's utility function is Cobb-Douglas.) (b) If the price of apples now increases to $6 and the price of bananas stays constant, what would Amy's income have to be in order...

Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's consumption...

Amy's utility function is U(x1 , x2) = x1x2, where x1 and x2 are Amy's consumption of banana and apple, respectively. The price of apples is $1, the price of bananas is $2, and his income is $40. (a) Find out the Amy's optimal consumption bundle. (Note that Amy's utility function is Cobb-Douglas.) (b) If the price of apples now increases to $6 and the price of bananas stays constant, what would Amy's income have to be in order to...

Bilal’s utility function is U(x1; x2) = x1x2 (assume x1 and x2 are normal goods). The...

Bilal’s utility function is U(x1; x2) = x1x2 (assume x1 and x2 are normal goods). The price of good 1 is P1, the price of good 2 is P2, and his income is $m a day. The price of good 1 suddenly falls. (a)Represent, using a clearly labelled diagram, the hicks substitution effect, the income effect and the total effect on the demand of good 1. (b) On a separate diagram, represent using a clearly labelled diagram, the slutsky substitution...

Linda sells an android app. Her firm’s production function is f (x1, x2) = x1 +...

Linda sells an android app. Her firm’s production function is f (x1, x2) = x1 + 2x2 where x1 is the amount of unskilled labor and x2 is the amount of skilled labor that she employs. Draw the isoquant at 20 units of output and another at 40 units of output. Does this production function exhibit increasing, decreasing, or constant return to scale? If Linda faces factor prices (w1, w2) = (1, 1), what is the cheapest way to produce...

Consider a firm using the following long-run technology: q=f(x1,x2)=1/3ln⁡(x1)+1/6ln⁡(x2) Where output and input prices are given...

Consider a firm using the following long-run technology: q=f(x1,x2)=1/3ln⁡(x1)+1/6ln⁡(x2) Where output and input prices are given by the non-negative constant vector (p,w1=2,w2=1). Which of the following is the correct expression for the firm's optimized profit function π(p)? 1/2(ln⁡(p/6)−1) 1/2p(ln⁡(p/6)−1) 1/2p(ln⁡(p/6)+1) 1/2(ln⁡(p/6)+1)

If the joint probability distribution of X1 and X2 is given by: f(X1, X2) = (X1*X2)/36...

If the joint probability distribution of X1 and X2 is given by: f(X1, X2) = (X1*X2)/36 for X1 = 1, 2, 3 and X2 = 1, 2, 3, find the joint probability distribution of X1*X2 and the joint probability distribution of X1/X2.

2.2.8. Suppose X1 and X2 have the joint pdf f(x1, x2) = " e−x1 e−x2 x1...

2.2.8. Suppose X1 and X2 have the joint pdf f(x1, x2) = " e−x1 e−x2 x1 > 0, x2 > 0 0 elsewhere . For constants w1 > 0 and w2 > 0, let W = w1X1 + w2X2. (a) Show that the pdf of W is fW (w) = " 1 w1− w2 (e−w/w1 − e−w/w2) w > 0 0 elsewhere . (b) Verify that fW (w) > 0 for w > 0. (c) Note that the pdf fW...

If a firm’s production is f(x1,x2) = 2x11/2 x21/4. If the price of factor 1 is...

If a firm’s production is f(x1,x2) = 2x11/2 x21/4. If the price of factor 1 is $5 and the price of factor 2 is $10, in what proportions should the firm use factors 1 and 2 if it wants to maximize profits? Please show all work clearly.

Amy has utility function u (x1, x2) = min { 2(x1)^2x2, x1*(x2)^2 }. Derive Amy's demand...

Amy has utility function u (x1, x2) = min { 2*(x1)^2*x2, x1*(x2)^2 }. Derive Amy's demand function for x1 and x2. For what values (if any) of m, p1, and p2 are the goods gross complements or gross substitutes of each other?

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