Practice Questions 3

Goal:

• Provide a review of basic concepts in Consumer Theory: budget constraint, marginal utility(MU) and Law of Diminishing MU, consumer choice for utility maximization, income and substitution effect of a price change.
• Provide a review of Production and Cost Functions: marginal product, marginal cost, Law of Diminishing Returns, and the relationship between total cost (TC), average cost (AC), and marginal cost (MC).

1. Fill in the missing utility values. Total utility equals 102 when zero units of Good X are consumed.

     Table 1

2. Suppose that the price of good X is  P_x = $2 and the price of good Y is P_y = $1.  Peter spends his entire income of $16 and purchases 4 units of good X and 8 units of good Y.

a.  Draw Peter's budget line (put good Y on the y axis) and label it Budget Line 1. What would happen to his budget line if  the price of good X decreases to $1.  Draw this new budget line on your graph and label it Budget Line 2. Suppose Peter chooses to consume 8 units of good X and 8 units of good Y when confronted with Budget Line 2.

b. Assume the price of good X is $1 and the price of good Y is $1.  Suppose Peter's income decreases by $4.  Draw Peter's new budget line and label it Budget Line 3.  Can Peter still afford to purchase the original bundle of 4 units of X and 8 units of Y?  Will Peter choose to consume the original bundle now that his income has decreased?  On your graph label the income and the substitute effect.

c.  If good X is a normal good and good Y is an inferior good what will the income-consumption line look like for these two goods?  Draw a graph with several budget lines and illustrate an income-consumption line where good X is a normal good and good Y is an inferior good.

3.  The total utility schedules of commodities X and Y in Table 2 are given by Table 2.

  Table 2    

a. Find the marginal utility of good X, MU_X, and  the marginal utility of good Y, MU_Y. Make a table showing both the marginal utilities and the total utilities for both goods.

b. Find the point  that maximizes the consumer's utility if the consumer's income is $5 and P_X = P_Y = $1.

c.  If the price of good X falls to $0.50, what will be the point that maximizes the consumer's utility?

d. Identify two points on this consumer's demand schedule for commodity X.  Show that the consumer buys more of a good when the price of the good decreases.

4. Suppose that a consumer has the MU_x of Table 3 and MU_y of Table 4. Suppose also that her money income is $10,  and P_x  = $2 and P_y = $1.

 Table 3

 Table 4

a.  Describe how this consumer should spend her income of $10 on goods X and Y in order to maximize her total utility. At which consumption bundle will she maximize her total utility?

b. What happens to her total utility if she modifies the bundle of goods in answer (a) to where she purchases either one more unit of good X or one more unit of good Y?

5. A firm pays $200,000 in wages, $ 50,000 in interest payments for capital, and $70,000 for the yearly rental of its factory building. If the owner worked for somebody else as a manager he would earn at most $40,000 per year, and if he lent out his money capital to somebody else in a similarly risky business, he would at most receive $10,000 per year. He owns no land or building.

a.  Calculate the owner's profit if he receives $ 400,000 from selling his yearly output.

b. How much profit is the owner earning from the point of view of the man in the street?  Why is this answer different from the answer you gave in part (a)?

c.  What would happen if the owner's total revenue were $360,000 instead?

6. Given the data in Table 5,

  Table 5

a.  Find the AFC, AVC, AC and MC schedules.

b. On one set of axes, plot and label the schedules found in part (a).

c.  Explain the shape of each curve and the relationship among the different curves.

7. Suppose that a tailor working alone can make 2 suits per month; 2 tailors working in the same shop can produce 5 suits; 3 tailors, 10 suits; 4 tailors, 14 suits; 5 tailors, 17 suits; and 6 tailors, 19 suits.

a.  Find the marginal product of labor (MP_L). The marginal product of labor is equal to the change in total output divided by the change in the number of units of labor.

b. When does the law of diminishing returns begin to operate? Why do you have increasing returns up to that point?

c.  Why do diminishing returns eventually set in?

8. Suppose that three of the alternative scales of plant that a firm can build in the long run are shown by the short run average cost curve (SRAC) schedules in Table 6.  (Columns 1 and 2 go together, columns 3 and 4 go together, and columns 5 and 6 go together.)

a.  Sketch these three SRAC curves on the same graph.

b. Show the firm's long run average cost curve (LRAC curve) if these three plants are the only ones that are feasible technologically.

c.  Define the firm's long run average cost curve (LRAC curve) if the firm could build an infinite number of plants.

   Table 6