5. Assume than a non-competitive firm faces a downward sloping firm demand curve, P(Q), and has the cost curve, C(Q)= cQ. Suppose that the government taxes firm profits at a rate of t (the firm keeps profits of (1-t)π) a) What will be the impact of the tax on the profit maximizing quantity of the firm? What will be the effect on the price charged?

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Please help solve part d, e, and f only. Thank you

5. Assume than a non-competitive firm faces a downward sloping firm demand curve, P(Q),
and has the cost curve, C(Q)= cQ.
Suppose that the government taxes firm profits at a rate of t (the firm keeps profits of (1-t)n)
a) What will be the impact of the tax on the profit maximizing quantity of the firm?
What will be the effect on the price charged?
Suppose instead that the government imposes a tax on the price that the firm charges.
Specifically if the firm is charging P(Q) then after the imposition of the tax, the firm would
receive only (1-t)P(Q) where t is the tax rate.
b) Write the firm's profit function as a function of Q and t.
c) Write the first order conditions that define the profit maximizing level of output QM
for the firm. What is the impact of the tax on the MR of the firm?
For each tax rate t, a profit maximizing firm must choose a QM such that the first order
conditions hold. Thus the FOC define an implicit relationship between t and QM.
d) Using the FOC find the derivative
dQM
dt
of the implicitly defined relationship
between QM and t.
Suppose that P(Q) = a - bQ.
e) Show that you can write the derivative from part (b) as
dQM
dt
C
(1-1) 2b
What is
the sign of this derivative?
f) In a diagram illustrate the demand, marginal cost, and revenue curves. Include two
MR curves (before and after the tax) and indicate the profit maximizing quantities
before and after the tax.
Transcribed Image Text:5. Assume than a non-competitive firm faces a downward sloping firm demand curve, P(Q), and has the cost curve, C(Q)= cQ. Suppose that the government taxes firm profits at a rate of t (the firm keeps profits of (1-t)n) a) What will be the impact of the tax on the profit maximizing quantity of the firm? What will be the effect on the price charged? Suppose instead that the government imposes a tax on the price that the firm charges. Specifically if the firm is charging P(Q) then after the imposition of the tax, the firm would receive only (1-t)P(Q) where t is the tax rate. b) Write the firm's profit function as a function of Q and t. c) Write the first order conditions that define the profit maximizing level of output QM for the firm. What is the impact of the tax on the MR of the firm? For each tax rate t, a profit maximizing firm must choose a QM such that the first order conditions hold. Thus the FOC define an implicit relationship between t and QM. d) Using the FOC find the derivative dQM dt of the implicitly defined relationship between QM and t. Suppose that P(Q) = a - bQ. e) Show that you can write the derivative from part (b) as dQM dt C (1-1) 2b What is the sign of this derivative? f) In a diagram illustrate the demand, marginal cost, and revenue curves. Include two MR curves (before and after the tax) and indicate the profit maximizing quantities before and after the tax.
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