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Maths/Econ help????

Hi could someone help me out with these maths/economics questions please? I have the answers but I don't understand HOW to do them, so a simple explanation would be great. Thanks


(a) A firm’s short run marginal revenue and marginal cost functions are given as follows:

mr = 43 – 8Q mc = 3Q2 – 18Q + 46

The firm faces fixed costs of 10.

(i) Find the firm’s profit function.





(b) Consider the following dynamic macroeconomic model:

Ct = a + bYt-1
Yt = Ct + I*
where C represents consumption, Y, income and I* is exogenous investment

(i) Suggest sensible restrictions for a and b.
(ii) Find the difference equation for Yt .
(iii) Find the general solution for the difference equation for Yt .



(c) A macroeconomic model takes the form:

Y = C + I + G
C = α + b (Y – T)
T = tY

where Y = income
T = Tax revenue
C = consumption
I = investment
G = Government expenditure

(i) Rewrite this model in matrix form where Y, C and T are the variables.


(ii) Suggest sensible restrictions on the values of α, b and t .






(c) Consider the following macroeconomic model.

Ct = α + bYt-1
Yt = Ct + I

(i) Find the complementary function for Yt.

(ii) Find the general solution for Yt.

(iii) Comment on the stability of the model.

Find the General Solution and the equilibrium value of Yt if β = 0.8, α = 200, I = 100 and Y0 = 1600.
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ztibor
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Original post by Dragons
Hi could someone help me out with these maths/economics questions please? I have the answers but I don't understand HOW to do them, so a simple explanation would be great. Thanks


(a) A firm’s short run marginal revenue and marginal cost functions are given as follows:

mr = 43 – 8Q mc = 3Q2 – 18Q + 46

The firm faces fixed costs of 10.

(i) Find the firm’s profit function.



Profit =TR-TC

MR=dTR/DQ -> TR=∫MRdQ=43Q−4Q2+cTR=\int MR dQ=43Q-4Q^2+c whre c=0 when Q=0
MC=dTC/dQ -> TC=∫MCdQ=Q3−9Q2+46Q+CTC=\int MC dQ=Q^3-9Q^2+46Q+C where C=10 when Q=0 (fixed costs)
The profit function
π(Q)=TR−TC\pi (Q)=TR-TC now you can calculate

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