1. (Linear equation) A shoemaker at the Black Shoe  Company is paid 25cents for each pair of shoes he or she makes. At the White Shoe Company, a shoemaker is paid $50 per day regardless of the number of shoes he or she makes.

a. Find and plot an equation that describes the daily salary of a shoemaker (SB) at the Black Shoe

Company as a function of the number of pairs of shoes made each day.

Find and plot an equation that describes the daily salary of a shoemaker (SW) at the White Shoe

Company as a function of the number of pairs of shoes made each day.

b. Under what conditions would a shoemaker be

better off financially working for the Black Shoe Company? The White Shoe Company? Explain   your answer.

2. (Linear Break-even model) The cost $C(q) of

producing q units of a certain commodity in a

month is given by y = C(q) = 5q + 12,000 and each unit of that commodity sells for $8.

a. What is the fixed cost per month?

b. What is the number of units of the commodity that should be produced and sold per month to make

sure that the business breaks even? Write your conclusion.

3. (Nonlinear Break-even model) A company making   personal computers (PCs) found that the cost $C(q)

of producing q PCs permonth is given by

y = C(q) = 0.5q2  + 1000 q + 1,125,000

provided that q is between 0 and 2000. It also

found that the revenue $R(q) from the sales of q PCs permonth is given by

y = R(q) = −q2  + 4000 q

provided that q is between 0 and 2000.

a. Find the level of production at which the company will break even. State your conclusion.

b. At what level of production will the company make a profit? Explain.

4. (Nonlinear D-S model) Find the equilibrium price and quantity for the following demand and supply equations: q2 + 5q – p + 1 = 0 (demand) and 2q2  + p – 9 = 0 (supply)

5. (Linear D-S model) The demand for a commodity is described by q = D(p) = 15,000 – 150p where

q is the quantity demanded (measured in thousands of units) and p is the price (measured in dollars per unit).

The supply function for this commodity is

described by q = S(p) = -200 + 100p where q is the quantity supplied (measured in thousands of units)

and p is the price (measured in dollars per unit).

Find the equilibrium price and quantity.

6. (Nonlinear D-S model) Demand function for a commodity is described by

q = D(p) = −100p + 1500 + 10I

where q is the quantity demand (measured in

thousands of units),p is the price (measured in

dollars per unit), and I is the consumer’s average income.

Supply function for the same commodity is defined by

q = S(P) = 300  

where q is the quantity supplied (measured in

thousands of units) and p is the price (measured in dollars per unit). Note that p > 7.5 since 8p – 60 must be positive.

a. Find the equilibrium price and quantity when the consumer’s average income is given by I = 350.  Explain your answer.

b. Same as part (a) with I = 590. Explain your answer.

7. (D-S model + Tax) The demand and supply

functions for a commodity are defined by q = D(p) = -3p + 139 and q = S(p) = 2p – 11,respectively,    where q is the number of units (measured inthousands) and p is the price (measured in dollars per unit).

a. Find the equilibrium price and quantity.

b. Suppose that the government imposes a tax of $7.5 per unit on the commodity. Find the new

equilibrium price and quantity. (Assume that the  tax is included in the price paid by the consumer)

c. What percentages of the tax do the consumers and producers pay respectively?

8. (D-S model + subsidy) The demand and supply

functions for a commodity are defined by q = D(p) = -2p + 89 and q = S(p) = 6p - 7,respectively,

where p is the price (measured in dollars per unit) and q is the quantity (measured in thousands of units).

a. Find the equilibrium price and quantity.

b. Suppose the government pays the suppliers a

subsidy of $4 per unit, find the new equilibrium price and quantity.

b. What are the distribution of subsidy for both consumers and producers?

9. (Linear National Income model) Given the

national income model, Y = E, E = C + I + G:

C = 200 + 0.7Yd

I = 100

G = 10

T = 20 + 0.1Y

Calculate the equilibrium level of national income YE. State your conclusion.

10.  (Linear National Income model) Given the

national income model, Y = E, E = C + I + G + (X- M):

C = 250 + 0.8 Yd

I = 75

G = 150

X = 100

M = 30 + 0.2Y

a. Find the value of equilibrium level of income. State your conclusion.

b. If C decreased by 50, find the new value of

equilibrium level of income. State your conclusion.