Econ 604



Econ 604. Problem Set #1

1. Statistical evidence indicates that equations defining the demand and supply functions of 1 pound bags of Starbucks Coffee at The Ukrops near VCU to be

Qd = 1050 - 50P - 100Ps + .1I

Qs = 60 + 20P - 40w

Where P is the price of a 1 pound bag of coffee

Ps is the price of maple walnut scones ABD

I is mean per capita monthly disposable income of students.

w is the mean hourly wage pad to coffee roasters.

Currnelty I = $1,000

Ps = $1.50

w = $8

a. Write the demand and supply curves for Starbucks coffee

b. Solve for the equilibrium price and quantity

c. Graph your solution.

Suppose that Starbucks employees negotiate a $2 per hour wage increase.

d. Find the new supply curve

e. Find the new equilibrium

f. Graph the change on your chart

g. Analyze the changes. When did a change in supply occur? When did a change in quantity supplied occur?

2. Suppose that a society’s capacity to produce medical goods and military goods is given by the equation

3X2 + 2Y2 = 100

where X represents Bradley fighting vehicles and Y represents doctors trained.

a. Graph this relationship. In your chare illustrate the following

- Inefficient points and efficient by unattainable points

- Increasing marginal opportunity cost

b. Find the slope of the above expression. Use it to analytically illustrate the notion of increasing marginal opportunity costs.

c. Suppose that the right hand side of the above expression increased to 200. What effect would that have on your production possibilities frontier? What economic explanation might motivate such a change?

2.2. If we cut four congruent squares out of the corners of a square piece of cardboard 12 inches on a side, we can fold up the four remaining flaps to obtain a tray without a top. What size square should be cut in order to maximize the volume of the tray?

2.7 Suppose a firm’s total revenues depend on the amount produced (q) according to the function

TR = 70q – q2

Total costs also depend on q:

TC = q2 + 30q + 100

a. What level of output should the firm produce in order to maximize profits (TR-TC)?

b. Show that the second-order conditions for a maximum are satisfied at the output level found in part (a)

c. Does the solution calculated here obey the “marginal revenue equals marginal cost rule? Explain

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