Question

In the economy of Ricardia, two consumer goods, X and Y, are produced from a single...

  1. In the economy of Ricardia, two consumer goods, X and Y, are produced from a single factor input, labor, according to the production functions:

    Y = 3Ly and X = 3Lx

    where Ly and Lx are the quantities of labor used in the production of Y and X respectively. The total amount of labor available is 66 units.

    (a) Derive the equation for the economy's production possibility frontier. Confirm that the marginal rate of transformation is equal to MPLy/MPLx.

    (b) All consumers in Ricardia have identical tastes which can be represented by a utility function

    U(X, Y) = 5X2/3Y1/3

Homework Answers

Answer #1

ANSWER 1

Remember that the production possibilities frontier represents the amount of production that can be obtained from a certain number of factors. Therefore, goods (production) must be in function, since the factors are exogenous and given.

We have:

and are the units of labor dedicated to each good. And we know that:

  Total available labor is distributed between the two goods.

We can express the workforce of each good as the product of the production of the good by the work requirement per unit of product for each good, in this way:

,

,

Where and are the requirements.

If we isolate any good, in this case X, we have to:

is the marginal rate of transformation or the rate at which the economy can transform X for Y.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
An island economy has a labor endowment of 60 units to produce consumption goods x and...
An island economy has a labor endowment of 60 units to produce consumption goods x and y. The production functions are x = 0.2Lx and y = 0.10Ly, where Lx and Ly represent the labor allocation. The utility function is u(x,y) = 2x + 8y. (a.) What is the equation for the PPF? (b.) What is the optimal basket (x*,y*) in a closed economy? (c.) In an open economy, if the price of x is Px = $6 and the...
Consider two goods, x and y, each produced using two inputs, labor l and capital k....
Consider two goods, x and y, each produced using two inputs, labor l and capital k. Which of the following statements is correct? a. If production functions exhibit diminishing returns to scale, the production possibility frontier will be concave. b. If inputs are homogeneous and production functions exhibit constant returns to scale, the production possibility frontier will be concave if goods x and y use inputs in different proportions. c. If inputs are homogeneous and production functions exhibit constant returns...
Consider a consumer with preferences represented by the utility function: U(x,y) = 3x + 6 √...
Consider a consumer with preferences represented by the utility function: U(x,y) = 3x + 6 √ y   Are these preferences strictly convex? Derive the marginal rate of substitution Suppose, the utility function is: U(x,y) = -x +2 √ y   Are there any similarities or differences between the two utility functions?
2. Consider a consumer with preferences represented by the utility function: u(x,y)=3x+6sqrt(y) (a) Are these preferences...
2. Consider a consumer with preferences represented by the utility function: u(x,y)=3x+6sqrt(y) (a) Are these preferences strictly convex? (b) Derive the marginal rate of substitution. (c) Suppose instead, the utility function is: u(x,y)=x+2sqrt(y) Are these preferences strictly convex? Derive the marginal rate of sbustitution. (d) Are there any similarities or differences between the two utility functions?
Consider a consumer with preferences represented by the utility function u(x,y)=3x+6 sqrt(y) (a) Are these preferences...
Consider a consumer with preferences represented by the utility function u(x,y)=3x+6 sqrt(y) (a) Are these preferences strictly convex? (b) Derive the marginal rate of substitution. (c) Suppose instead, the utility function is: u(x,y)=x+2 sqrt(y) Are these preferences strictly convex? Derive the marginal rate of substitution. (d) Are there any similarities or differences between the two utility functions?
A country has 100 units of labor (L) and production functions x = (Lx)^0.5 and y...
A country has 100 units of labor (L) and production functions x = (Lx)^0.5 and y = 4Ly, where Lx and Ly describe the labor allocation. When the country divides its labor equally between producing x & y, what is the rate of product transformation (slope) for the PPF? a. 49.3 b. 56.7 c. 61.1 d. 71.0
Consider a consumer with the following utility function: U(X, Y ) = XY. (a) Derive this...
Consider a consumer with the following utility function: U(X, Y ) = XY. (a) Derive this consumer’s marginal rate of substitution, MUX/MUY (b) Derive this consumer’s demand functions X∗ and Y∗. (c) Suppose that the market for good X is composed of 3000 identical consumers, each with income of $100. Derive the market demand function for good X. Denote the market quantity demanded as QX. (d) Use calculus to show that the market demand function satisfies the law-of-demand.
Suppose a consumer has the utility function u(x, y) = x + y. a) In a...
Suppose a consumer has the utility function u(x, y) = x + y. a) In a well-labeled diagram, illustrate the indifference curve which yields a utility level of 1. (b) If the consumer has income M and faces the prices px and py for x and y, respectively, derive the demand functions for the two goods. (c) What types of preferences are associated with such a utility function?
Quantitative Question 2 Consider a situation where a consumer demands two goods, x and z with...
Quantitative Question 2 Consider a situation where a consumer demands two goods, x and z with the utility function U¯ = x 0.2 z 0.8 (a) Derive the marginal rate of substitution (b) Derive the demand functions for x and z as a function of income (Y ), the price of good x, (px) and the price of good z (pz) (c) Let Y = 200, px = 4, and pz = 8. Find the equilibrium quantities demanded for this...
5. The utility function of a consumer is u(x, y) =x2y i. Find the demand functions...
5. The utility function of a consumer is u(x, y) =x2y i. Find the demand functions x(p1,p2,m) and y(p1,p2,m). ii. What is the consumers indirect utility?
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT