# I need help with Mathematical Economics homework please

Anonymous
timer Asked: Aug 21st, 2015

### Question Description

1.6 Problems 1. Find the equilibrium solution of the following model: Qd = 3 − P 2, Qs = 6P − 4, Qs = Qd. 2. The demand and supply functions of a two-commodity model are as follows: Find the equilibrium of the model. 3. (The effect of a sales tax) Suppose that the government imposes a sales tax of t dollars per unit on product 1. The partial market model becomes . Eliminating and , the equilibrium price is determined by D(P1 + t) = S(P1). (a) Identify the endogenous variables and exogenous variable(s). (b) Let D(p) = 120−P and S(p) = 2P. Calculate P1 and Q1 both as function of t. (c) If t increases, will P1 and Q1 increase or decrease? 4. Let the national-income model be: Y = C + I0 + G CG= = (a) Identify the endogenous variables. (a > 0,0 < b < 1) (0 < g < 1) (b) Give the economic meaning of the parameter g. (c) Find the equilibrium national income. (d) What restriction(s) on the parameters is needed for an economically reasonable solution to exist? 5. Find the equilibrium Y and C from the following: Y = C + I0 + G0, C = 25 + 6Y 1/2, I0 = 16, G0 = 14. 6. In a 2-good market equilibrium model, the inverse demand functions are given by . (a) Find the demand functions Q1 = D1(P1,P2) and Q2 = D2(P1,P2). (b) Suppose that the supply functions are Q1 = a−1P1, Q2 = P2. Find the equilibrium prices ( ) and quantities ( ) as functions of a.

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