Econ 201 Stage 2 Microeconomics

Tutorial 3

Question 1:

Thomas consumes two goods X and Y. His utility function is given by U(x, y) = x*y. Good X costs $5 per unit and Good Y costs $10 per unit. Thomas has $100 to spend. Which of the following statements is NOT CORRECT?

(a) Thomas can buy 20 units of Good X if he wants.

(b) Thomas can buy 10 units of Good Y if he wants.

(c) Thomas can buy 10 units of Good X and 5 units of Good Y if he wants.

(d)  Thomas can buy 20 units of Good Y if he wants.

Question 2:

Thomas consumes two goods X and Y. His utility function is given by U(x, y) = x*y. Good X costs $5 per unit and Good Y costs $10 per unit. Thomas has $100 to spend. Which of the following statements is CORRECT?

(a) In order to maximize his utility, Thomas will buy 10 units of X and 5 units of Y. The corresponding level of utility is 50.

(b) In order to maximize his utility, Thomas will buy 5 units of X and 10 units of Y. The corresponding level of utility is 2.

(c) In order to maximize his utility, Thomas will buy 10 units of X and 10 units of Y. The corresponding level of utility is 1/2.

(d) In order to maximize his utility, Thomas will buy 5 units of X and 5 units of Y. The corresponding level of utility is 25.

Question 3:

Thomas consumes two goods X and Y. His utility function is given by U(x, y) = x*y. The price of Good used to be $5 per unit but has recently increased to $10 per unit. The price of Good Y has remained unchanged $10 per unit. Thomas has $100 to spend. Which of the following statements is CORRECT?

(a) Prior to the change in the price of Good X, to maximize his utility, Thomas was buying 5 units of X and 5 units of Y. Now he will buy 10 units of X and 5 units of Y.

(b) Prior to the change in the price of Good X, to maximize his utility, Thomas was buying 10 units of X and 5 units of Y. Now he will buy 5 units each of both X and Y.

(c) Prior to the change in the price of Good X, to maximize his utility, Thomas was buying 10 units of X and 5 units of Y. Now he will buy 10 units each of both X and Y.

(d) Prior to the change in the price of Good X, to maximize his utility, Thomas was buying 5 units of X and 5 units of Y. Now he will buy 10 units each of both X and Y.

Question 4:

Thomas consumes two goods X and Y. His utility function is given by U(x, y) = x*y. The price of Good X used to be $5 per unit but has recently increased to $10 per unit. The price of Good Y has remained unchanged $10 per unit. Thomas has $100 to spend. Suppose the government wants to give Thomas enough money so that he can still consume the amount of X and Y that he was consuming when the price of X was $5 per unit and the price of Y was $10 per unit. Which of the following statements is CORRECT?

(a) At the earlier prices, Thomas would consume 10 units of X and 10 units of Y. This bundle now costs $200. So, the government needs to give Thomas an additional $100 to afford the original bundle. But if the government gave Thomas an additional $100 then Thomas would prefer to consume 20 units each of X and Y.

(b) At the earlier prices, Thomas would consume 10 units of X and 5 units of Y. This bundle now costs $150. So, the government needs to give Thomas an additional $50 to afford the original bundle. But if the government gave Thomas an additional $50 then Thomas would prefer to consume 10 units each of X and Y.

(c) At the earlier prices, Thomas would consume 10 units of X and 5 units of Y. This bundle now costs $150. So, the government needs to give Thomas an additional $50 to afford the original bundle. But if the government gave Thomas an additional $50 then Thomas would prefer to consume 7.5 units each of X and Y.

(d) At the earlier prices, Thomas would consume 5 units of X and 5 units of Y. This bundle now costs $100. So, the government does not need to given Thomas any additional amount since he has enough money to afford the original bundle.

Question 5:

Thomas consumes two goods X and Y. His utility function is given by U(x, y) = x*y. The price of Good used to be $5 per unit but has recently increased to $10 per unit. The price of Good Y has remained unchanged $10 per unit. Thomas has $100 to spend. Suppose the government wants to give Thomas enough money so that he can still get the same amount of utility that he was getting before. Which of the following statements is CORRECT?

(a) The government needs to give Thomas approx. $150 or an additional $50 for him to get the same utility of 50 units as before. Given this additional income, Thomas would consume X = Y = 10.  

(b) The government needs to give Thomas approx. $150 or an additional $50 for him to get the same utility of 50 units as before. Given this additional income. Thomas would consume X = Y = 7.07.  

(c) The government needs to give Thomas approx. $150 or an additional $50 for him to get the same utility of 50 units as before. Given this additional income. Thomas would consume X = Y = 5.  

(d) The government needs to give Thomas approx. $141.4 or an additional $41.4 for him to get the same utility of 50 units as before. Given this additional income. Thomas would consume X = Y = 7.07.  

Question 6:

On the basis of your answers to Questions 2, 3 and 5, which of the following statements is CORRECT?

(a) When the price of X was $5 per unit and the price of Y was $10 per unit, Thomas was consuming 10 units of X and 5 units of Y. When the price of X increased to $10 per unit. Thomas consumes 5 units of X and 5 units of Y. This movement can be decomposed into parts. An income effect via which Thomas would consume X = Y = 7.07 and a substitution effect via which Thomas consumes X = Y = 5.

(b) When the price of X was $5 per unit and the price of Y was $10 per unit, Thomas was consuming 10 units of X and 5 units of Y. When the price of X increased to $10 per unit. Thomas consumes 10 units of X and 10 units of Y. This movement can be decomposed into parts. A substitution effect via which Thomas would consume X = Y = 7.5 and an income effect via which Thomas consumes X = Y = 5.

(c) When the price of X was $5 per unit and the price of Y was $10 per unit, Thomas was consuming 10 units of X and 5 units of Y. When the price of X increased to $10 per unit. Thomas consumes 5 units of X and 5 units of Y. This movement can be decomposed into parts. A substitution effect via which Thomas would consume X = Y = 5 and an income effect via which Thomas consumes X = Y = 7.5.

(d) When the price of X was $5 per unit and the price of Y was $10 per unit, Thomas was consuming 10 units of X and 5 units of Y. When the price of X increased to $10 per unit. Thomas consumes 5 units of X and 5 units of Y. This movement can be decomposed into parts. A substitution effect via which Thomas would consume X = Y = 7.07 and a further income effect via which Thomas consumes X = Y = 5.

Question 7:

Draw a neatly labelled diagram to show the total effect on Thomas’ consumption if he has $100 and the price of X changes from $5 per unit to $10 per unit while the price of Y remains unchanged at $10 per unit. On your diagram depict the difference between what happens when the government gives Thomas an extra $50 following the increase in the price of X and what happens when the government gives Thomas an extra $41.4 following the same price increase.