RTS, Market Demand, Price Elasticity

1. In what ways are firms' isoquant maps and individuals' indifference curve maps based on the same idea? What are the most important ways in which these concepts differ?

2. Bottles are produced according to the production function, q = 3K + L, where
q = output per hour
K = capital input per hour
L = labor input per hour
A. If K = 20, how much L is needed to produce 100 bottles per hour?
B. If K = 50, how much L is needed to produce 100 bottles per hour?
C. What is the RTS along the q = 100 isoquant?

3. Taxes can obviously affect firms' costs. Explain how each of the following taxes would affect total, average, and marginal cost. Be sure to consider whether the tax would have a different effect depending on whether one discusses short-run or long-run costs:
A. A franchise tax of $10,000 that the firm must pay in order to operate
B. An output tax of $2 on each unit of output
C. An employment tax on each worker's wages

4. A. Consider a demand curve of the form, Qd = -4P + 60, where Qd is the quantity demanded of a good and P is the price of the good. Also, the supply curve is Qs = 4P + 4, where Qs is the quantity supplied. At what values of P and Q are the two equations in equilibrium? (Hint, where Qd = Qs) (5 points - show your work!)
B. Now suppose that the demand curve shifts to, Qd' = -4P + 8. At what values of P and Q does the new demand curve intersect the old supply curve? (Hint: where Qd' = Qs) (show your work)
C. Now finally, suppose the supply curve shifts to Qs' = 4P - 12. At what values of P and Q does Qd' = Qs'? (show your work!)
(Points: 15)

5. The market demand for peanuts is given by
Q = 5,200 + 2I - 600P + 100P',
where Q = Annual demand in number of peanuts
I = Average income in dollars per year
P = Price of peanuts
P' = Price of potato chips
Given that I = $10,000, P = $2, and P' =$3, determine:
A. The price elasticity, e(Q,P)
B. The income elasticity, e(Q,I)
C. The cross price elasticity, e(Q,P')

6. Widgets International faces a demand curve given by Q = 10 - P, and has a constand marginal and average cost of $3 per widget produced.
A. Complete the following list for q = 2, 5, and 10

P
TR (=P*q)
MR
MC
AC
TC
profit

7. Elizabeth makes $200 a week and spends her entire weekly income on new running shoes and designer jeans, since these are the only two items that provide utility to her. Furthermore, Elizabeth insists that for every pair of jeans she buys, she must also buy a pair of shoes (without the shoes, the new jeans are worthless.) Therefore, she buys the same number of pairs of shoes and jeans in any given week.
A. If jeans costs $20 and shoes cost $20, how many will Elizabeth buy of each? (Show your work)
B. Suppose that the price of jeans rises to $30 a pair. How many shoes and jeans will she buy? (Show your work)
C. To what effect (income or substitution) do you attribute the change in utility levels between part a and b?

8. Suppose the demand curve for flyswatters is given by, Q = 500 - 5P, where Q is the number of flyswatters demanded per week and P is the price in dollars.
A. How many flyswatters are demanded at a price of $2? How about a price of $3? $4? Suppose flyswatters were free; how many would be bought?
B. Suppose during July the flyswatter demand curve shifts to Q = 1,000 - 50P. Answer the questions in part A for this new demand curve.

9. The market demand for potatoes is given by
Q = 1,000 + 0.3I - 300P + 29P'
where
Q = Annual demand in pounds
I = Average income in dollars per year
P = Price of potatoes in cents per pound
P' = Price of rice in cents per pound
A. Suppose I = $10,000 and P' = $.25; what would be the market demand for potatoes? At would price would Q = 0?
B. Suppose I rose to $20,000 with P' staying at $.25. Now what would the demand for potatoes be? At what price would Q = 0?

10. Trapper Joe, the fur trader, has found that his production function in acquiring pelts is given by
q = 2*sq rt(H)
where q = the number of pelts acquired in a day, and H = the number of hours Joe's employees spend hunting and trapping in one day. Joe pays his employees $8 an hour.
A. Calculate Joe's total and average cost curves (as a function of q).
B. What is Joe's total cost for the day if he acquires four pelts? Six pelts? Eight pelts?