Ssuppose a consumer has a cobb-Douglas utility function type:

U(x,y)= x^0.5y^0.5

^{where x and y represent the two goods.}

^{a ) derive the marshallian demand function for goods x and y}

^{b ) show that the demand functions obtained in (a) are decreasing in prices and increasing in income}

^{c ) derive an expression showing the maximum utility that the consumer derives from the consumption of the two goods}

^{d ) suppose you are given that p}_x = 1, P_y =4 and income is 8. Find the value of the consumers maximum utility in (c)

e ) determine the expenditure function