Question

ECON 2023 Spring 2019: Homework #1 Let the utility derived from goods X and Y be as follows for a rational individual: Unit of Good TUX TU_Y 8 utils 5.5 utils 15 utils 10.5 utils 21 utils 15 utils 26 utils 19 utils 30 utils 22.5 utils 33 utils 25.5 utils 35 utils 28 utils 36 utils 30 utils 36 utils 31.5 utils What is a commodity bundle (you can assume a two-commodity world)? What is the functional form of the utility function in a two-commodity world? Be sure to identify each element. Assume that the Total Utility from the above is TU = TU_X + TU_Y. Construct the Utility Matrix and identify at least two separate indifference curves. Be sure to include the commodity bundles and the total utility. Arrive at the marginal utility structure for each good individually. 5. What is the income equation and the budget line? Be sure to draw the budget line in commodity space and identify the intercepts and slope. 6. Find the original consumer equilibrium given: M = $12, p_X = $2, p_Y = $1, and draw it on a graph. Note that you will need two separate graphs for this, to be placed at the top. Be sure to identify the consumer equilibrium commodity bundle and the maximum utility. What is the algebraic condition for Consumer Equilibrium? 7. Let the income change such that it falls to M = $8. Find the new consumer equilibrium, draw this on one of the original graphs, and under that draw the Engel curve. Is X a normal or inferior good? How do we know this? Write the formula and identify the value of the income elasticity of demand. 8. Let the own-price change such that it falls to p_X = $1. Find the new consumer equilibrium, draw this on one of the original graphs, and under that draw the demand curve. Is X an ordinary or Giffen good? How do we know this? Write the formula and identify the value of the own-price elasticity of demand. 9. Let the Cobb-Douglas utility function take the following form: U = f(X,Y) = AX^aY^(1-a). Let A = 100 and a = X. Find the MRS. 10. Find the original consumer equilibrium using the budget line in #6 above and draw it on a graph. 11. Find the new consumer equilibrium using the budget line in #8 above and draw it on the same graph. 12. Draw the demand curve under the graph. Write the formula and identify the value of the own-price elasticity of demand.

ECON 2023 Spring 2019: Homework #1

Let the utility derived from goods X and Y be as follows for a rational individual:

Unit of Good
TUX TU_Y
8 utils 5.5 utils
15 utils 10.5 utils
21 utils 15 utils
26 utils 19 utils
30 utils 22.5 utils
33 utils 25.5 utils
35 utils 28 utils
36 utils 30 utils
36 utils 31.5 utils

What is a commodity bundle (you can assume a two-commodity world)? What is the functional form of the utility function in a two-commodity world? Be sure to identify each element. Assume that the Total Utility from the above is TU = TU_X + TU_Y. Construct the Utility Matrix and identify at least two separate indifference curves. Be sure to include the commodity bundles and the total utility. Arrive at the marginal utility structure for each good individually.

5. What is the income equation and the budget line? Be sure to draw the budget line in commodity space and identify the intercepts and slope.

6. Find the original consumer equilibrium given: M = $12, p_X = $2, p_Y = $1, and draw it on a graph. Note that you will need two separate graphs for this, to be placed at the top. Be sure to identify the consumer equilibrium commodity bundle and the maximum utility. What is the algebraic condition for Consumer Equilibrium?

7. Let the income change such that it falls to M = $8. Find the new consumer equilibrium, draw this on one of the original graphs, and under that draw the Engel curve. Is X a normal or inferior good? How do we know this? Write the formula and identify the value of the income elasticity of demand.

8. Let the own-price change such that it falls to p_X = $1. Find the new consumer equilibrium, draw this on one of the original graphs, and under that draw the demand curve. Is X an ordinary or Giffen good? How do we know this? Write the formula and identify the value of the own-price elasticity of demand.

9. Let the Cobb-Douglas utility function take the following form: U = f(X,Y) = AX^aY^(1-a). Let A = 100 and a = X. Find the MRS.

10. Find the original consumer equilibrium using the budget line in #6 above and draw it on a graph.

11. Find the new consumer equilibrium using the budget line in #8 above and draw it on the same graph.

12. Draw the demand curve under the graph. Write the formula and identify the value of the own-price elasticity of demand.