Question
In: Economics
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 of X and Y?
Solutions
Rahul Sunny answered 2 years agoRelated Solutions
. 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...
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...
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...
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 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....
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.
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...
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