Jacks faces the following demand function for its jack in

Question

Questions 1 - 6

Jack's faces the following demand function for its Jack in the Boxes: Q = 13000 - 8P.  Jack produces the Jack in the Boxes in two facilities.  The cost functions in each facility are:

TC1 = 110,000 + 40Q1 + .09Q1²

TC2 = 200,000 + 80Q2 + .05Q2²

1. Calculate the Q at which average cost is a minimum in facility 1.  What is minimum average cost?
2. Graph the average cost, marginal cost and average variable cost functions for facility 1.
3. Calculate the profit maximizing amount of Q to make and the profit maximizing price.
4. Calculate the amount of Q that will be made in each facility. 
5. Calculate the overall profits of the firm.
6. Calculate the marginal revenue at the profit maximizing amount of Q.

Questions 7 - 11

Marion the monopolist faces the following demand function: Q = 22,000 - 8P.  She faces the following cost function: TC = 5,000,000 + 140Q.

1. Calculate the price and quantity at which profits are a maximum.
2. What are the maximum profits?
3. Graph the demand, marginal revenue, marginal cost and average cost functions.
4. Shade in the area that represents the profits of the firm.
5. Now assume that regulators have decided to regulate Marion so that price = average cost.  What price and quantity does this correspond to?

Questions 12 - 14

The demand for boobles can be written as: Q = 11,000 - 8P.

1. Calculate the price, quantity, total revenue and marginal revenue when the elasticity of demand = -2.2.
2. Calculate the price, quantity, total revenue and elasticity of demand when MR = $60.
3. Calculate the price and quantity at which total revenue is a maximum.  What is maximum revenue?

Questions 15 - 19

Felicia has the following production function: Q = 6K^1/2L^1/2.  She faces the following demand function: Q = 12,000 - 8P.  The price per unit of K is $500 and the price per unit of L is $2,500.

1. Calculate the amount of K and L that Felicia will use.
2. Calculate the profit maximizing amount of output and the profit maximizing price.
3. Calculate the maximum profits of the firm.
4. Calculate the marginal revenue at the profit maximizing amount of Q.
5. Calculate the marginal product of labor at the K and L in question 15.

Questions 20 - 21

Reefer sells refrigerators to two classes of consumers.  The first class has the less elastic demand.  The second class is known as the "rebaters".  They have a higher elasticity of demand.  Assume the elasticity of demand of the first group is -1.9 and the elasticity of demand of the second group is -2.2 and the marginal cost of a refrigerator is $500.

1. What price should Reefer set for the refrigerator?
2. What should the rebate be if Reefer wants to sell to both classes of consumers?

Questions 22 - 25

Samson's faces the following production function: Q = 400L + 16L²  - .5L³. 

1. Calculate the L at which Q is a maximum.  What is the maximum Q?
2. Calculate the L at which the marginal product of L is a maximum.  What is the maximum marginal product of L?
3. Calculate the L at which the average product of L is a maximum.  What is the maximum average product of L?
4. Assume each unit of Q sells for $4 and each unit of L costs $1,000.  How much L should the firm hire if it is to maximize profits?  What are its maximum profits?

Questions 26 - 29

Sam can sell all of the output he wants at a price of $1000.  He has the following cost function:

                        TC = 200,000 + 80Q + .08Q²

1. Calculate the profit maximizing quantity.
2. Calculate the maximum profits of the firm.
3. Graph the demand, marginal revenue, marginal cost and average cost functions.
4. Shade in the area that represents the profits of the firm.

Questions 30 - 34

When P = 710, the demand for flugles is 4950.  When P = 1150, the demand for flugles = 2750. 

1. Using these two points and assuming the demand for flugles is a straight line, calculate and graph the demand function and the marginal revenue function for flugles.
2.  Now assume that the cost function for flugles can be written as:

TC = 140,000 + 90Q + .07Q²

Graph the marginal cost and average cost functions on the same graph that you just graphed demand and marginal revenue.

1.  Calculate the profit maximizing price and quantity of flugles and mark the points a (profit maximizing quantity) and b (profit maximizing price) on your graph.
2.  What is the average cost at the profit maximizing quantity?  Mark this point on your graph and label it c. Shade in the area that represents the profit of the firm.
3. Graph the total revenue and total cost functions and mark the profit maximizing level of output on the graph.

Questions 35 - 38

Below is a graph of the marginal cost, average cost, demand and marginal revenue functions of the Flooble firm. Fixed costs are $180,000.

1. a=
2. b=
3. c=
4. d=