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 per month 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 per month 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  8p − 60

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 in           thousands) 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 ofthe 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