Value: 20 points--10% of grade. All work must be shown or explained to earn credit.
 
 

1. Management believes that the demand for its product is: Q = 25,000 - 500P where P is the price in dollars and Q denotes unit sales per year. The total cost function is: TC = 140,000 + 10Q.
 
 

a. Determine the inverse demand equation. (1)
 
 

2. Determine the firm's total revenue and marginal revenue functions. (2)

c. Determine the firm's profit function. (2)
 
 

d. Determine the firm's marginal profit function. (1)
 
 

e. Calculate the profit-maximizing price and quantity and the maximum profit that can be earned. (3)
 
 

f. Determine the revenue maximizing price and quantity. (2)
 
 

7. Why will the revenue maximizing quantity in general be greater than the profit maximizing quantity? (1)

2. A firm sells in a highly competitive market in which the going price is $15 per unit. Its total cost equation is: TC = 25 + 0.25Q².
 
 

a. Find the profit maximizing level of output and corresponding profits. (3)
 
 

b. Find the firm's breakeven point(s). (2)
 
 

3. Consider again the firm in question 2 selling a fixed price of $15 per unit. Assume now that the firm's total cost function is: TC = 200 + 4Q.
 
 

1. Graph the firm's total revenue and total cost curve below. Label the axes and your curves. (2)

b. Determine the breakeven quantity. (1)
 
 
 

ANSWERS
 

1
a:  P = 50-0.002Q
b.  TR=50Q-0.002Q*2 and MR=50-0.004Q
c.   Profit=-140,000+40Q-0.002Q*2
d.  Marginal Profit=40-0.004Q
e.  P=30, Q=10,000, Profit=60,000
f.  P=25, Q=12,500
g.  With revenue maximization, MR=0.  With profit maximization MR=MC, thus MR>0.  This occurs with smaller Q.
2
a.  Q=30, Profit=200
b.  Q=58 and 1.7
3
b. Q=18.2