Supply and Demand and Following Profit Function
Show your work.
Required Problems:
1) Find the slope of the following functions at X = 3.
a. Y = 4 + 3X2
b. Y = 5X + 6X3
c. Y = 6X
d. Y = (6X + 3)2 / 4X
2) If a firm’s Total Cost equation is TC = 200 + 3Q + 7Q2:
a. What is the equation for the firm’s marginal cost?
b. What is the firm’s marginal cost when Q =1? Q= 5?
3) At the Peoria Company, the relationship between profit and output is as follows:
( = -40 + 20Q – 2Q2
a. What value of Q maximizes profit?
b. How can you be certain that this quantity maximizes (as opposed to minimizes) profit? Demonstrate this.
4) A firm produces 2 goods, Q1 and Q2, and has the following profit function.
( = -80 + 30Q1 + 25Q2 – 4Q12 – 3Q22 - 2Q1Q2
a. Find the partial derivative, with respect to Q1, of the firm’s profit function.
b. In terms of economics, how would you interpret this partial derivative?
5) Given the following equation for the demand for good X:
QD = a1Px + a2I + a3Py
Where Px = the price of good X, I = Income, and Py = the price of a related good, Y.
A) What sign would expect a2 to have if good X is a normal good?
B) If Px = 8, I = 10, Py = 6, a1 = -4, a2 = 20 and a3 = -3, what is the total quantity demanded?
C) Using the relevant information provided in part B, solve for the demand equation (Q=f(P)) for good X.
6) Given the demand function in question 5, and given the following supply function for good X as follows:
Qs = 20*Px -5*Pz - 15W, where Px is the price of good X, Pz is the price of a related good and is equal to 7, and W is the wage rate and is equal to 12.
a) What is the market equilibrium price for good X? What is the equilibrium quantity?
b) Allow the wage rate to increase to 14. What is the new
Required Problems:
1) Find the slope of the following functions at X = 3.
a. Y = 4 + 3X2
b. Y = 5X + 6X3
c. Y = 6X
d. Y = (6X + 3)2 / 4X
2) If a firm’s Total Cost equation is TC = 200 + 3Q + 7Q2:
a. What is the equation for the firm’s marginal cost?
b. What is the firm’s marginal cost when Q =1? Q= 5?
3) At the Peoria Company, the relationship between profit and output is as follows:
( = -40 + 20Q – 2Q2
a. What value of Q maximizes profit?
b. How can you be certain that this quantity maximizes (as opposed to minimizes) profit? Demonstrate this.
4) A firm produces 2 goods, Q1 and Q2, and has the following profit function.
( = -80 + 30Q1 + 25Q2 – 4Q12 – 3Q22 - 2Q1Q2
a. Find the partial derivative, with respect to Q1, of the firm’s profit function.
b. In terms of economics, how would you interpret this partial derivative?
5) Given the following equation for the demand for good X:
QD = a1Px + a2I + a3Py
Where Px = the price of good X, I = Income, and Py = the price of a related good, Y.
A) What sign would expect a2 to have if good X is a normal good?
B) If Px = 8, I = 10, Py = 6, a1 = -4, a2 = 20 and a3 = -3, what is the total quantity demanded?
C) Using the relevant information provided in part B, solve for the demand equation (Q=f(P)) for good X.
6) Given the demand function in question 5, and given the following supply function for good X as follows:
Qs = 20*Px -5*Pz - 15W, where Px is the price of good X, Pz is the price of a related good and is equal to 7, and W is the wage rate and is equal to 12.
a) What is the market equilibrium price for good X? What is the equilibrium quantity?
b) Allow the wage rate to increase to 14. What is the new