Suppose there are 1000 identical firms producing diamonds. Diamond miners receive the wage rate w. Assume that the short-run cost function for each diamond-producing firm is C(q) = wq + q2.

a. If w = 10, what is the supply curve of an individual firm? What is the market supply curve?
b. How many diamonds will the 1000 firms produce (in total) if the market equilibrium price is $25 and w = 10?
c. Assume w = 10 and that the market demand for diamonds is Q = 7000 – 100P. What is the short-run equilibrium price and (market) quantity?
d. Suppose public pressure for improving diamond mining conditions increases w to 13. How does this affect individual and market supply? How does this affect the equilibrium price and quantity of diamonds?

I am sorry for the spelling mistake. Matt, you have violated the UNC Honor Code and will thereby need to speak with me after our section tomorrow.

a. To find the supply curve of an individual firm, we need to determine the quantity of diamonds the firm is willing to supply at different prices. We can do this by finding the profit-maximizing quantity for the firm at different prices.

In the short-run cost function C(q) = wq + q^2, the first term represents the wage cost and the second term represents the cost of producing the diamonds.

If we treat the market price as the variable P, then the revenue for the firm is Pq. The profit is given by the difference between revenue and cost: π = Pq - (wq + q^2).

To find the profit-maximizing quantity, we take the derivative of the profit function with respect to q and set it equal to zero:
dπ/dq = P - (w + 2q) = 0

Solving for q, we get: q = (P - w) / 2

This equation gives us the profit-maximizing quantity for an individual firm at a given price. If we plug in w = 10, we can obtain the individual firm's supply curve.

To find the market supply curve, we multiply the quantity supplied by the number of firms (1000) because all firms are identical:
Qs = 1000 * q

b. If the market equilibrium price is $25 and w = 10, we can use the profit-maximizing quantity equation from part a to find the quantity supplied by an individual firm:
q = (P - w) / 2
q = (25 - 10) / 2
q = 7.5

Since there are 1000 firms, the total quantity supplied is:
Qs = 1000 * q
Qs = 1000 * 7.5
Qs = 7500

Therefore, the 1000 firms will produce a total of 7500 diamonds.

c. If w = 10 and the market demand for diamonds is Q = 7000 - 100P, we can find the short-run equilibrium price and quantity by setting the quantity demanded equal to the quantity supplied.

Quantity demanded: Qd = 7000 - 100P
Quantity supplied: Qs = 1000 * q (from part a)

Setting Qd equal to Qs, we get:
7000 - 100P = 1000 * q

Substituting the profit-maximizing quantity equation from part a [(P - w) / 2] for q, we have:
7000 - 100P = 1000 * [(P - w) / 2]

Simplifying the equation:
7000 - 100P = 500 * (P - 10)
7000 - 100P = 500P - 5000
600P = 12000
P = 20

So the short-run equilibrium price is $20. To find the equilibrium quantity, we substitute P = 20 into the quantity demanded or supplied equation:
Q = 7000 - 100P
Q = 7000 - 100(20)
Q = 7000 - 2000
Q = 5000

Therefore, the short-run equilibrium price is $20 and the equilibrium quantity is 5000.

d. If public pressure increases the wage rate w to 13, the individual firm's supply curve will shift upwards. This means that at any given price, the firm will supply a smaller quantity of diamonds compared to when w = 10. The increase in wage rate raises the cost of production, making it less profitable for the firm to produce diamonds.

Similarly, the market supply curve will also shift upwards since it is the aggregate of the individual firm supply curves. As a result, the total quantity supplied in the market will decrease at any given price compared to when w = 10.

The equilibrium price and quantity of diamonds will be affected as follows:

- The equilibrium price will increase because the decrease in supply puts upward pressure on prices.
- The equilibrium quantity will decrease because the decrease in supply reduces the total quantity traded in the market.

The exact changes in price and quantity will depend on the specific shifts in the supply and demand curves. But in general, an increase in the wage rate would result in a higher equilibrium price and a lower equilibrium quantity of diamonds.

This is the violation of the UNC Honor Code.