1. For each of the following cases, calculate the arc price elasticity of demand and state whether the demand is elastic, inelastic or unit elastic.
a. When the price of gas falls from $2.99 to $2.15 per gallon, the quantity demanded increases from 90 to 100 gallons.
b. When the rent on apartments increases from $1375 to $1500, the quantity demanded decreases from 1000 to 990.
2. For each of the following cases, what is the expected impact on total revenue of the firm? Explain your reasoning.
a. Price elasticity of demand is known to be -0.5, and the firm raises price by 10 percent.
b. Price elasticity is 0, and the firm raises prices by 50%.
c. Price elasticity of demand is known to be -1.0, and the firm raises prices by 1%.
3. The demand curve is determined to be:
Qd = 526 - 2P
a. Find the total revenue function.
b. Find the marginal revenue function.
c. Graph the total revenue and marginal functions.
d. At what price will total revenue be maximized, and what is the value of revenue at this point.
e. Identify the elastic and inelastic regions of the demand curve.
4. Suppose that a firm's only variable input is labor. When 50 workers are employed by the firm, the average product of labor is 50, and the marginal product of the 50th worker is 75. The wage rate is $80, and the total cost of the fixed input is $500.
a. Determine the average variable cost?
b. Determine the marginal cost?
c. Calculate the average total cost?
d. Determine the following as TRUE or FALSE.
1. Marginal cost is increasing.
2. Average cost is increasing.
3. Average total cost is decreasing.
5. Suppose you win $15 on a lotto ticket. You decide to spend all your winnings on candy bars and peanuts for a party with friends. Candy bars cost $0.75 each while bags of peanuts cost $1.50 each.
a. What is the budget line equation?
b. What is the slope of the budget line equation?
c. What is the opportunity cost of one more candy bar? What is the opportunity cost of one more bag of peanuts? How do the opportunity costs change (rise, fall, or remain constant) as additional units are purchased.
d. Suppose you had won $30 on your lotto ticket, not $15. Has the number of available combinations of candy bars and peanuts increased or decreased?