Answer to Question #240107 in Economics for sajal

Question

1. A company has a linear total cost function and has determined that over the next three months

it can produce 2,000 units at a total cost of $700,000. This same manufacturer can produce 3,000

units at a total cost of $960,000. The units sell for $225 each.

a) Determine the revenue, cost, and profit functions using q for a number unit.

b) What is the fixed cost?

c) What is the marginal cost?

d) Find the break-even quantity.

e) What is the break-even dollar volume of sales.

Answer 1

Revenue function is TR=225q; cost function is TC=FC+AVC×q, where FC is fixed cost, AVC is tge average variable cost. They can be found from the equations FC+2000AVC=700,000; FC+3000AVC=960,000; 700,000-2000AVC=960,000-3000AVC; 1000AVC=260,000; AVC =260; so FC=700,000-260×2000=180,000. Thus, total cost function is TC= 180,000+260q. Marginal cost is MC=TC'= 260. Then, profit function is PR=225q-180,000-260q=-180,000-35q. Under such conditions, the profit will always be negative, because the price doesn't exceed variable cost per unit.