Question

1. Given the following functions which represent an open economy: Consumption: C=100+0.8Y Investment: I= 50 Government Expenditure: G=130 Exports: X=100 Imports: M=50+0.2Y Equilibrium: Y=C+I+G+X-M a) determine the values of the equilibrium level of income, and b) determine the values of C and M at the equilibrium

2. Given the following functions: Consumption: C=50+0.8Y Investment: I= 750 -30r Money supply: Ms=4000 Transaction-Precautionary demand for money: L1=100 Speculative demand for money: L2=3825-20r Determine the values of the national income (Y), and interest rate (r), on the assumption that both the commodity and the money markets are in equilibrium

3. Which of the following production functions are homogeneous? For those functions which are homogenous write down their degrees of homogeneity and comment on their returns to scale. a) Q=300K1/4L1/3 b) Q=5LK + L2 c) Q=L+5L3K2

4. Consider the following equations for a product Demand function: P=120-2Q Fixed cost: FC=100 Variable cost: VC=2Q+12 Find the expressions (equations) for the following functions: a) Total Revenue (TR) b) Total Cost (TC) c) Total Profit (π) d) Average Cost (AC) Find Q at which total profit is zero

Answer 1

q.1

in eqm

Y = c+ i + g+ +( x-m)

Y =100 + 0.8Y +50+ 130 + 100 - 50 -0.2Y

Y = 330 +0.6Y

0.4Y = 330

Y = 825'

C = 100 + 0.8*825 = 760

M = 50 + 0.2*825 = 215

q.2

in eqm y = c+ i ( assuming g and net exports are excluded from this eqn , since nothing is mentioned)

Y = 50 + 0.8Y +750 - 30r

0.2Y = 800 - 30r

Y = 800 - 30r / 0.2

also

md = ms

md = l1 + l2 = 100 + 3825- 20r = 3925 - 20r

ms= 4000

3925 - 20r = 4000

r = 75/20 = 3.75

Y = 800 - 30*3.75 / 0.2 = 3438(approx)

q.3

a) Q=300K^1/4L^1/3 = homogenous of degree 1

b) Q=5LK + L² = homogenous of degree 2

c) Q=L+5L³K²= non homogenous

q.4

total revenue = p* q= (120 - 2q)

total costs = fc + vc = 112 + 2q

average costs = tc/q = 112 + 2q/q

profits = (120 - 2q)q - 112 - 2q

diff wrt to q

0 = 120 - 4q - 2

118 = 4q

q = 29.5