Homework 4-

1. George has $100 in income to be spent on hamburgers (H) and milk (M). The price of milk is $1 per unit and George is currently consuming at a point on his budget line that consists of 10 hamburgers and 10 units of milk.

a. Draw George's budget line in a graph with milk measured on the horizontal axis and hamburgers on the vertical axis. Label this graph clearly and completely.

b. Given the above information, what is the price of a hamburger?

c. Write an equation for George's budget line? (Keep your equation with improper fractions rather than converting the equation to decimals.)

d. Given the above information and your calculations identify whether the combinations of milk and hamburgers below are on George's budget line, are inside his budget line, or are beyond his budget line.

2. The price of a movie ticket is $8 and the price of a box of popcorn is $5. Sue always consumes a box of popcorn when she goes to the movies. She never consumes less than one box or more than one box however.

a. Draw an image of Sue's indifference curve map that includes at least three indifference curves. In your graph, measure movies along the horizontal axis and popcorn along the vertical axis.

b. Suppose Sue has $130 a year that she can spend on movies and popcorn. On your indifference curve map depict Sue's budget line and her optimal consumption bundle given this information.

3. Joey has $200 to spend on cereal and steak. For this problem assume that Joey always spends all of his available income and he always selects that consumption bundle that maximizes his satisfaction. Suppose when the price of steak is $10 he purchases 4 steaks and 40 boxes of cereal. However, Joey finds that if the price of steak increases to $20 he purchases only 2.8 steaks. Assume that only the price of steak changes in this problem.

a. Given the above information, what is the price of cereal?

b. How many boxes of cereal does Joey purchase when the price of steaks increases to $20?

c. From the above information write Joey's demand curve for steak. Assume that this demand curve is linear. Hint: After deriving your demand curve verify that both (Q, P) points you used are actually on this demand curve.

4. Jung's income is $100 and he spends all of this income on good X and good Y. Good X costs $10 per unit while good Y costs $10 per unit. Jung maximizes his utility given this information when he selects point A which corresponds to Jung consuming 5 units of good X and 5 units of good Y.

a. In a graph with good X on the horizontal axis and good Y on the vertical axis draw Jung's budget line, BL1, given the above information. Mark point A on your graph and indicate the quantity of good X and good Y associated with point A.

Suppose that the price of good X decreases to $5 per unit while nothing else changes. When the price of good X decreases Jung maximizes his utility when he selects point B. Point B corresponds to Jung consuming 8 units of good X and 6 units of good Y.

b. On the same graph draw Jung's new budget line, BL2, based on the above information.  Mark point B which corresponds to Jung consuming 8 units of good X and 6 units of good Y.

c. In this part of the question we want to find the income and substitution effects with respect to good X for Jung when the price of good X decreases. Suppose you are told that if Jung had to pay the new prices for the two goods but was constrained to have the initial level of utility, he would choose to consume at point C which corresponds to Jung consuming 7 units of good X and 4.5 units of good Y.

i. Given this information what level of income would Jung need to have in order to be at point C? (Hint: the decrease in the price of good X effectively makes Jung's $100 have greater purchasing power. If Jung is going to be constrained to be back on indifference curve 1 that implies that his income would need to be decreased from its $100 level.)

ii. In your graph draw this new budget line, BL3, and label both the x and y intercepts for this budget line. In your graph also mark point C.

iii. With respect to good X, what is the value of the substitution effect for Jung?

iv. With respect to good X, what is the value of the income effect for Jung?

v. According to your work, is good X a normal or inferior good? Explain your answer.

vi. According to your work, is good Y a normal or inferior good? Explain your answer.

5. You are given the following table and asked to complete the table. You are also told that the price of labor (L) is $2 per unit of labor and the price of capital (K) is $5 per unit of capital. After completing the table there are a number of fill in the blank questions for you to do.

a. ATC =

b. ATC = _______ + _________

c. MC = ________________________________/___________________________

d. VC = ___________________*_____________________

e. VC/(price of labor) = _______________________________

f. TC = ___________________*___________________________

g. AFC = ____________________ - ___________________________

h. MPl = ______________________________/_____________________________

6. Use the graphs below of a perfectly competitive industry to answer this question. The graph on the left represents a typical firm in this industry while the graph on the right represents the entire industry. For this question assume all firms are identical.

a. Given the above graphs, is this a short-run or long-run equilibrium? Explain your answer.

b. Given the above graphs, what is fixed cost equal to for a representative firm?

c. In the short-run how many units of the good does a representative firm produce?

d. Given the above graphs, in the short-run what is the equilibrium market quantity?

e. Given the above graphs, how many firms are currently in the market?

f. Given the above graphs, what do you predict will happen in this industry in the long run?

g. Holding everything else constant, how many firms will be in the industry in the long run? (Hint: partial firms are okay for your answer here.)