In: Economics

consider a representative consumer with the utility function ?(?, ?) = ?? + ? and the budget constraint ??? + ??? ≤ ?. Assume throughout that all prices and quantities are positive and infinitely divisible.

Assume initially that ?? = ?? = 1 and ? = 10. Derive the consumers equilibrium cross-price elasticity between goods ? and ? and evaluate the value of this elasticity at the initial parameter values given .

Consider a representative consumer with the utility function
?(?, ?) = ?? + ? and the budget constraint ??? + ??? ≤ ?. Assume
throughout that all prices and quantities are positive and
infinitely divisible.
Find the equation of an arbitrary indifference curve for this
utility function (evaluated at ̅ utility level ?).
Sketch of graph of this indifference curve (be sure to justify
its shape and to derive/demark any points of intersection with the
axes).

Consider a representative consumer with the utility function
?(?, ?) = ?? + ? and the budget constraint ??? + ??? ≤ ?.
Assume throughout that all prices and quantities are positive
and infinitely divisible.
1.a.Derive the consumer’s indirect utility function ?(∙).
b.Then, derive the consumer’s expenditure function, e(∙),
directly from ?(∙).
c.Finally, derive the consumer’s Hicksian/compensated demand
functions (denoted ? and ? , respectively) from e(∙). ??
2.Assume initially that ?? = ?? = 1 and ? = 10....

Following the conventional notation, consider a representative
consumer with the utility function
?(?,?)=??+?
and the budget constraint ???+???≤?. Assume throughout that all
prices and quantities are positive and infinitely divisible.
Derive the consumer’s indirect utility function ?(∙). Assuming
initially that ??=??=1 and ?=10, calculate the change in the
consumer’s utility if the price of good ? doubles, all else
equal.

Consider an economy where the representative consumer has a
utility function u (C; L) over consumption C and leisure L. Assume
preferences satisfy the standard properties we saw in class. The
consumer has an endowment of H units of time that they allocate to
leisure or labor. The consumer also receives dividends, D, from the
representative Örm. The representative consumer provides labor, Ns,
at wage rate w, and receives dividends D, from the representative
Örm. The representative Örm has a...

Tax on labor income - Consider a one-period economy where the
representative consumer has a utility function u(C;L) over
consumption C and leisure L. Assume preferences satisfy the
standard properties we assumed in class. The consumer has an
endowment of one unit of time. She earns the wage w per unit of
labor supplied to the market and has wealth A which yields an
interest rate r, so her income is partly coming from labor, partly
from capital.
Suppose that...

Consider the utility function of a consumer who obtains utility
from consuming only two goods, ?1 and ?2 , in fixed proportions.
Specifically, the utility of the consumer requires the consumption
of two units of ?2 for each unit of ?1.
i. Report the mathematical expression of the utility function of
the consumer.
ii. Provide a diagram of the corresponding indifference
curves.
iii. Provide at least one example and economic intuition.
Suppose that the consumer has available income equal to...

Consider the utility function of a consumer who obtains utility
from consuming only two goods, ?1 and ?2 , in fixed proportions.
Specifically, the utility of the consumer requires the consumption
of two units of ?2 for each unit of ?1. A.
i. Report the mathematical expression of the utility function of
the consumer.
ii. Provide a diagram of the corresponding indifference
curves.
iii. Provide at least one example and economic intuition.
Suppose that the consumer has available income equal...

Consider a consumer with the utility function U(X, Y) = X^2 Y^2
. This consumer has an income denoted by I which is devoted to
goods X and Y. The prices of goods X and Y are denoted PX and
PY.
a. Find the consumer’s marginal utility of X (MUX) and marginal
utility of Y (MUY).
b. Find the consumer’s marginal rate of substitution (MRS).
c. Derive the consumer's demand equations for both goods as
functions of the variables PX,...

Consider the following utility function: U(x, y) = 10x + 2y. A consumer faces prices of px = 1 and py = 2. Assuming that graphically good x is on the horizontal axis and good y is on the vertical axis, suppose the consumer chooses to consume 5 units of good x and 13 units of good y. What is the marginal rate of substitution (MRS) equal to?

Consider the following utility function:
U = 100X0.10 Y 0.75.
A consumer faces prices of Px = $5 and Py =$5.
Assuming that graphically good X is on the horizontal axis and good
Y is on the vertical axis, suppose the consumer
chooses to consume 7 units of good X and 15 units of good Y.
Then the marginal rate of substitution6 is equal to:
MRS = . (Enter your response rounded to two decimal places. Do
not forget to...

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