Question

1. The long-run cost function for LeAnn's telecommunication firm is: C(q)=0.03q². A local telecommunication tax of $0.01 has been implemented for each unit LeAnn sells. This implies the marginal cost function becomes: MC(q,t)=0.06q+t
   1. If LeAnn can sell all the units she produces at the market price of $0.70, calculate LeAnn's optimal output before and after the tax.
   2. What effect did the tax have on LeAnn's output level?
   3. How did LeAnn's profits change?

Answer 1

a)

c(q) = 0.03q2  

MC = 0.06q

Since fim can sell its output at market price thus optimal output is given by  

P = MC  

0.70 = 0.06q  

q = 0.70/0.06

= 11.67

after tax

c(q) = 0.03q2 + tq  

c(q) = 0.03q2 + 0.01q

MC = 0.06q + 0.01

P = MC  

0.70 = 0.06q + 0.01  

0.70 - 0.01 = 0.06q  

0.69 = 0.06q  

q = 11.5

b) After tax optimal level of output has gone down from 11.67 to 11.50 or by 0.17

c) Profit before tax

Profit = pq - c(q)

= pq - 0.03q2

= (p - 0.03q)q

= (0.70 - 0.0311.67)(11.67)

= (0.70 - 0.3501)(11.67)

= (0.3499)(11.67)

= 4.0834

After tax

Profit = pq - 0.03q2 - 0.01q  

= q(p - 0.03q - 0.01)

= (11.50)(0.70 - 0.0311.50 - 0.01)  

= (11.50)(0.70 - 0.345 - 0.01)

= (11.50)(0.345)

= 3.9675

Thus profit, after tax, has gone down from 4.0834 to 3.9675 or by 0.1159