Q1)assume that market labour demand (Ld) and labour supply (Ls) can be represented by the following equations.
Ld=c-dw d>0
Ls=f+gw g>0
where w is the real wage rate.
Equilibrium in the labour market requires that labour supply equals labour demand (Ld=Ls=L).
(a) Write the system of equations in the form Ax=b, where A is a matrix and x is a vector containing the
endogenous variables (L and w).
(b) Find A-1
and use this to find the equilibrium values for the employment level and the real wage.
2. A consumer’s utility function is given by u(x1,x2) = 2x1x2 + 3×1
where x1 and x2 denote the number of items of two goods G1 and G2 that are consumed. Each item of G1
costs €1 and each item of G2 costs €2. Find the optimal consumption bundle when the consumer’s income is
€83. What is the level of utility associated with this optimal bundle? Estimate the new optimal utility level if
the consumer’s income rises by €1