Question

3 , 4 , 5 and 6

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 TU X 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)? 1. 2. What is the functional form of the utility function in a two-commodity world? Be sure to id element. Assume that the Total Utility from the above is TU TU, TU, Construct the U tility Matrix and identify least two separate indifference curves. Be sure to include the commodity bundles and the 3 Assume that the Total Utility from the above is TUg TU,+T total utility. Arrive at the marginal utility structure for each good individually 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. 4 5. 6. Find the original consumer equilibrium given: Mo-125 : p. 2%. : p-17, a nd draw in a graph (note yo will need two separate graphs of this to be placed at the "top"). Be sure to identify the consumer equilibrium commodity bindle and the maximum utility. What is the algebraic condition for Consumer Equilibrium? 7. Let the income change such that it falls to M- 85. Find the new consumer equilibrium, draw this in one the original graphs, and under that draw the Engel curve. Is X a normal or inferior good? How do we kno this? Write the formula and identify the value of the income elasticity of demand. Let the own-price change such that it falls to p-1%. Find the new consumer equilibrium, draw this in of the original graphs, and under that draw the demand curve. Is X an ordinary or Giffen good? How do know this? Write the formula and identify the value of the own-price elasticity of demand. 8, Let the Cobb-Douglas utility function take the following form 9, Let A 100 and a %. Find the MRS. 10, Find the original consumer equilibrium using the budget line in #6 above and draw in a graph. 11. Find the new consumer equilibrium using the budget line in #8 above and draw in 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.

Answer 1

ood-X is an ordinary good because as the price of good X falls (from 2 to1) its consumption increases (from 3 to1). However, giffen goods are those goods whose consumption falls when the price falls.

Elasticity of demand = percentage change in quantity demanded / percentage change in price

In our example, percentage change in quantity demanded = 100 ( increases from 3 to 6)

Also, Percentage change in price = 50 ( falls from 2 to 1)

So, elasticity of price = 100/50 = 2. Elasticity greater than 1 is said to be highly elastic demand.