Question

In: Economics

. A firm produces two goods: widgets (X) and woozles (Y). Its profit function is given...

. A firm produces two goods: widgets (X) and woozles (Y). Its profit function is given by:  = 55X – 2X2 – XY – 3Y2 + 100Y and its maximum output capacity is X + Y = 17. (a) Use the Lagrangian method to calculate the output mix the firm should produce. (b) Estimate the effects on profits if output capacity is expanded by 1 unit. (c) You are hired by the firm to evaluate a proposal from its Engineering Department that the firm’s output capacity be expanded to 33. Do you agree with the proposal? If not, what output capacity would you recommend?

Solutions

Expert Solution

Rahul Sunny answered 2 years ago
Next > < Previous

Related Solutions

7. a) A firm producing two goods (X and Y) has the following profit (?) function:...
7. a) A firm producing two goods (X and Y) has the following profit (?) function: Profit: ? =80X-2X2 - XY-3Y2 +100Y Maximum Capacity: X+Y=12 What are the values of X and why that maximizes profits subject to the firm’s maximum capacity? b) Consider the following utility function for a consumer, who consumes goods X and Y whose prices are $8 and $12respectively. Utility function: U=XY+3X+Y If the consumer’s money income (budget is $112), what are the utility maximizing values...
A consumes two goods, x and y. A ’s utility function is given by u(x, y)...
A consumes two goods, x and y. A ’s utility function is given by u(x, y) = x 1/2y 1/2 The price of x is p and the price of y is 1. A has an income of M. (a) Derive A ’s demand functions for x and y. (b) Suppose M = 72 and p falls from 9 to 4. Calculate the income and substitution effects of the price change. (c) Calculate the compensating variation of the price change....
4. For the following total profit function of a firm, where X and Y are two...
4. For the following total profit function of a firm, where X and Y are two goods sold by the firm: Profit = 226X – 5X2 –XY -2.5Y2 +150Y -210 (a) Determine the levels of output of both goods at which the firm maximizes total profit. (b) Calculate the profit. c) Do problem 4 again, but this time with a constraint of X + Y =40. a. To work problem 5 use the constraint equation to find an equation for...
13. Pip consumes two goods, x and y. Pip’s utility function is given by u(x, y)...
13. Pip consumes two goods, x and y. Pip’s utility function is given by u(x, y) = x 1/2y 1/2 The price of x is p and the price of y is 1. Pip has an income of M. (a) Derive Pip’s demand functions for x and y. [5 marks] (b) Suppose M = 72 and p falls from 9 to 4. Calculate the income and substitution effects of the price change. [5 marks] (c) Calculate the compensating variation of...
Leon consumes two goods, X and Y. His utility function is given by U(X,Y) = 56XY....
Leon consumes two goods, X and Y. His utility function is given by U(X,Y) = 56XY. The price of X is $14 a unit; the price of Y is $8 a unit; and Leon has $672 to spend on X and Y. a. Provide the equation for Leon’s budget line. (Your answer for the budget line should be in the form Y = a – bX, with specific numerical values given for a and b.) b. Provide the numerical value...
Ron consumes two goods, X and Y. His utility function is given by U(X,Y) = 33XY....
Ron consumes two goods, X and Y. His utility function is given by U(X,Y) = 33XY. The price of X is $11 a unit; the price of Y is $4 a unit; and Ron has $352 to spend on X and Y. a. Provide the equation for Ron’s budget line. (Your answer for the budget line should be in the form Y = a – bX, with specific numerical values given for a and b.) b. Provide the numerical value...
Suppose that there are two goods, X and Y. The utility function is ?(?, ?) =...
Suppose that there are two goods, X and Y. The utility function is ?(?, ?) = 5?2 ?. The price of Y is $2 per unit, and the price of X is P. Income is $2,400. A.) Derive the demand curve and state the law of demand in relation to your product or service. B.) ? = 800 − 10?0.5 . Calculate elasticity of demand when Q=100, Is the good elastic? C.) ? = 800 − 10?0.5 − 0.5?. Calculate...
Suppose that there are two goods, X and Y. The utility function is ?(?, ?) =...
Suppose that there are two goods, X and Y. The utility function is ?(?, ?) = 5?2 ?. The price of Y is $2 per unit, and the price of X is P. Income is $2,400. A.) Derive the demand curve and state the law of demand in relation to your product or service. B.) ? = 800 − 10?0.5 . Calculate elasticity of demand when Q=100, Is the good elastic? C.) ? = 800 − 10?0.5 − 0.5?. Calculate...
A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x)...
A consumer purchases two goods, x and y and has utility function U(x; y) = ln(x) + 3y. For this utility function MUx =1/x and MUy = 3. The price of x is px = 4 and the price of y is py = 2. The consumer has M units of income to spend on the two goods and wishes to maximize utility, given the budget. Draw the budget line for this consumer when M=50 and the budget line when...
For two goods x and y, the individual’s preferences are measured by the utility function ?(?,?)=...
For two goods x and y, the individual’s preferences are measured by the utility function ?(?,?)= ?0.5?0.5, the price of good y is $10, income equals $100, and the price of good x increase from $5 to $10. Draw the price consumption curve for x and y and compute the slop of the price consumption curve. Show your calculation step by step.
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT